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PerFEC: perceptually sensitive forward error control

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PerFEC: perceptually sensitive forward error control

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Content PERFEC: PERCEPTUALLY-SENSITIVE FORWARD ERROR CONTROL by Antonia Marie Boadi __________________________________________________________________ A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (ELECTRICAL ENGINEERING) August 2007 Copyright 2007 Antonia Marie Boadi ii DEDICATION This dissertation is dedicated to my mother, Creola Martinez, and the generations of strong women who shaped my values and character. My mother has never had to tell me that education was important because she lives it every day. She set a marvelous example by riding several buses to college – with two children in tow - while her husband fought in Vietnam. My mother is still an inspiration to me; at seventy, she is writing a book on the literary contributions of Richard Wright. I am grateful to my grandmother, Creola Armstead, who passed away shortly after I began my doctoral studies. Although she did not have the opportunity to pursue a college degree, she encouraged me by ending every conversation with two simple admonitions: ‘Get your lesson’ and ‘Praise the Lord’. I have tried to do both and in the process have discovered that the former is impossible without the latter. I thank God for the fearless example set by my Aunt Lorene Love. When the Alabama schools were integrated during the 1960’s, Aunt Lorene, a poor coalminer’s wife, stood guard on her porch – armed with a shotgun – to iii make sure that the Klan didn’t torch her home while her children slept. Her courage and tenacity were passed on to her Ivy League educated children. My fears and insecurities quickly dissolve after a telephone conversation with Aunt Lorene. Lastly, I am thankful to my nephews Cody and Ryan for helping me to see the humor in all things. iv ACKNOWLEDGEMENTS For a dream comes with much business and painful effort (Ecclesiastes 5:2a, Amplified Bible) I am extremely grateful to the members of my dissertation committee: John Silvester, Antonio Ortega and Behrokh Khosnevis for their patience, encouragement and insightful comments. I am especially grateful to Dean Margery Berti, of the Viterbi School of Engineering, for her longstanding support and encouragement. I wish to thank the staff, faculty and administrators of The Viterbi School of Engineering and The Graduate School. I am grateful for Dr. Garry Hart of California State University Dominguez Hills for encouraging me to spread my wings. I wish to thank The California State University Chancellor’s Office, The Powell Foundation, The Xerox Corporation, The Aerospace Corporation, The RAND Corporation and NASA for their financial support. v I am grateful to Pastor Argie Taylor and my church family at The Christian Agape Circle. I could not have done this if you had not taught me that The Lord is, and always will be, my Shepherd. TABLE OF CONTENTS ACKNOWLEDGEMENTS IV LIST OF TABLES IX LIST OF FIGURES XIII ABSTRACT XV CHAPTER I INTRODUCTION 1 1.1 MOTIVATION 1 1.2 RESEARCH FOCUS 3 1.3 RESEARCH GOALS 5 1.4 DOCUMENT ORGANIZATION 7 CHAPTER II NATURAL SIMULATION SPECIFICATION 10 2.1 INTRODUCTION 10 2.2 MODEL PARAMETERS 13 2.3 ANALYTICAL REFERENCE MODELS 16 2.3.1 Rayleigh Distribution 18 2.3.2 Rice Distribution 18 2.4 LEVEL CROSSING RATE AND DURATION OF FADES 19 2.5 GENERATION OF MOBILE WIRELESS SIMULATOR 27 2.5.2 Implementation of Fading Channel Simulator 30 2.6 DISCRETE CHANNEL MODELS 31 2.7 NATURAL LANGUAGE DESCRIPTORS 41 2.8 SUMMARY 44 vii CHAPTER III TURBO CODE PERFORMANCE 47 3.1 INTRODUCTION 47 3.2 PRODUCT CODE PERFORMANCE 49 3.3 UMTS TURBO CODE PERFORMANCE 52 3.4 SUMMARY 59 CHAPTER IV ADAPTIVE QUALITY CONTROL 62 4.1 INTRODUCTION 62 4.2 PARTIALLY OBSERVABLE MARKOV DECISION PROCESSES (POMDP) 64 4.3 MEASUREMENT OF PERCEPTUAL VIDEO QUALITY 80 4.4 GENERATION OF PARAMETER DATABASE 85 4.5 MULTIVARIABLE OPTIMIZATION OF PERCEPTUAL QUALITY REQUIREMENTS 87 4.6 SIMULATION RESULTS 89 4.6 SUMMARY 92 CHAPTER V FUZZY PERCEPTUAL QUALITY MODELING AND CONTROL 94 5.1 INTRODUCTION 94 5.2 THE ANALYTIC HIERARCHY PROCESS 95 5.3 FUZZY ANALYTIC HIERARCHY PROCESS 106 5.4 FUZZY PREFERENCE PROGRAMMING 130 CHAPTER VI APPLICATION OF PERFEC TO WIMAX ENVIRONMENT 138 6.2 SYSTEMS ENGINEERING PROCESS 141 6.3 ALTERNATIVE DESIGN 144 6.4 CONCLUSION 145 CHAPTER VII FUTURE DIRECTIONS 146 viii BIBLIOGRAPHY 148 APPENDIX 177 ix LIST OF TABLES Table 1 Root Mean Square Values 21 Table 2 Doppler Frequency for Cellular Scenarios 24 Table 3 Statistical Fade Data for Transmission to Pedestrian (Velocity 4 mph, 2GHz) 25 Table 4 Statistical Fade Data for Transmission within Urban Environment 26 Table 5 Statistical Fade Data for Transmission within High Speed Environment (Velocity 80 mph, 2GHz) 27 Table 6 Typical Profile for Rural Areas 35 Table 7 Profile for Hilly Terrain 35 Table 8 Profile for Urban Area 36 Table 9 PCS Outdoor Models 36 Table 10 Relative Tap Strengths for Outdoor Models 37 Table 11 PCS Indoor Models 37 Table 12 Channel Impulse Response Model Parameters 38 Table 13 Indoor Office Test Equipment Tapped Delay Line Parameters 39 Table 14 Outdoor to Indoor Tapped Delay Line Parameters 40 Table 15 Vehicular Test Environment Tapped Delay Line Parameters 40 x Table 16 Product Code Parameters 50 Table 17 Block Turbo Code Performance 52 Table 18 Description of UMTS Simulation Scenario Parameters 54 Table 19 Mapping of UMTS Frame Length to SNR Range 61 Table 20 Decoder Errors Relative to Decoder Iteration 73 Table 21 Perceptual Quality Benchmark Data 86 Table 22 Structure of Decoder Output Table 87 Table 23 Translation of Natural Language Requirement into Simulation Specification 91 Table 24 Linguistic Descriptors 98 Table 25 Fuzzy Ranking of Evaluation Criteria 99 Table 26 Alternative Rankings Relative to Blurring Metric 103 Table 27 Ranking of Alternatives Using Eigenvector Method 103 Table 28 Numerical Ranking of Candidate Codes 105 Table 29 Final Ranking of Candidate Codes 106 Table 30 Linguistic Descriptors 112 Table 31 Membership Functions of Linguistic Descriptors 115 Table 32 Relative Performance of Main Criteria 119 xi Table 33 Relative Importance of Sub-Criteria Associated with Network Conditions 119 Table 34 Relative Importance of Sub-Criteria Associated with Bandwidth Efficiency 119 Table 35 Relative Importance of Sub-Criteria Associated with Video Impairments 120 Table 36 Fuzzy Quantification of Relative Performance of Main Criteria 120 Table 37 Fuzzy Quantification of Alternatives Relative to BER 121 Table 38 Fuzzy Quantification of Alternatives Relative to FER 121 Table 39 Fuzzy Quantification of Alternatives Relative to Network Fading 122 Table 40 Fuzzy Quantification of Alternatives Relative to Code Rate 122 Table 41 Fuzzy Ranking of Alternatives Relative to Code Structure 122 Table 42 Fuzzy Ranking of Alternatives Relative to Spectral Efficiency 123 Table 43 Fuzzy Ranking of Alternatives Relative to Blurring Metric 123 Table 44 Fuzzy Ranking of Alternatives Relative to Blocking Metric 123 xii Table 45 Fuzzy Ranking of Alternatives Relative to Overall Perceptual Quality 124 Table 46 Ranking of Evaluation (Sub) Criteria 128 Table 47 Ranking of Code Weight Criterion 129 Table 48 Ranking of Picture Quality Subcriteria 129 Table 49 Final Ranking of Criteria 129 Table 50 PerFEC Rules for Fuzzy Inference System 132 Table 51 WiMAX Transmission Environments 139 Table 52 WiMAX Code Configuration and Transmission Characterization 140 Table 53 WiMAX Error Correction Code Trade Space 142 Table 54 Performance of Rate ½ Convolutional Code 143 Table 55 Performance of (1024, 821) Low Density Parity Check Code 144 xiii LIST OF FIGURES Figure 1 Doppler Effect 14 Figure 2 Jakes Impulse Response and Power Spectral Density 29 Figure 3 Summary of Satellite Latency Studies 55 Figure 4 Summary of Cellular Latency Studies 58 Figure 5 Rate 2/3 Code 74 Figure 6 Rate 1/3 Code 75 Figure 7 Rate 2/9 Code 76 Figure 8 Rate 1/6 Code 77 Figure 9 AHP Problem Formulation 97 Figure 10 Ranking of Evaluation Criteria 102 Figure 11 Ranking of Code Alternatives 104 Figure 12 Membership Functions - Picture Quality 109 Figure 13 Multicriteria Decision Model 110 Figure 14 User Preference Membership Functions 117 Figure 15 Inverse Membership Functions 118 Figure 16 Membership Function - Picture Quality 133 Figure 17 Membership Function - Network Conditions 134 xiv Figure 18 Membership Function - Degree of Protection 135 Figure 19 Fuzzy Inference System Solution Surface 136 Figure 20 WiMAX Problem Hierarchy 141 xv ABSTRACT The global telecommunications system has evolved into a ubiquitous, integrated network capable of delivering a variety of video applications. The reliable delivery of these services requires the use of flexible protocols that consider human perceptual issues. Legacy protocols are based on traditional network design objectives such as bit-error-rate (BER), cell loss rates, and peak-signal-to-noise-ratio (PSNR). This thesis proposes an adaptive FEC protocol that supports the reliable delivery of compressed video streams. The design philosophy employed in this study represents a shift from the use of traditional network- centric design requirements to a more comprehensive approach that utilizes both traditional and perceptual quality metrics. The methodology includes a linguistic framework that facilitates the articulation of user perceptual quality requirements using a fuzzy inference model. The resulting system employs a flexible, adaptive turbo-based coding scheme that is both quality-of-service (QoS) and quality-of-perception (QoP) configurable. PerFEC, the Perceptually-Sensitive Forward Error Control system, provides the system engineer with the ability to maximize xvi throughput, improve reliability, and minimize energy and bandwidth consumption while reducing system complexity. 1 CHAPTER I INTRODUCTION 1.1 Motivation The ever-evolving nature of the telecommunications industry has fostered a climate in which system designers must respond to market trends years before business strategies or product specifications have been clearly articulated. Sound systems engineering practice requires the definition of clear specification of requirements whose correctness can be validated {INCOSE, 2004 #317}. The front-end of the design process is dominated by stakeholders who may have difficulty translating subjective goals into quantifiable performance requirements. The complexity of the design problem increases exponentially when considered in the context of a ‘system of systems’ – each with its own conflicting and/or competing objectives. Recently domestic and international law enforcements agencies have employed video sensor surveillance technology in counter-terrorism activities {Akyildiz, #318}. Although these systems can be inexpensively constructed by equipping sensors with inexpensive CMOS cameras, the front-end systems engineering task of defining user perceptual quality requirements is not straightforward. The rapid and accurate identification of potential terrorists requires the use of network technologies capable of protecting video imagery. The mitigation of wireless channel impairments is 2 also important in the commercial sector. Providers of video content over cellular or satellite delivery systems strive to provide their customers with the same grade of viewing experience as those provided by their cable-delivery counterparts. The difficulty in articulating performance requirements is also evident in this arena. The reliable delivery of video services requires a framework for articulating human perceptual performance requirements and translating them into network performance requirements. This framework must incorporate flexible protocols that consider human perceptual issues; on the contrary, legacy protocols are based on traditional network design objectives such as bit-error-rate (BER), cell loss rates, and peak-signal-to-noise-ratio (PSNR). Because of the time-varying nature of the wireless channel, there must also be a mechanism for adaptively adjusting the network transmission parameters so that the transmitted video stream is resilient to channel impairments and video artifacts {Butler, 1994 #28} {Campbell, 2005 #2} {Dongyan, 1999 #290} {Ferguson, 1998 #74} {Fester, 1995 #5} {Forum, 1999 #4}. An important contribution of this thesis is the concept of a fuzzy requirement. A fuzzy requirement is expressed using language that is easily understood by the key stakeholders in a system. Fuzzy requirements are multi-tiered and facilitate the characterization and implementation of 3 simulation models that provide initial estimates of system performance. The template for a fuzzy requirement consists of several components: velocity, transmission environment, application type, bandwidth constraints and perceptual quality. The translation of the velocity and transmission environment into performance requirements that can be verified and validated is described in Chapter 2. The error control adaptation mechanism is described in Chapter 3. Quality-of-service issues related to the data type are discussed in Chapter 4. Linear programming techniques are used to select an error control strategy that optimizes perceptual quality given quality-of-service and bandwidth constraints. Chapter 5 applies fuzzy reasoning to our problem. The crisp linear programming problem introduced in Chapter 4 is developed into a fuzzy multicriteria decision problem (MDM). This MDM is characterized by the use of fuzzy linguistic variables that describe the perceptual quality component of the requirement template. The use of a fuzzy antecedent in the objective function yields a rich solution set that is more appropriate for this application. 1.2 Research Focus This thesis proposes an adaptive forward error control (FEC) algorithm that supports the reliable delivery of compressed video streams. The proposed system employs a flexible, adaptive turbo-based coding 4 scheme that is both quality-of-service (QoS) and quality-of-perception (QoP) configurable. The design philosophy employed in this study represents a shift from the use of traditional network-centric design requirements to a more comprehensive approach that utilizes both traditional and perceptual quality metrics. Forward error control (FEC) is an attractive candidate to combat the effects of transmission errors. This thesis will identify candidate code structures that are effective at mitigating the effects of wireless channel impairments. Because channel conditions are time-varying, static FEC techniques are inefficient. An adaptive FEC is needed to adjust coding parameters based upon input from some network feedback mechanism. In order to gain insight into the relationship between traditional quality-of- service parameters and perceptual quality measures, the design space must be extended to include perceptual quality requirements. In order to implement an adaptive error control system, the system architecture must provide a return channel so that the receiver can provide the transmitter with information regarding the accuracy of the received messages; a decision can then be made regarding the selection of a new error control code. This simple scheme permits the implementation of an adaptive error control scheme in the modem with a modest increase in hardware cost [Vucetic, 1988 #113]. 5 PerFEC employs a linguistic framework that facilitates the articulation of user perceptual quality requirements using a fuzzy inference model. The performance optimization algorithm introduced in this thesis employs is based on a fuzzy formulation of the problem using linguistic variables. This application of fuzzy simulation methodology facilitates system-level performance testing although the functional relationships between FEC code parameters, quality metrics and network conditions are not clearly understood. PerFEC, the Perceptually-Sensitive Forward Error Control agent, provides the systems engineer with the ability to maximize throughput, improve reliability, reduce energy, and minimize bandwidth consumption. The design philosophy employed by this study represents a paradigm shift from the use of traditional network-centric design requirements to a more unified approach that utilizes both traditional and perceptual quality metrics. PerFEC’s approach to system specification is developed from a fuzzy approach to front-end system specification and simulation into a multicriteria-decision system composed of linguistic variables, membership functions and fuzzy optimization functions. 1.3 Research Goals The goals of this research activity are as follows: 6 1. Develop a framework that allows the user to specify high-level perceptual quality requirements using natural language descriptors. 2. Investigate the relationship between natural language descriptors and perceptual quality metrics. 3. Identify a set of perceptual quality metrics that can be used to qualitatively and quantitatively describe the visual impairments that characterize wireless video communications. 4. Develop a mapping between the perceptual quality metrics and network performance metrics. 5. Identify a mechanism for monitoring channel conditions. This information will be provided to the transmitter so that the forward-error-control (FEC) code parameters can be adjusted to maintain a predefined level of video quality. 6. Identify a set of error control codes that are robust enough to satisfy the user’s perceptual performance requirements. Quantify the performance of each candidate code in a variety of scenarios. 7. Develop a set of framework for modeling transmission in various network environments using natural language 7 descriptors. (For example, a vehicle traveling 50 mph in a rural environment). 1.4 Document Organization A bottoms-up approach will be adopted in the exploration of this problem; as a result, the research issues will be addressed in reverse numerical order. This dissertation is structured as follows: Chapter 2, entitled Natural Simulation Specification, addresses Research Topic #7: it describes the analytical and simulation frameworks necessary for the characterization and modeling of the satellite, fixed and mobile wireless channels. A major contribution of this chapter is the use of a requirement template that uses natural language constructs to describe and parameterize terrestrial and satellite channel simulations. Natural language constructs consist of clauses containing fuzzy linguistic variables. Natural simulation parameterization represents a departure from conventional simulation methodology which defines events and conditions using crisp numbers. The nature of channel conditions and their impact on perceptual quality requires the definition of events and variables in terms of imprecise values. This innovation facilitates the definition of the trade space and supports the validation of the system model. 8 Chapter 3, entitled Turbo Code Performance, explores the performance of turbo codes in the simulation environments described in Chapter 2. The code employed by the Universal Mobile Telecommunications System (UMTS) communication systems is used as the basis of the analysis in this chapter. Trade excursions probe the impact of packet size, modulation scheme and latency on quality-of-service. This chapter addresses Research Topic # 6. Chapter 4, entitled Adaptive Quality Control, develops an algorithm for using information output from the decoder to estimate channel conditions and adapt the coding mechanism to maintain a predefined level of quality. Results from Markov Decision Theory are used to solve this problem. The simulation results generated in Chapter 2 provide the statistical characterization of the Hidden Markov Model (HMM) used to describe the channel state. The chapter concludes with a discussion of perceptual quality metrics that can be used to describe video artifacts and degradations in perceptual quality. This chapter addresses Research Topics 3, 4 and 5. Chapter 5, entitled Fuzzy Perceptual Quality Modeling and Control, extends the methodology presented in Chapter 4 to encompass problems characterized by conflicting or imprecisely specified objectives. One limitation of the crisp problem specification used in Chapter 4 is its inability to address scenarios in which the constraints, goals or consequences associated with a policy are partially unknown or are difficult to quantify. 9 This is particularly true in applications involving the specification of human judgments and preferences. Conversely, fuzzy problem specifications permit a richer description of the design goals, evaluation criteria and alternatives. The proposed methodology draws upon results from fuzzy inference systems. The use of fuzzy linguistic constructs facilitates the articulation of design preferences by stakeholders who may not be domain experts and provides the user with a richer framework for specifying perceptual preferences. This chapter addresses Research Topics 1 and 2. Chapter 6 discusses the application of the PerFEC methodology to the WiMAX environment. Chapter 7 discusses extensions of this work. CHAPTER II NATURAL SIMULATION SPECIFICATION 2.1 Introduction It is important to frame this chapter in the context of our overall problem. The goal of this thesis is to develop an algorithm that adaptively maintains a predefined level of perceptual video quality in the presence of wireless channel impairments. We must first create a framework that allows the systems engineer to generate preliminary performance data based upon a user requirement that has been expressed as simply as ‘A vehicle traveling 45 miles per hour in an urban setting should be able to receive a movie that has no discernible blockiness’. Because perceptual quality is not readily quantifiable, we adopt a linguistic framework that allows content providers and end users to describe video quality using natural language. In Chapter 5, this approach to front-end system specification is expanded into a fuzzy multicriteria decision system composed of linguistic variables, membership functions and fuzzy optimization equations. Although partially tutorial, this chapter develops the analytical and simulation framework necessary to determine how video quality is affected when a video stream is transmitted in urban, metropolitan, satellite or rural environments. The preliminary results presented in this chapter provide a 11 coarse estimate of the impact of channel fading on bit error rate. This estimate shapes the trade space of candidate codes to be used by the adaptive error control algorithm. This chapter introduces a methodology called natural simulation specification that bridges the gaps between several levels of abstraction: (1) the link between the non-technical terms used by an end- user or non-technical stakeholder to specify desirable levels of perceptual quality and the output of a video coding simulation which yields perceptual quality data (2) the relationship between the output of the symbol-level simulation which models the impact of channel coding and interleaving and perceptual quality metrics (3) the output of a waveform level simulation which provides uncoded BER performance data (resulting from multipath effects) and the performance of channel coding and interleaving schemes (4) the relationship between a finite state channel model, BER performance data and power spectral data and, (5) the relationship between analytical reference models and power spectral data The template for a system-level perceptual quality requirement is introduced in this chapter. The template consists of several components: velocity, transmission environment, data type, bandwidth constraints and perceptual quality. The first two components, velocity and transmission 12 environment, are characterized in this chapter. A description of the relationship between the natural language descriptions analytical and mathematical characterizations of perceptual quality performance requirements is presented. The chapter begins with a description of the analytical reference models used to characterize wireless transmission environments. Parameters of particular interest are the Doppler frequency, vehicle velocity, delay spread, level crossing rate, and average fade duration these parameters are important because they impact the received quality of the transmitted video stream. Section 2.2 presents an overview of the multipath fading effect characteristic of mobile wireless channels. Section 2.3 describes the Gaussian, Rayleigh and Rice models, which serve as reference models for the wireless mobile channel [Rice, 1944 #220; Rice, 1945 #221] {Haykin, 2003 #328}. Parameters that quantify the multipath fading channel are presented and related to field measurements. Section 2.4 describes the average fade duration and level crossing rate, two important indicators of the frequency and severity of fade events. The effect of the fading phenomenon on the channel’s instantaneous bit error rate is quantified. The instantaneous bit error rate is a critical performance 13 indicator because it influences the selection of a forward error correction scheme. Section 2.5 describes a computationally efficient procedure for modeling the wireless channel. Section 2.6 presents discrete channel models based on field measurements. Section 2.7 describes how simulation parameters are translated into natural language constructs for use in front-end system specification. Section 2.8 summarizes the results presented in this chapter. 2.2 Model Parameters We are concerned with modeling the behavior of mobile channels. For the sake of simplicity, we will assume that the transmitter is stationary. The receiver could be a vehicle traveling at 60 miles per hour or a pedestrian walking at the rate of 4 miles per hour. In most environments, the electromagnetic waves that represent the transmitted video application do not reach the receiver’s antenna via a direct path. The waves may be reflected off buildings or scattered by trees or other terrain features. This results in the decomposition of the original wave into several partial-waves, each of which may provide a positive or negative contribution to the strength of the original signal, a phenomenon known as the multipath effect. 14 This section presents techniques for computing the primary parameters of the simulation model. The target model will simulate the behavior of a vehicle receiving data while traveling at constant velocity as depicted in Figure 1 (adapted from {Rappaport, 2002 #331}). Figure 1 Doppler Effect The phase relations of the partial waves determine whether they decrease or increase the strength of the received signal. Because of this, the strength of the received signal is a function of the receiver’s position; in the case of a mobile receiver, signal strength is also a function of time. Receiver motion results in a shift in frequency, referred to as the Doppler shift. The arrival direction of the partial waves result in different Doppler shifts; the 15 cumulative sum of the scattered and reflected components is a continuous spectrum of Doppler frequencies, referred to as the Doppler power spectral density. The target model will simulate the behavior of a vehicle receiving data while traveling at constant velocity. The Doppler shift of the n th wave can be expressed as: (1.1) cos n n v f = In the simplest case in which there are N distinct paths from the mobile unit to the base station, the received signal is: 1 ( ) ( ) ( ( )) N n n n y t a t x t t = = (2.1) In the above equation a n(t) represents the attenuation while ( ) n t represents the propagation delay of the n th multipath component; both are functions of time because they change as the vehicle moves. As a result of the Doppler Effect, the arriving waves experience different shifts; collectively the partial waves span a continuous range of frequencies, called the Doppler power spectral density. The power spectral density (PSD), of a random process captures the frequency-domain properties of the underlying process and can be expressed as {Haykin, 2003 #328}: 16 (2.2) 2 , , , 1 ( ) ( ) ( ) 4 i i i N i n i n i n n S f f f f f c µµ = = ++ % where is the Dirac delta function. The power spectral density has the following properties [Jeruchim #0]: 1. i i S µµ (f) is real and nonnegative 2. i i S µµ (f) = i i S µµ (-f) 3. If the random process has periodic components, then i i S µµ (f) will have impulses at the frequencies corresponding to the periodic components. It is therefore a symmetric line spectrum with impulses at f= , i n f ± weighted by c 2 i,n. The autocorrelation function, ~ ( ) i i rµµ has the following properties: (2.3) ~ ~ ~ ( ), m even, ( / 2) ( ), m odd, i i i i i i i r r mT r µµ µµ µµ += 2.3 Analytical Reference Models Three of the most commonly used models of mobile wireless channels are: the AWGN channel for fixed terminal-satellite applications; the flat- 17 fading Rice channel for mobile terminal applications; and the flat-fading Rayleigh channel mobile terminal-base station applications {Patzold, 2002 #208}. The model must take into account the effects of noise and multipath fading. The additive white Gaussian Noise (AWGN) channel is degraded by thermal noise and is appropriate for space communications, certain wire line networks and transmissions via coaxial cable. However, in situations in which multiple indirect paths exist between the transmitter and receiver, the Rayleigh channel model is the appropriate choice. The Rayleigh model is best for situations in which no dominant path exists between the transmitter and receiver. The Rice model generalizes the Rayleigh model by adding a direct free-space path to the indirect multipath components. The Rice fading model is appropriate when there is a direct line-of-sight (LOS) path in addition to several indirect paths. The Rice model is often used when modeling indoor environments; similarly, the Rayleigh model is often used for modeling outdoor urban settings. Our analysis will focus on the use of the Gaussian and Jakes power spectral densities to approximate the Doppler spectrum. The use of reference models that approximate the Doppler power spectral density is critical to the proper estimation of system performance. The next section reviews some important terms related to the analysis of 18 wireless mobile channels. Of special interest are the probability density functions associated with the Rayleigh, Rice, Suzuki distributions. 2.3.1 Rayleigh Distribution For two zero-mean, statistically independent, normally distributed random variables 1 µ and 2 µ , each with variance 2 0 . A Rayleigh distributed random variable can be defined as 2 2 1 2 µµ =+ . The probability density function of can is given by [Patzold, 2002 #208] 0 ( ) ( , ) , r 0 where p represents the jo nt N r x p r x dx pdf = (2.4) The expected value and variance of are defined as [Patzold, 2002 #208]: (2.5) 0 [ ] 2 E = (2.6) [] 2 0 2 2 Var ! = "# $% 2.3.2 Rice Distribution Again consider two zero-mean, statistically independent, normally- distributed random variables 1 µ and 2 µ , each with variance 2 0 . The 19 random variable defined as 2 1 2 ( )2 & µ ' µ =+ + where ' ( , is called the Rice-distributed random variable. The probability density function of& is [Patzold, 2002 #208] (2.7) 2 2 2 0 2 0 2 2 0 0 0 ( ) 0 0 x x x e I x p x x ' & ' + ! "# = $% < where 0 ( ) N r x = && denotes the 0 th order modified Bessel function. The expected value of & is defined as [Patzold, 2002 #208] (2.8) 2 2 0 2 2 2 2 4 0 0 1 2 2 2 2 0 0 0 0 [ ] 1 2 2 4 2 4 E e I I ' ' '' ' & ! ! ! =+ + "#" # " # $%$ % $ % 2.4 Level Crossing Rate and Duration of Fades In order to properly model the behavior of wireless mobile channels, it is necessary to have information about the level-crossing rate and the average length of fades, statistics which can be used to design error control and diversity schemes for mobile communication systems {Rappaport, 2002 #331}. As previously described, the transmitted signal undergoes wide fluctuations which can dramatically increase the bit error rate. In order to develop an adaptive coding system, it is important to know how often fades occur. 20 Level Crossing Rate The level-crossing rate, ( ) N r , describes how often a stochastic process crosses a threshold r (from low-to-high). As described in {Rappaport, 2002 #331} [Rice, 1945 #221; Rice, 1948 #222] [Jakes, 1974 #215], the level crossing rate is: (2.9) 2 0 ( , ) 2 R m N rp R r dr f e ' ' == &&& , the number of level crossings per second, represents the expected rate at which the Rayleigh rading envelope (normalized to the local root mean squared signal level, crosses a specified level. r R N r & epresents the time derivative of r(t) ( , ) represents the joint density function of R and r when r = R represents the maximum Doppler frequency = represents the value of the threshold, R, m rms p R r f R R ' & & when normalized to the local root mean square amplitude of the fading envelope Table 1 (taken directly from {Rappaport, 2002 #331}) contains values of the rms (root mean square) delay spread in a variety of environments. These values will be used to compute simulation parameter values for our performance evaluation scenarios. 21 Table 1 Root Mean Square Values Environment Frequency (MHz) rms Delay Spread ( ) Comments Reference URBAN 910 avg:1300 ns std dev: 600 ns max: 3500 ns New York City {Cox, 1975 #332} URBAN 892 10-25 µs San Francisco - Worst case {Rappaport, 1990 #335} SUBURBAN 910 200-310 ns Extreme case (Typical) {Cox, 1972 #333} SUBURBAN 910 1960-2110 ns Extreme case (averaged) {Cox, 1972 #333} INDOOR 1500 10-50 ns median: 25 ns Office building {Devasirvatham, 1990 #334} INDOOR 850 max: 270 ns Office building {Saleh, 1987 #336} INDOOR 1900 avg: 70-94 ns max: 1470 ns Three buildings in San Francisco {Seidel, 1991 #337} Average Fade Duration The average fade duration, denoted ( ) T r refers to the average length of time that the channel amplitude falls below a certain threshold r {Rappaport, 2002 #331} 22 (2.10) 2 max 1 ( ) 2 r e T r rf = Computation of Instantaneous Bit Error Rate The average fade duration (AFD) can be used to estimate the number of bits that will be lost during a fade and, subsequently, to compute an estimate of the instantaneous bit error rate (BER) {Rappaport, 2002 #331}. Both the level crossing rate and the average fade duration are dependent upon the speed of the pedestrian or mobile. The AFD is inversely proportional to the maximum Doppler frequency {Rappaport, 2002 #331}. The system’s fade margin can be designed by determining the frequency at which input signals fall below a particular threshold as well as the average length of time the signal remains below the threshold. Therefore the signal- to-noise ratio that occurs during a fade can be related to the instantaneous BER. 23 The computation of the instantaneous bit-error-rate is performed as follows: Step 1: Compute the maximum Doppler frequency shift for the velocity of interest using {Rappaport, 2002 #331}or the data contained in Table 2-2: (2.11) cos therefore d v f * = (2.12) where m c velocity c f f == Step 2: Compute the number of level crossings for the threshold of interest using Number of level crossings = (2.13) 2 2 r r m N f re = {Rappaport, 2002 #331} Step 3: Compute the instantaneous BER using {Rappaport, 2002 #331} (2.14) data rate r N BER = The adaptive mechanism used by PerFEC uses the decoder output to estimate the instantaneous bit error rate. The BER estimate is then compared to the information contained in Table 2-2 to determine the severity of the fade conditions and to select a coding scheme that will maintain the desired level of video quality while satisfying power, bandwidth or other performance requirements. Using the information presented in this section, a fade resulting in the desired BER can be induced. Tables 2 thru 4 below indicate 24 the BER for a variety of scenarios. This data will be used in the design of the adaptation module. Table 2 Doppler Frequency for Cellular Scenarios Doppler Frequency Velocity (miles/hour) Velocity (meters/second) 900 MHz (GSM) 1800 MHz (PCS) 2 GHz (UMTS) 4 1.8 5.4 10.7 11.9 30 13.4 40.2 80.4 88.4 45 20.1 60.4 120.8 133 60 26.8 80 160 176 80 35.76 107.3 214.6 236.6 25 Table 3 Statistical Fade Data for Transmission to Pedestrian (Velocity 4 mph, 2GHz) Normalized Threshold Level () Data rate (kbps) Average Fade Duration (seconds) Number of Level Crossings (per second) Instantaneous Bit Error Rate 1.0 5.8e-2 11 1.7e-004 0.1 3.4e-3 3 4.7e-005 0.01 3.4e-004 1 1.6e-005 0.001 64 3.4e-005 .03 4.7e-007 1.0 5.8e-2 11 2.9e-005 0.1 3.4e-3 3 7.8e-006 0.01 3.4e-004 1 2.6e-006 0.001 384 3.4e-005 1 2.6e-006 1.0 5.8e-002 11 5.5e-006 0.1 3.4e-003 3 1.5e-006 0.01 3.4e-004 1 5.0e-007 0.001 2000 3.4e-005 1 5.0e-007 26 Table 4 Statistical Fade Data for Transmission within Urban Environment (Velocity 45 mph, 2GHz) Normalized Threshold Level Data rate (kbps) Average Fade Duration (seconds) Number of Level Crossings (per second) Instantaneous Bit Error Rate 1.0 5.1e-3 124 1.9e-3 0.1 3e-4 34 5.3e-4 0.01 3e-5 4 6.3e-5 0.001 64 3e-6 1 1.6e-5 1.0 5.1e-3 124 3.2e-4 0.1 3e-4 34 8.9e-5 0.01 3e-4 4 1e-5 0.001 384 3e-6 1 2.6e-6 1.0 5.1e-3 124 6.2e-5 0.1 3e-4 34 1.7e-5 0.01 3e-5 4 2e-6 0.001 2000 3e-6 1 5e-7 27 Table 5 Statistical Fade Data for Transmission within High Speed Environment (Velocity 80 mph, 2GHz) Normalized Threshold Level Data rate (kbps) Average Fade Duration (seconds) Number of Level Crossings (per second) Instantaneous Bit Error Rate 1.0 64 3.9e-3 165 2.6e-3 0.1 2.2e-4 45 7.0e-3 0.01 2.2e-5 5 7.8e-5 0.001 2.2e-6 1 1.5e-5 1.0 3.9e-3 165 4.3e-4 0.1 2.3e-4 45 1.2e-4 0.01 2.2e-5 5 1.3e-5 0.001 384 2.2e-6 1 2.6e-6 1.0 3.9e-3 165 8.3e-5 0.1 2.3e-4 45 2.3e-5 0.01 2.2e-5 5 2.5e-6 0.001 2000 2.2e-6 1 5.0e-7 2.5 Generation of Mobile Wireless Simulator This section will describe a computationally efficient method for implementing a wireless fading simulator. The algorithm makes use of Jakes’ Method, one of the most popular methods used to compute the Doppler power spectral density it was developed at Bell Laboratories by William Jakes and others {Jakes, 1974 #215}. A frequency domain representation of the input signal is used to approximate the Jakes Power Spectral Density. 28 2.5.1 Jakes Method Jakes Method uses a deterministic sum of sinusoids expression to model Rayleigh fading. The Jakes PSD is of the form {Rappaport, 2002 #331} [Tranter, 2004 #213]: (2.15) c 2 1.5 , f-f ( ) 1 0, otherwise z m c E m m f f f S f f f + ! = "# $% where m f represents the maximum Doppler frequency. Figure 2 depicts the impulse response and power spectral density of the Jakes filter. 29 Figure 2 Jakes Impulse Response and Power Spectral Density 30 2.5.2 Implementation of Fading Channel Simulator A signal with the desired Doppler PSD can be generated by passing a white Gaussian noise source through a filter whose frequency response is equal to the square root of the desired Doppler spectrum {Rappaport, 2002 #331}. Figure 3 (depicts this process. A Rayleigh fading simulator can be generated as follows {Rappaport, 2002 #331} : Step 1. Select the number of points used to represent the Jakes PSD (N should be a power of 2). Step 2: Define T, the duration of the fading waveform. T is inversely proportional to the spacing between the spectral lines. Select the maximum Doppler Frequency fm so that it corresponds to the velocity of interest. (2.16) 1 T f = . (2.17) 2 1 m f f N ! = "# $% Step 3: Use a Gaussian random generator to produce a baseband line spectrum. The spectrum will have complex weights in the positive range of the frequency band. The maximum component in the line spectrum corresponds to the maximum Doppler frequency, f m {Tranter, 2004 #213}. Step 4: Construct the negative components of the line spectrum by taking the conjugate values of the spectral values generated in Step 3. 31 Step 5: Multiply the quadrature and in-phase noise components by the square root of the Jakes PSD fading as shown in Figure 2-3. Step 6: Compute the Inverse Fast Fourier Transform (IFFT) of the N- length frequency domain signals corresponding to the in-phase and quadrature components of the noise source. This step will yield two N- length series. Add the squares of each signal point. Step 7: Compute the square root of the sum of the two series generated in Step 6. This will yield an N-length time series of a fading signal with the desired Doppler spread. 2.6 Discrete Channel Models Sections 2.4 and 2.5 described the generation of fading signals that correspond to the movement of a receiver at various velocities. The models presented in this section will integrate the effect of hills, buildings, trees and other terrain features into the simulation. As discussed in Section 2.2, these factors cause electromagnetic waves to be decomposed into several partial- waves, which may not reach the receiver’s antenna via a direct path. This section introduces representative discrete channel models that facilitate the development of simulations that include the delays associated with multipath effects. Discrete channel models are based on the idea of using a tapped delay line model to simulate a wireless channel {Tranter, 2004 #213}. They can be 32 generated using a multiple instances of the Rayleigh fading simulator discussed in the previous section. Each tap represents a discrete fading path and its corresponding delay and average power gain. We will use representative models based on empirical data. The models are flexible enough to simulate performance in a variety of environments specified using natural language descriptors. The discrete channel models under consideration are based on field measurements used in the design of Global System for Mobile Communications (GSM) {(ETSI), 1988 #338}, Personal Communications Systems (PCS) {(ANSI), 1995 #339} and UMTS-IMT2000 {(ITU), 1997 #340} applications. Tables 6 thru 11 contain the model parameterizations. The tables contain entries for the number of paths (taps), path delay and average path gain. Each tap corresponds to a discrete path that is modeled as an independent Rayleigh (for outdoor environments) or Ricean (for indoor environments) fading process. Associated with each path is a delay and path gain. Finally, each path is modeled according using the Jakes or Ricean Doppler spectrum. As described in Section 2.3, a channel’s Doppler power spectrum provides information about the spectral broadening of a narrowband input signal in the frequency domain {Jeruchim, #214}. The Doppler PSD estimates the broadening of the signal as a result of variations 33 in channel conditions. The power spectral densities presented in each model’s parameterization are represented as: Jakes Spectrum {Jakes, 1974 #215} (2.18) [] 1 2 2 ( ) , , 1 d d d A S f f f f f f = ( ! "# ,- $% Ricean Spectrum {Jeruchim, #214} (2.19) () [] 1 2 2 0.41 ( ) 0.91 0.7 , 2 1 d d d d d S f f f f f f f f f =+ ( ! "# ,- $% The channel is modeled as a linear finite-impulse-response (FIR) filter with tap weights generated according to {Jeruchim, #214}. The output signal can be generated by using the relationship: (2.20) ( ) ( ) ( ) n n y t s t nT g t = = (2.21) () () ( ) ( , )sinc B where B represents the channel's bandwidth. n where g t c t nT d = The output signal y(t) is generated from the input signal s(t) using a sum-of-sinusoids approach. The desired signal y(t) can be generated by passing s(t) through a tapped delay line with taps g(n) spaced T seconds apart. This is equivalent to multiplying the Fourier transform of the input 34 signal by the appropriate power spectral density. The path gains are simulated by (1) generating a sample of white Gaussian noise; and (2) passing the noise through a filter whose power spectrum corresponds to the appropriate power spectral density. The signal samples must be generated so that the sample period is consistent with that of the input signal. Also, the signals amplitudes must be consistent with the average path gain. 2.5.1 GSM Reference Models The European group COST ( European Cooperation in the Field of Scientific and Technical Research) developed channel models for typical propagation environments {COST207, 1989 #329}. These environments can be classified as being characteristic of areas with rural character, areas typical of city and suburban environments, densely built urban areas with adverse propagation conditions and hilly terrain. The GSM standard is based upon these parameterizations; the standard addresses mobile communications in the frequency band between 1 and 2 GHz {Tranter, 2004 #213}. 35 Table 6 Typical Profile for Rural Areas {Jeruchim, #214} {COST207, 1989 #329} Path Number Relative time of arrival (µsec) Avg. Path Gain (dB) Doppler PSD 1 0.0 0.0 Rice 2 0.1 -4.0 Jakes 3 0.2 -8.0 Jakes 4 0.3 -12.0 Jakes 5 0.4 -16.0 Jakes 6 0.5 -20.0 Jakes Table 7 Profile for Hilly Terrain {Jeruchim, #214} Path Number Relative Time (µsec) Average Path Gain (dB) Doppler Spectrum 1 0.0 0.0 Jakes 2 0.1 -1.5 Jakes 3 0.3 -4.5 Jakes 4 0.5 -7.5 Jakes 5 15.0 -8.0 Jakes 6 17.2 -17.7 Jakes 36 Table 8 Profile for Urban Area {Jeruchim, #214} Path Number Relative Time (µsec) Average Path Gain (dB) Doppler Spectrum 1 0.0 -3.0 Jakes 2 0.2 0.5 Jakes 3 0.5 -2.0 Jakes 4 1.6 -6.0 Jakes 5 2.3 -8.0 Jakes 6 5.0 -10.0 Jakes 2.5.2 PCS Reference Models PCS communication systems operate in the 2-GHz band {Jeruchim, #214}. The discrete channel models address indoor and outdoor environments. The strength of each constituent path is: 2 k k E a ' = (2.22) Table 9 PCS Outdoor Models {Jeruchim, #214} Environment Path #1 ( sec) µ Path #2 ( sec) µ Path #3 ( sec) µ Doppler Spectrum Doppler Bandwidth (Hz) Pedestrian 0 1.5 14.5 Flat 12 Wireless Local Loop 0 1.5 14.5 Gaussian 12 Vehicular 0 1.5 14.5 Jakes 180 37 Table 10 Relative Tap Strengths for Outdoor Models {Jeruchim, #214} Tap (Path) Number Average Path Gain (dB) 10 10 log k ' 1 0 2 -3 3 -6 Table 11 PCS Indoor Models {Jeruchim, #214} Environment Tap (Path) Spacing (ns) Number of Paths Doppler Spectrum Doppler Bandwidth (Hz) Residential 50 2 Gaussian 3 Office 50 4 Gaussian 3 Commercial 50 12 Flat 30 2.5.3 UMTS Reference Models The Universal Mobile Communications Systems (UMTS) {(ITU), 1997 #341}{(ETSI), 2005 #342}standards has developed propagation models for broadband communications in indoor and outdoor environments. Each terrestrial test environment is associated with a channel impulse response model. The model’s components include the number of paths, time delay (relative to the first tap) and average power (relative to the strongest tap). 38 The rms delay spread can vary significantly within the same environment; as a result, two multipath channels are used to capture large delay spreads {Jeruchim, #214}. In tables 13 thru 15, Channel A represents the low-delay- spread case while channel B represents the median-delay-spread case. Table 2-12 indicates the percentage of time that the two channel models occur. Tables 12 thru 15 provide the tapped-delay-line parameterizations associated with each environment. Table 12 Channel Impulse Response Model Parameters {Jeruchim, #214} Test Environment Average rms for low- delay spread case (Case A) Probability (rms= average value for Case A) Average rms for median- delay spread case (Case B) Probability (rms= average value for Case B) Indoor Office 35 50 100 45 Outdoor-to- Indoor and Pedestrian 45 40 750 55 Vehicular, High Antenna 370 40 4000 55 39 Table 13 Indoor Office Test Equipment Tapped Delay Line Parameters {Jeruchim, #214} Channel A Channel B Doppler Spectrum Path (Tap) Number Relative Delay (ns) Average Path Gain (dB) Relative Delay (ns) Average Path Gain (dB) Doppler Spectrum 1 0 0 0 0 Flat 2 50 -3.0 100 -3.6 Flat 3 110 -10.0 200 -7.2 Flat 4 170 -18.0 300 -10.8 Flat 5 290 -26.0 500 -18.0 Flat 6 310 -32.0 700 -25.2 Flat 40 Table 14 Outdoor to Indoor Tapped Delay Line Parameters {Jeruchim, #214} Channel A Channel B Doppler Spectrum Path (Tap) Number Relative Delay (ns) Average Path Gain (dB) Relative Delay (ns) Average Path Gain (dB) Doppler Spectrum 1 0 0 0 0 Jakes 2 110 -9.7 200 -0.9 Jakes 3 190 -19.2 800 -4.9 Jakes 4 410 -22.8 1200 -8.0 Jakes 5 - - 2300 -7.8 Jakes 6 - - 3700 -23.9 Jakes Table 15 Vehicular Test Environment Tapped Delay Line Parameters {Jeruchim, #214} Channel A Channel B Doppler Spectrum Path (Tap) Number Relative Delay (ns) Average Path Gain (dB) Relative Delay (ns) Average Path Gain (dB) Doppler Spectrum 1 0 0.0 0 -2.5 Jakes 2 310 -1.0 300 0.0 Jakes 3 710 -9.0 8900 -12.8 Jakes 4 1090 -10.0 12,900 -10.0 Jakes 5 1730 -15.0 17,100 -25.2 Jakes 6 2510 -20.0 20,000 -16.0 Jakes 41 2.7 Natural Language Descriptors The primary objective of this chapter was to develop a simulation methodology for articulating and validating system requirements that have been expressed using terminology common to end-users such as: ‘A vehicle traveling 45 miles per hour in an urban setting should be able to receive a movie that has no discernible blockiness’. This requirement has 5 components: velocity, transmission environment, data type, bandwidth constraints and perceptual quality. This chapter addressed the first two components: speed and transmission environment. The basic template for this partial requirement is as follows: A pedestrian strolling through an office building velocity environment Receiver velocity, coupled with communication network architecture, influences the Doppler shift, the primary parameter of the analytical and simulation models of mobile channels. The Doppler shift represents the maximum that the received signal will be from the carrier frequency. A velocity of 45 miles per hour corresponds to a maximum Doppler shift of 60.4 Hz in a GSM cellular network; it corresponds to 120.8 Hz in a PCS network, 42 and to 133 Hz in a UMTS network. Table 2-2 presents the mapping between velocity and Doppler shift. Once the maximum Doppler shift has been determined, the simulation must be parameterized to reflect the transmission environment: satellite, indoor or outdoor. The satellite environment is the most benign: the received signal can be modeled by simply adding samples from a Gaussian random number generator to the original signal. Signals transmitted in indoor environments are decomposed into several sub-components, however there is a dominant path, referred to as the line-of-sight component; these signals are modeled using the Ricean power spectral density as described in Section 2.3. A mobile channel simulation can be generated from natural language requirement as follows: 1. Use the velocity component to compute Doppler Shift using Table 2 or Equation 2.13. 2. Use the transmission environment to select the appropriate Doppler Spectrum. Set f d equal to the Doppler Shift computed in Step 1 . 43 3. Select the appropriate discrete channel model from Tables 6 thru 15. Generate the appropriate samples using the Doppler Spectrum identified in Step 2. 4. Implement the discrete channel model using the appropriate number of instances of the fading channel simulator described in Section 2.5. 44 2.8 Summary The overarching goal of this chapter was to develop a framework that allows system stakeholders with varying technical backgrounds to articulate system level performance requirements as they relate to the reliable transmission of video streams over wireless networks. The template of such a requirement consists of 5 components: velocity, network environment, data type, quality of perception and impairment type; this chapter addressed the first two components: speed and network environment. Subsequent chapters expand the natural simulation specification framework to address the remaining components. The multipath fading effect characterizes mobile communication channels. Multipath causes the transmitted signal to travel along multiple paths to the receiver. The receiver’s velocity influences the Doppler Shift, the difference in frequency between the transmitted and the received signals; the Doppler shift is a key simulation parameter and can be used to estimate the instantaneous bit error rate as described in Section 2.4. Chapters 3 and 4 describe how to use output from the decoder to obtain an independent estimate of the instantaneous bit error rate. This information can be used to determine whether the network is experiencing a fade and to take compensatory action if necessary. 45 Multipath fading phenomena can be modeled by multiplying the frequency domain representation of the transmitted signal by the appropriate power spectral density. The Jakes power spectral density is used when the signal is transmitted in an outdoor cellular network. The Ricean power spectral density is used when the signal is transmitted in an office or indoor environment. Satellite communications do not suffer from multipath fading; the received signal is modeled by adding white Gaussian noise to the original signal. The simulation designer may also use representative models based upon empirical data. Existing models are based on field experiments performed during the design of the GSM, PCS and UMTS communication systems. The models include estimates of the number of independent paths traveled by the signals sub-components as well as the amount of delay experienced by each sub-signal. These models can be implemented using a tapped delay line and an estimate of the maximum Doppler shift. Section 2.7 presented a linguistic framework that facilitates the specification and validation of communication requirements expressed using language characteristic of non-technical system stakeholders. This methodology, referred to as natural simulation specification, bridges the knowledge gap between non-technical system stakeholders and communications engineers. In Chapter 5, the natural simulation specification 46 methodology will be further enhanced to include fuzzy linguistic constructs which allow the quantification of the parameters introduced in this chapter. We first lay the groundwork for this fuzzy, adaptive quality control system by investigating the trade space associated with error control techniques. Chapter 3 presents performance data associated with error control codes. Chapter 4 describes techniques for measuring and controlling perceptual quality. 47 CHAPTER III TURBO CODE PERFORMANCE 3.1 Introduction Communication systems that operate in fading environments typically employ a combination of techniques to combat the effects of multipath fading. Typical approaches include differential modulation, equalization schemes and rake receivers in conjunction with channel coding techniques. This chapter investigates the effectiveness of turbo codes in maintaining a predefined level of video quality. Turbo codes are a class of error-correcting codes that offer performance that approaches theoretical limits {Berrou, 1996 #122}{Benedetto, 1996 #115}. They are a natural choice for mitigating the destructive effects of wireless channel impairments {Berrou, 1993 #86}. Turbo codes are currently used in third-generation cellular communication systems {(ETSI), 2005 #342}. Simulation studies will investigate the influence of code structure, latency, decoder complexity, transmission environment and code rate on quality-of-service. Two turbo code structures are considered: product codes and convolutional turbo codes. The interested reader is referred to {Barbulescu, 1996 #136}{Benedetto, 1996 #115}{Benedetto, 1996 #84}{Benedetto, 1996 #197}{Berens, 1999 #138}{Berrou, 1999 #121}{Berrou, 1993 #86}{Berrou, 1996 #122}{Divsalar, 1995 #82}{Dolinar, 1998 #135} for 48 tutorial material on turbo codes. Product codes are considered because they have no error floor {Pyndiah, 1998 #343}{Zhou, 2004 #344}. The performance of the rate UMTS rate 1/3 convolutional code is studied because it has already been implemented in a commercial system. Output from the turbo decoder will be used to estimate the instantaneous bit error rate. This metric will be compared to the estimate generated in Section 2.4 to gain insight into the state of the channel. The correct error control code can be selected to maintain the appropriate level of quality. These simulations can then be used to calibrate the performance of PerFEC’s adaptation mechanism. This work is extended in Chapter 4 so that the optimal code is selected based upon the bandwidth, quality of service and/or perceptual quality requirements. Because perceptual quality requirements are difficult to quantify using crisp numbers, Chapter 5 introduces a fuzzy representation of this optimization problem. The chapter is organized as follows: Section 3.2 investigates the performance of turbo product codes in an AWGN channel. Section 3.3 investigates the performance of the UMTS turbo code. Trade studies explore the impact of latency, code rate, decoder type and channel on performance. Section 3.4 the results of the chapter’s simulation studies. 49 3.2 Product Code Performance Turbo coding is forward error-correction coding scheme that yields dramatic improvement over the conventional coding techniques {Berrou, 1999 #121}. Turbo codes differ from conventional codes because they are both systematic and recursive. A turbo code consists of two constituent systematic encoders linked by an interleaver. The interleaver scrambles the input sequence before inputting it to the second encoder. The resulting codeword is composed of the input sequence followed by the parity check bits from both encoders. Turbo codes have been shown to perform within 0.7 dB of the Shannon limit . The results presented in the seminal paper (Berrou and Glavieux 1996) on turbo codes have been extended to include a number of decoders, a family of concatenated coding schemes, criteria for interleaver design , turbo-coded modulation schemes, and the performance of turbo codes over fading channels (Valenti 1999) (Divsalar and Pollara 1995; Divsalar and Pollara 1995; Valenti 2000; Liew and Hanzo 2002). However, there has been little research activity that studies the effectiveness of turbo codes in satisfying multimedia quality-of-service requirements. This section explores the performance of block turbo codes which are also referred to as turbo product codes. A block turbo code (BTC) consists of a concatenation of block codes; the encoders may be concatenated either serially or in parallel. Product codes are an example of serial concatenated 50 block codes. A two-dimensional product code is constructed from constituent codes C 1 and C 2. C 1 and C 2 have lengths n 1 and n 2. The resulting product code has length n 1 x n 2. The parameters associated with a two- dimensional product code are described in Table 16 (Soleymani, Gao et al. 2002). Table 16 Product Code Parameters Parameter C1 C2 C1 x C2 code length n1 n2 n1 x n2 information length k1 k2 k1 x k2 minimum distance d1 d2 d1 x d2 code rate R1 R2 R1 x R2 Simulation experiments were performed to model the performance of product codes in AWGN and binary symmetric (BSC) channels. Quasi-error- free (QEF) performance was selected as the performance target. In DVB-S2 systems, QEF corresponds to a bit error rate of 10 -10 or less than one erroneous packet per hour at a data rate of 5 Mbps {Morello, 2006 #345}. The codes in the trade space were grouped by block size. Both two and three-dimensional codes were used; the results in Table 3-1 can be extended to three dimensional codes. Several codes for each candidate packet size were identified. Each code in a group has a different code rate. The goal is to design the adaptive mechanism to select a code from a group 51 with a higher code rate when the bandwidth requirements dictate a reduction in code redundancy. Ideally, the new code will improve throughput with only a slight degradation in quality-of-service. The table below describes the performance of codes capable of supporting ATM, MPEG-2, IP and deep-space applications. Codes 1 and 2 support the ATM packet size (with a 4-byte overhead). Because of the small block size, only one candidate code with acceptable performance was identified. When the network becomes congested, PerFEC may select a conventional code with a higher code rate. Codes 3-6 have a block size of 4096 bytes. Code 3 is well suited for communications systems requiring limited overhead and a large coding gain is required. It offers performance that is only 1.1 dB from channel capacity for this code rate. This code is capable of tolerating 384 burst errors in each code block. A 128-bit burst even only shifts the BER curve 1.2 dB. Codes 7-9 have a block size of 2048 bytes and are appropriate for the delivery of MPEG-2 transport streams. Codes 10 thru 13 can be used for applications requiring medium block size. Codes 14 thru 18 have a block size of 65,536. This large code size is only appropriate for deep space applications but results in exceptional performance {Berrou, 1993 #86}. The results in Table 17 suggest that product codes are robust enough to provide quasi-error-free performance in the presence of wireless channel impairments. 52 Table 17 Block Turbo Code Performance Code Code Parameters Block Size Code Rate Required E b/N 0 for BER = 10 -10 Code 1 (16,11) X (16,11) 256 .4727 4.6 Code 2 (32,26) X (16,11) 512 .5586 4.4 Code 3 (64,57) X (64,57) 4096 0.793 4.2 Code 4 (32,26) X (32,26) X (4,3) 4096 0.495 2.9 Code 5 (16,11) X (16,11) X (16,11) 4096 0.325 2.2 Code 6 (32,26) X (16,11) X (8,4) 4096 .2793 2.6 Code 7 (64,57) X (32,26) 2048 .7236 4.2 Code 8 (32,26) X (16,11) X (4,3) 2048 .4189 3.6 Code 9 (64,57) X (8,4) X (4,3) 2048 .3340 4.4 Code 10 (32,26) X (32,26) 1024 .6602 4.2 Code 11 (16,11) X (16,11) X (4,3) 2816 .1289 2.8 Code 12 (128,120) X (128,120) 16384 .8789 4.2 Code 13 (32,26) X (32,26) X (16,11) 16384 .454 1.8 Code 14 (32,26) X (32,26) X (16,15) 65536 .619 2.4 Code 15 (64,57) X (64,57) X (16,15) 65536 .744 2.3 Code 16 (64,57) X (64,57) x (32,31) 65536 .701 2.0 Code 17 (64,57) X (64,57) x (32,26) 65536 .588 1.3 Code 18 (64,57) X (64,57) x (16,11) 65536 .545 1.1 3.3 UMTS Turbo Code Performance Section 3.2 examined the performance of turbo product codes; however, because this code configuration has not been adopted for use in any wireless standard, the turbo code used in the Universal Mobile Telecommunications System (UMTS) communication systems will be used as 53 the basis for remainder of the analysis. The UMTS encoder consists of two encoders of constraint length 4. The output of the encoder is a code with rate 1/3; the resulting code may range from 40 to 5114 bits in length. This code is flexible enough to generate packet sizes ranging from the 53-byte ATM cell to the largest IP packet. The interested reader is directed to the UMTS website (http://www.3gpp2.org) for additional information. Trade excursions involving changes in frame size, decoder algorithm and code rate are described in Table 18. This section presents the results of trade studies that probe the relationship between latency, or frame size, and performance. These trade studies will provide benchmark data that indicates whether the code provides the minimum performance required to maintain satisfactory perceptual quality. Inspection of the plots will reveal the range of signal-to- noise-ratios for which the candidate code provides acceptable performance. Acceptable performance is defined as a bit error rate of less than 10 -6 as defined in the UMTS QoS requirements {Partnership, 1999 #346}. 54 Table 18 Description of UMTS Simulation Scenario Parameters Scenario Environment Frame Size (bits) Modulation Scheme Decoding Algorithm 1 Satellite 40 BPSK log-map 2 Satellite 190 BPSK log-map 3 Satellite 530 BPSK log-map 4 Satellite 640 BPSK log-map 5 Satellite 1060 BPSK log-map 6 Satellite 2020 BPSK log-map 7 Satellite 3460 BPSK log-map 8 Cellular 40 QPSK log-map 9 Cellular 190 QPSK log-map 10 Cellular 530 QPSK log-map 11 Cellular 640 QPSK log-map 12 Cellular 1060 QPSK log-map 13 Cellular 2020 QPSK log-map 14 Cellular 3460 QPSK log-map 55 3.3.1 Influence of Latency on Code Performance 3.3.1.1 Satellite Scenarios This section discusses the performance of the 7 candidate codes over a satellite channel. The satellite channel is more benign than a cellular channel. While a code may provide acceptable performance in a satellite network, it may not provide robust enough protection in a cellular network. Figure 3 Summary of Satellite Latency Studies 56 The plots in Figure 3 demonstrate the difficulty of achieving significant performance improvements in environments characterized by very low signal-to-noise ratios. The following comments apply to Figure 3: The 40-bit code is well suited for channel conditions characterized by signal-to-noise ratios within the 3-6 dB range. The 190-bit code meets the desired performance requirements when the SNR exceeds 2 dB. The perceptual quality function will be defined in a piecewise fashion. The previous code performed adequately within the range from 3-6 dB; this code can be used to encode video data when the SNR is estimated to fall within the range from 2 to 3 dB. Perceptual quality will be evaluated at the midpoint of this range. The 530-bit code meets the desired performance criteria for SNR greater than 1 dB. Similarly, this code can be used to encode video data when the SNR is estimated to fall within the range from 1 to 2 dB. Not surprisingly, the 640-bit code does not offer substantially better performance than the 530-bit code. It should perform well in environments characterized by SNR’s in excess of 1 dB. Although the 1060-bit code is twice as long as the 530-bit code, its performance is only slightly better (an improvement in .2 dB). 57 The performance of the 2020-bit code follows the same trend. It is nearly double the length of the previous code but only offers a slight improvement in performance. The performance of the 3460-bit code yields the best performance. 58 3.3.1.2 Cellular Scenarios Figure 4 Summary of Cellular Latency Studies This section compares the performance of the UMTS turbo code in satellite and cellular transmission environments. The following comments summarize the performance of the UMTS turbo codes in the cellular transmission environment as shown in Figure 4: The plots in Figure 4 indicate that the 40-bit frame does not provide the minimum performance in environments characterized by SNR’s less than 7 dB’s. 59 The 190-bit code offers significantly better performance than the 40-bit code. This code will provide the desired performance for fading conditions in excess of 4 dB. The 530-bit code will perform adequately at SNR’s above 3 dB. The 640-bit code is only 110 bits longer than the previous code and offers a 1 dB improvement in performance. Conversely, the 1060-bit code is twice the length of the 530-bit code but only offers a small improvement in performance. Similarly, the 2,020-bit code does not offer significantly superior performance than the 530-bit code. The 3,460-bit code offers the nearly same performance as the 2,020-bit code. 3.4 Summary The simulation experiments performed in this chapter provided benchmark performance data on turbo product codes and the UMTS turbo code. Turbo product codes were found to satisfy the Quasi-Error-Free performance requirement stipulated by the Digital Video Broadcasting Satellite (DVB-S2) standard. The UMTS turbo code satisfied the quality-of- service requirement imposed by that organization. Because the UMTS code is in operation in a commercial cellular system, the remaining studies will focus 60 on this code structure. The benchmark data provided insight into the SNR range most appropriate for each candidate frame size. The simulation results suggest that frame size has a dramatic impact on performance. Subsequent studies will focus on the use of large frame sizes. Table 19 provides a rough mapping of frame length to SNR range in satellite and cellular transmission environments. The table suggests that because some codes offer nearly identical performance, an adaptive scheme for the satellite environment would require only a subset of the candidate codes. 61 Table 19 Mapping of UMTS Frame Length to SNR Range Satellite Cellular Frame length (bits) Appropriate E b/N 0 Range (dB) Appropriate E b/N 0 Range (dB) 40 3-6 >6 190 >2 >4 530 >1 >2.7 640 >1 >2.9 1060 >.8 >2.4 2020 >.8 >2.0 3460 >.6 >1.9 62 CHAPTER IV ADAPTIVE QUALITY CONTROL 4.1 Introduction Chapter 2 introduced the concept of a requirement template. The template for a wireless multimedia performance requirement has six components: velocity, transmission environment, data type, bandwidth constraints and perceptual quality. Chapter 2 described techniques used to validate the velocity and transmission environment components of the template. Chapter 3 described the use of error control codes in the mitigation of channel impairments. Code rate indicates the amount of redundancy associated with a candidate code. A reduction in bandwidth requirements might lead to an increase in code rate. The experiments in this study are limited to the transmission of video data. This chapter will examine the relationships between error correction code parameters, perceptual quality metrics and the network environment through which the video is being transmitted. This chapter describes the implementation of PerFEC’s adaptation mechanism. In order to implement an adaptive error control system, the system architecture must provide a return channel so that the receiver can provide the transmitter with information regarding the accuracy of the received messages; a decision can then be made regarding the selection of a 63 new error control code. This simple scheme permits the implementation of an adaptive error control scheme in the modem with a modest increase in hardware cost [Vucetic, 1988 #113]. Results from Chapter 2 indicated that the UMTS turbo code was capable of combating the effects of wireless transmission errors. Because channel conditions are time-varying, an adaptive FEC mechanism is required to adjust coding parameters based upon input from some network feedback mechanism. In order to gain insight into the relationship between traditional quality-of-service parameters and perceptual quality measures, the design space must be expanded to include perceptual quality metrics. First, we must describe our approach to determining the current state of the network based upon information generated by the receiver during the decoding process. These observations will be used to generate an estimate of the instantaneous bit error rate which can be compared to the benchmark values generated in Section 2.4. The remainder of the chapter is organized as follows: Section 4.2 describes the theory underlying PerFEC’s selection of an error control code given the prevailing network conditions. 64 Section 4.3 describes the perceptual quality metrics used to evaluate the effectiveness of the UMTS code in the presence of wireless channel impairments. Section 4.4 presents the formulation of our problem as a multivariable optimization problem with constraints. The constraints correspond to the desired level of perceptual quality and bandwidth requirements. Section 4.5 presents performance data for the candidate codes under consideration. Section 4.6 summarizes the methodology and results presented in this chapter. 4.2 Partially Observable Markov Decision Processes (POMDP) This section describes our initial approach to developing a channel- adaptive quality control technique. This approach is an application of reinforcement learning theory {Sutton, 1998 #352}. Reinforcement learning is the process of training an agent to make decisions so that its rewards are maximized. We will apply this technique to the problem of developing an adaptive mechanism that selects the optimal combination of resources to meet user requirements. 65 The adaptive error control problem can be modeled as a special case of a Markov Decision Process (MDP) {Hernandez-Lerma, 1989 #321}{Hernandez-Lerma, 1999 #320}. The Markov property does not apply to our situation because the agent does not have perfect knowledge of the state of the wireless channel. An additional level of abstraction must be employed to apply this framework to the problem of channel estimation. Partially Observable Markov Decision Processes are similar to Hidden Markov Models (HMMs) {MacDonald, 1997 #319}, in that they define a function by extracting hidden information from system observations. The observation is based on the consequence of an action and the resulting state. In our application, the function would be based upon available network resources and QoP/QoS parameters. The goal of solving a POMDP is to define a policy, which specifies which action to take in each state; the selected policy will maximize a long term reward function. In the context of PerFEC, the quality-control mechanism should sequentially select error control parameters so that the user receives the ‘best’ video quality given a set of network constraints. The trade space is large and the agent cannot determine the immediate consequence of selecting every possible combination of design parameters. Because the goal is to maximize the long term average visual quality of a video 66 sequence, the size of the decision/reward space grows exponentially, which could lead to prohibitively long simulation runs. In order to select the optimal policy given the current channel state, it is necessary for the agent to consider the impact of various state sequences. The model designer must face the following dilemma: should the agent explore the rewards associated with visiting more states or reduce the problem size/complexity and risk identifying potentially more rewarding states? This is referred to as the exploration-exploitation tradeoff {Sutton, 1998 #352}. In this problem, it is important to define a state space that is rich enough to satisfy performance requirements for a variety of transmission environments, user requirements and video types. This objective must be balanced by the practical necessity of not increasing the state space to such a degree that policy definition becomes unacceptably burdensome. It would be cumbersome to explore the result of backpropagating the reward signal throughout a large number of trajectories. In models comprised of large state spaces, the time required to reach a rewarding state via random exploration can be impractical as well as computationally burdensome. One approach is to define a higher level of abstraction that allows us to determine the rewards more quickly; this is referred to as generalization, the reduction of the state space. The definition of heuristics for this step will be important to the success of our adaptive error control mechanism. 67 4.2.1 POMDP Model Definition The decision-making agent will employ principles from Markov Decision Theory to a complex and time-varying optimization problem. Our goal is to identify an optimal parameter selection policy that adapts to fluctuations in a time-varying wireless channel. The policy will encompass traditional quality-of-service (QoS) and video Quality-of-Perception (QoP) criteria. The system description consists of the collection of system states together with the input observation, transition and reward functions. The observation received by the agent describes the history of the frame errors. In the POMDP model framework, the agent makes its decisions on the basis of an observation, sometimes referred to as the state signal. The state signal received by the decision agent captures the history of the decoder feedback for the past several time instants. Although specific details regarding decoder actions may be lost, the state signal captures the essence of the information required to make a decision. It is important to consider the immediate as well as long-term consequences of the selected action. The decision agent will be confronted with several alternative actions. The actions consist of selecting one of the candidate code structures presented in the table below. The immediate effects of an action are often easy to see, but the long term effects are not 68 always as transparent. Policies resulting in an action that may appear to have less than optimal immediate effects may have better long term ramifications. The policy selection algorithm should balance the tradeoffs between the immediate rewards and the future gains, to yield the best possible solution. The decision-making agent will make trajectories through the state space in order to collect statistics; policy definition will be performed based on the analysis of this data using gradient-based optimization schemes. The next section will detail the specifics of the model. Modified Markov Decision Process The adaptive quality control mechanism will be modeled by a modified Markov Decision Process with a finite state space S={1,2,…,M}. At any state s(S, an action is selected from a finite action space D(s) and applied to the MDP. A policy is a mapping L:S->D which identifies an action (D(s) for every state s. 1 represents the finite policy space. A policy L (1 describes the behavior of the PerFEC agent. There is a reward function R(s, ) associated with each state x and each control action (D(s). Our goal is to identify the optimal policy L opt that maximizes the reward function over the policy space 1 . The above description must be modified because our decisions will not be based on the actual state of the system, but on observations made about the system. Because these observations may be probabilistic, it is necessary 69 specify an observation model that describes the probability of each observation for each state in the model. Although the underlying dynamics of a POMDP are Markovian {Cassandra, 1998. #353}, we must maintain a history of the observations. The history at any point in time consists of our knowledge about our starting situation, all actions performed and data about all observations. This requirement may be satisfied by defining the probability distribution over all of the states. The distribution function is updated by updating the transition and observation probabilities after each action. 4.2.2 Calculation of State Transition Function The description of the frame history is similar to the model proposed in 1962 by E. N. Gilbert {Gilbert, 1960 #117}. The Gilbert model consisted of a two-state Markov chain used to generate error bursts. The two states were referred to as G (for good) and B (for bad or burst). In state G the noise digit is always 0; when in state B, a coin is tossed to decide the value of the received bit (0 or 1). {Zorzi, 1997 #260} and {Zorzi, 1995 #259} show that Gilbert’s model can be used to model the behavior of a correlated Rayleigh fading channel. Zorzi’s work demonstrates that the success/failure of a packet’s transmission can be approximated by a two-state Markov chain, as described by the state transition diagram and transition matrix below: 70 1 1 p p q q ! "# $% (4.1) Here p refers to the probability that the jth frame contains no transmission errors, given that the j-1st frame was successful. The steady state transport block error rate, P BL can be computed as follows: 1 2 BL p P p q = (4.2) {Zorzi, 1995 #259} shows that for a Rayleigh fading channel with fading margin F, the average transport block error rate (P BL) can be expressed as: -1/F BL P = 1-e (4.1) 1/ ( , ) 1 1 F Q q e *'* = (4.2) 2 2 ( ) 2 0 ( , ) ( ) x w y Q x y e J xw wdw + = (4.3) 71 (Q is the Marcum Q-function {Zorzi, 1997 #260} (Zorzi and Rao 1997) 2 2 / 1 F * ' = (4.4) ( is the correlation coefficient between successive samples separated by T seconds; f d is the Doppler frequency) Using the above, the relationship between the block error rate and the Markov parameter can be derived as follows: (1 ) ( , ) ( , ) 1 BL BL P Q Q q P * '* * '* = (4.5) All that is necessary to compute this relationship and parameterize the Gilbert-Elliot 2-state Markov model is the block error rate P BL. P BL will be obtained from simulations involving various coding strategies. 4.2.3 Observation History The observations in our model are obtained from processing information received from the decoder. The receiver uses a return channel to provide the transmitter with information regarding the decoder output. The transmitter then selects an appropriate code based upon a set of predefined 72 requirements. The receiver can provide information regarding the history of the most recent N frames. If the frames are numbered 0,1,2…, N, we can describe the transmission status of frame j as x j. x j = 1 if the jth frame was correctly received and x j = 0 otherwise. The observation after transmission of the jth frame is defined as a vector x(j) = {x j-N+1, x j-N-2,.., x j}. N must sufficiently large enough to ensure that x j is independent of x j-N. For N= 100, the observation vector could resemble the following sequence: 0 5 1 4 001010 86 . The exponents represent run lengths, 0 86 indicates that the last 86 frames contained an unacceptable number of transmission errors. This observation suggests the need to adapt the quality control parameters to employ a more robust coding strategy. For our previous example, there would be 2 100 possible observations. Because of the size of the observation space associated with large N, it is helpful to identify a secondary model to use in conjunction with the information communicated by the frame history. We will analyze decoder output under various conditions for each code. This will provide us with input as to whether the channel conditions require the use of a more appropriate code. For example, consider the history of frame errors for the 640-bit, rate 1/3 UMTS code over 9 SNR points. 73 Table 20 Decoder Errors Relative to Decoder Iteration Decoder Iteration Number of Errors Per SNR Data Point 0.0 dB 0.2 dB dB 0.4 dB 0.6 dB 0.8 dB 1.0 dB 1.2 dB 1.4 dB 1.6 dB 1 99 169 368 1291 5999 26058 123901 402151 1001945 2 99 168 354 1188 4900 16060 48168 81176 88441 3 95 152 261 675 1769 3361 5291 4545 2805 4 90 129 161 336 622 782 979 641 374 5 80 99 111 195 270 304 312 229 156 6 71 82 86 139 154 174 160 130 98 7 66 72 78 106 104 109 112 89 80 8 63 68 73 85 80 82 90 70 73 9 61 63 63 71 72 68 66 61 67 10 60 60 60 60 60 60 60 60 60 For a given code, we would compute the average and standard deviation of the number of errors that occurred in a frame within the SNR range of interest. In the above example, if the decoder reported an excess of 200 errors per frame for a particular observation interval, the decision agent should probably select a more robust code. Conversely, if the decoder recorded fewer than 5 errors per frame during a time window, a more bandwidth efficient code should be selected. The plots below depict the probability of a block error for codes of rates 2/3, 1/3, 2/9 and 1/6. 74 Figure 5 Rate 2/3 Code 75 Figure 6 Rate 1/3 Code 76 Figure 7 Rate 2/9 Code 77 Figure 8 Rate 1/6 Code The graphs illustrate that there is little variation in the number of frame errors for a wide range of signal-to-noise values. Therefore, receipt of a value outside of this range would suggest the occurrence of a fade. PerFEC would respond by applying more robust error correction. 78 4.2.4 Solving the POMDP We now have all of the information required to generate the probability distribution of the observation function for our reduced 2-state Markov model. Recall that our goal is to find a mapping from observations to actions. We can refer to a probability distribution over states as a belief state and the entire probability space as the belief space {Cassandra, 1998. #353}. We can now perform the mapping from observation to action. Because there are only two states, the belief state can be represented by a single bit; in addition, because a belief state is a probability distribution, the sum of all probabilities must sum to 1. As described in the previous section, the probability of being in one of the states is 'p', and the probability of being in the other state must be '1-p'. In our model, state G corresponds to benign channel conditions, while state B corresponds to hostile or fading conditions. If we begin our simulation in belief state B, take action a1, and receive observation z1 after taking that action. The next belief state is now completely defined. Because we are assuming that there are a finite number of actions and observations, given a belief state, there are a finite number of possible next belief states. These correspond to each possible combination of action and observation. Since observations are probabilistic, each resulting belief state has a 79 probability associated with it. Therefore, if we take an action and obtain an observation, we know with certainty what our next belief state is. However, before we decide to take an action, each resulting belief state has a particular probability associated with it and there are as many possible next belief states as there are observations for a given action. {Cassandra, 1998. #353} shows that the process of maintaining the belief state is Markovian; the next belief state depends only on the current belief state (and the current action and observation). The problem of finding the optimal policy can now be solved iteratively, a process known as value iteration. 4.2.5 POMDP Model Parameterization The core of our adaptive quality control algorithm is the use of a two-state POMDP to define the optimal policy for selecting an FEC coding scheme based on a processed observation. The observation consists of a frame history. The frame history provides an indication as to whether the current quality control strategy is robust enough for the current channel conditions or whether a more robust approach is necessary. The adaptive control mechanism, or POMDP agent, will iteratively determine the impact of the various candidate coding choices to ensure that the selected action ensures the best long-term video quality. 80 4.3 Measurement of Perceptual Video Quality Video quality is affected by many factors but there is no comprehensive study that describes the impact of these factors on perceptual quality. Studies currently described in the literature focus on the effect of network parameters without considering encoding factors, or vice versa. For example, cell loss rate and burst length metrics are studied in (Hands and Wilkins 1999), while {Wu, 1998 #161} investigates the effect of bit rate. {Ghinea, 1998 #163} investigates the impact of frame rate on video quality. In order to develop adaptive control mechanisms that deliver the best video quality given certain network conditions, it is necessary to identify a set of parameters that reflect a representative set of parameters and correlate well with human perception. We will consider video quality in terms of network as well as perceptual quality requirements. Quality of Perception (QoP) describes the ability of the user to perceive, synthesize and analyze the informational content of multimedia presentations [Ghinea, 1998 #163] [Ghinea, 1999 #143]. Therefore, the problem of quantifying and monitoring application level performance requires a unifying approach that encompasses both the user’s perspective and the performance and specification of the underlying network. 81 4.3.1 Mean Opinion Score The Mean Opinion Score, recommended by the Institute for Telecommunication Sciences (ITS) of the National Telecommunications and Information Administration (NTIA), is among the most frequently used metrics ((ITU) ). The computation of this metrics involves having a group of human observers rate the quality of a set of video clips. It is approximated by collecting p measurements m i and p+1 constants (c i) that allow the estimation of the subjective mean opinion score, which is computed as follows: 0 1 p i i i s c c m = =+ 4.3.2 Mean Squared Error (MSE) Mean Squared Error (MSE) is one of the most popular metrics used to measure the difference between an image and a corrupted version of the original image. This metric is not effective between it does not correlate well with subjective quality measures [Uddenfeldt, 1998 #166]. MSE and related metrics cannot measure a human observer’s perception of artifacts of image distortion; in addition, it does not correlate well with additive noise. Many models try to emulate the response of the Human Visual System (HVS) {Girod, 1997 #167}{Bahl, 1998 #169}{Grillo, 1998 #168}{Lin, 1984 #170} 82 {Illgner, 1995 #173}{Fischer, 1996 #172} {Girod, 1996 #174} {Talluri, 1998 #175} {Girod, 1999 #177}. An important factor in evaluating the effectiveness of a metric is its flexibility and applicability to wide variety of scenarios. Some metrics only measure specific types of distortions or artifacts (Grillo 1998) while some are appropriate for a particular video coding standard (Bahl and Girod 1998) (Lin, Costello et al. 1984). 4.3.3 Swiss Federal Institute of Technology Metrics Researchers at the Swiss Federal Institute of Technology have proposed three objective video quality measures {van den Branden Lambrecht, 1997 #159}{Verscheure, 1998 #34}{van den Branden Lambrecht, 1999 #158}{Wu, 1996 #160}. Moving Picture Quality Metric (MPQM), Color MPQM (CMPQM), and the Normalization Video Fidelity Metric (NVFM). These metrics consider luminance and chrominance values but are not suitable for real-time evaluation of video quality. They do not perform consistently over all bit ranges and do not consistently correlate with subjective ratings. The metric has been normalized to fall within a range between 0 and 1. 0 indicates a minimal impairment, 1 indicates the most severe impairment {Wu, 1998 #355}. 83 4.3.4 ITS VQEG Metrics The Institute for Telecommunication Services (ITS) Video Quality Experts Group (VQEG) has proposed guidelines on the selection of appropriate perceptual video quality measurement equipment for use in digital cable television applications. In order to be accurate, digital video quality measurements have to be based on perceived picture quality and have to be made in-service using the actual video being sent by the users of the digital video system. The primary reason for this requirement is that the performance of digital video systems is variable and depends upon the dynamic characteristics of both the input video (e.g., spatial detail, motion) and the digital transmission system (e.g., bit-rate, error-rate). The VQEG has proposed five models, collectively referred to as VQM, for evaluating video quality applications; the value of the metric has been normalized to fall within a range between 0 and 100, where 0 indicates a minimal impairment, 100 indicates the most severe impairment {Wolf, 2002 #180}: The general model suitable for systems spanning a wide range of quality levels. The developer’s model is less accurate than the general model but executes several times faster. 84 The television model is appropriate for Digital Video Broadcast and other broadcast television and DVD applications. The videoconference model has been optimized for videoconferencing applications such as H.261, H.263 and MPEG-4. The PSNR model is based on the peak-signal-to-noise-ratio metric, a variation of MSE. The VQM methodology requires two video sequences as input: (1) the original video sequence and (2) a video sequence that has been processed by a video system or corrupted by another process. The two sequences are calibrated to remove spatial and temporal shifts. VQM then computes the perceived video using one of the five metrics above. The VQM methodology has been shown to have a degree of correlation with subjective assessments over a variety of conditions and transmission scenarios {Wolf, 2002 #180}. This methodology is described in more detail in ANSI T1.801.03, "American National Standard for Telecommunications - Digital Transport of One-Way Video Telephony Signals - Parameters for Objective Performance Assessment", which specifies a framework for measuring video quality impairments introduced by a video codec or digital transmission channel. The ANSI standard contains 85 parameters derived from three types of features that have proven useful: (1) scalar features, where the information associated with a specified video frame is represented by a scalar; (2) vector features, where the information associated with a specified video frame is represented by a vector of related numbers; and (3) matrix features, where the information associated with a specified video frame is represented by a matrix of related numbers. The VQM performance metrics will be used to benchmark the effectiveness of the candidate code structures. 4.4 Generation of Parameter Database The design and implementation of an adaptive error control system requires a bi-directional control protocol to request and indicate new parameter settings. The UMTS High Speed Downlink Packet Access (HSDPA) system was selected as the simulation environment for this phase of the study because it supports Adaptive Modulation and Coding (AMC) as well as provides return channels for the support of packet-based multimedia services. These features allow PerFEC to adjust the error control parameters synchronously between the sender and receiver. The UMTS HSDPA code of length 3226 data bits was selected for this study. The experiments performed in Chapter 3 indicate that a code of 86 approximately this length provided the best performance. The 3226-bit UMTS code with code rates of 1 1 1 , ,and 3 9 6 was used to benchmark performance. The adaptive FEC algorithm adjusts the code rate according to channel conditions. The first step in the process of benchmarking code performance is the collection of perceptual quality metric data for each code rate. The PerFEC database is populated by tables that contain benchmark performance data. A data structure similar to Table 21below is populated for each candidate code structure. Data on the probability of block errors were obtained from the decoder’s output generated during these experiments. Table 22 describes the format of the tables describing the decoder output observed for each SNR point. Table 21 Perceptual Quality Benchmark Data Code Rate Required E b/N 0 for BER = 10 -6 PSNR General Developer …other metrics 2 3 1 3 2 9 1 6 87 Table 22 Structure of Decoder Output Table Code Rate Average Number of Errors Detected by the Decoder 2 3 1 3 2 9 1 6 SNR Point 1 SNR Point 2 . . . SNR Point N 4.5 Multivariable Optimization of Perceptual Quality Requirements The goal of this section is to develop a policy for adaptively selecting the appropriate code for the prevailing channel conditions. The code selection algorithm uses the data in each code’s table to implement the POMDP described in Section 4.2.4. The reward associated with each decision is a function of the change in perceptual quality as quantified by the VQM metrics. This process is implemented as follows: Step 1: Select the length of the observation interval, T. Step 2: Select an initial policy L 0 , which is a mapping from X , the belief space (observations describing the frame history) to an action ( ) X from the decision space ( ) D X . Initialize k to 0. 88 Step 3: Observe system behavior under policy L k for T simulation epochs. If the observation vector indicates that the channel is experiencing or entering a fade, invoke the reward optimization function in Step 4 to select a new policy. Otherwise, proceed to Step 6. Step 4: Compute the reward function associated with each candidate policy. Select the policy that maximizes the reward. Perform the action associated with this new policy. Establish this new policy as L k+1 . Step 5: Estimate P BL (probability of block error, Equation 4.2) and the corresponding entries of the transition probability matrix for the belief state for this sample path. Monitor the probability of being in the Good state. (This parameter is an important indicator of the long-range effectiveness of the algorithm. Although the policy cannot prevent a channel from experiencing a fade, the selection of a robust quality control strategy can create the perception that channel conditions are benign.) Step 6: Perform Step 3. 89 The reward optimization function associated with our policy can be described as follows: Maximize - 1 N i i i p 2 = where i 2 refers to the weight assigned to parameter i p subject to the following constraints: p 1 + user defined tolerance 1 p 2 + user-defined tolerance 2 etc. 4.6 Simulation Results This section describes the simulation experiments that were performed to measure the effectiveness of the UMTS error correcting codes in maintaining perceptual video quality. The channel modeling techniques described in Chapter 2 were used to generate a database composed of video samples transmitted during various network conditions. The original and corrupted video clips were analyzed using the VQM tool described in Section 4.3. The VQM rankings and the corresponding parameter values are stored in the database. The VQM software compares the original and corrupted video sequences and generates values for five video quality metrics. Each perceptual video quality metric is ranked on a scale from 0 to 5, where 0 90 indicates that no impairment was detected; 5 indicates the most severe impairment. These values were adjusted to conform to the Double Stimulus Continuous Quality Scale which provides values in the range from 0 to 100 {Pinson, #348}. In addition, VQM provides Root Cause Analysis (RCA) information that indicates whether the impairment was the result of blurring, jerky/unnatural motion, global noise or block distortion. RCA information is reported in terms of the percentage of users who perceived each impairment type as a primary artifact. The data resulting from the simulation experiments can be used to implement the template for a fuzzy requirement introduced in Chapter 1. Recall that a requirement template consists of five components: velocity, transmission environment, application type, bandwidth constraints and perceptual quality. Table 23 describes the translation of a performance requirement expressed in natural language into a simulation parameterization. 91 Table 23 Translation of Natural Language Requirement into Simulation Specification Requirement: A pedestrian strolling through an office building should experience no blurriness or unnatural movement when participating in a videoconference. Natural language descriptor Requirement Component Simulation Approach pedestrian strolling velocity Doppler Frequency parameter of Discrete Channel Model Office building Transmission environment Rice Discrete Channel Model with parameters in Table 11 blurriness Perceptual quality VQM Root Cause Analysis Unnatural movement/jerkiness Perceptual quality VQM Root Cause Analysis Videoconference Environment VQM Videoconference Model The requirement in Table 23, which has been expressed in natural language, can then be directly mapped to the appropriate parameters in the PerFEC performance database. As network conditions or bandwidth requirements change, the POMDP will determine the optimal code configuration. Notice that the bandwidth requirement is not explicitly expressed. The bandwidth constraints are dictated by the cellular or satellite service provider. 92 4.6 Summary This chapter described the implementation of PerFEC as a Partially Observable Markov Decision Model (POMDP). The PerFEC POMDP agent interacts with its environment to collect observations about the condition of the wireless channel. The observations are processed to determine the necessity of changing quality control parameters. If it becomes necessary to adjust code configurations, the agent selects the optimal policy based on iteratively examining the consequences of each action for a fixed number of simulation epochs. At each time step, the agent implements a mapping from the belief state to the values of the reward function associated with each candidate action. The agent's goal is to maximize the total amount of reward it receives over the long run. The simulation tools and parameterizations presented in this chapter make it possible to translate a naturally-expressed perceptual quality requirement into a simulation specification. One limitation of this approach is that it cannot account for scenarios in which the constraints, goals or consequences associated with a policy are partially unknown or are difficult to quantify. This is always true in 93 applications involving the specification of human judgments and preferences. Chapter 5 presents an extension of this approach that permits a richer description of the design goals, evaluation criteria and alternatives. The approach is based upon principles from fuzzy logic. 94 CHAPTER V FUZZY PERCEPTUAL QUALITY MODELING AND CONTROL 5.1 Introduction This chapter extends the decision methodology presented in Chapter 4 to encompass problems characterized by conflicting or imprecisely specified objectives. System designers are frequently confronted with multiple criteria problems characterized by varying degrees of fuzziness. The front-end of the design process is dominated by stakeholders who often have difficulty translating subjective goals into quantifiable performance requirements. The complexity of the design problem increases exponentially when considered in the context of a ‘system of systems’ – each with its own conflicting/competing objectives and performance requirements. This chapter employs the use of linguistic constructs to articulate the design preferences of stakeholders who may not be domain experts. Fuzzy linguistic variables can then be translated into conventional performance requirements. We apply a fuzzy version of Saaty’s Analytic Hierarchy Process [Saaty, 1980 #301] to the problem of adaptive video/multimedia quality control. The chapter is organized as follows: Section 5.2 describes the Analytic Hierarchy Process (AHP) and applies it to the problem of adaptive quality control. Section 5.3 implements a fuzzy extension of the AHP that provides 95 the user with a richer framework for specifying perceptual preferences. Section 5.4 applies Fuzzy Preference Programming to our problem. Section 5.5 summarizes the results presented in the chapter. 5.2 The Analytic Hierarchy Process The Analytic Hierarchy Process (AHP) [Saaty, 1980 #301] provides a methodology for modeling complex, unstructured problems in the social, economic, management or engineering sciences. AHP decomposes the problem into objectives, criteria and alternatives; the problem is solved in three stages as described below. Phase 1: Define the problem hierarchy by identifying an overarching goal, the criteria for evaluating the satisfaction of the goal. Phase 2: Perform a pairwise comparison of the alternatives relative to each other. This stage will yield numerical weights that quantify the relative importance of the alternatives as they relate to the criteria. This stage encompasses two subtasks: 1) the quantification of the relative importance of the criteria; and, 2) the determination of the relative standing of each alternative with respect to each criterion. 96 Phase 3: Assign a composite score to each alternative. This score will be used in the objective function of the fuzzy or linear programming problem used to make the final decision. We will now discuss the application of the AHP to our problem. Phase 1: Decompose Problem Objective: Maintain a pre-defined level of video quality in the presence of channel impairments. Criteria: We will consider a subset of perceptual quality metrics: Blocking, Blurring, and VQM. Alternatives: The alternative actions consist of a set of candidate codes; for this example, we will consider four candidate codes: Code 1, Code 2, Code 3, and Code 4. 97 Figure 9 AHP Problem Formulation Maintain User-Specified Level of Perceptual Quality General Videoconference Television Code1 Code 2 Code 3 Code 4 Code1 Code 2 Code 3 Code 4 Code1 Code 2 Code 3 Code 4 98 Phase 2: Comparison of Alternatives During this phase, the criteria will be ranked using pairwise comparisons. The relative importance of the criteria will be quantified using the scheme described in [Ghinea, 2001 #283]. Table 24 Linguistic Descriptors Importance Description 1 The criteria are equally important 3 One alternative is moderately more important than the other 5 One criterion is significantly more important than the other 7 One criterion is demonstrably more important than the other 9 One criterion is absolutely more important than the other 2,4,6,8 These are intermediate values Reciprocals of any of the above The values assigned to criteria are reciprocal. For example, if the comparison of criterion a to b results in a value of 2, then the comparison of criterion b to a results in a value of ½. 99 Suppose that a ranking of the criteria resulted in the table below: Table 25 Fuzzy Ranking of Evaluation Criteria General Videoconference Television Blurring 1/1 1/2 3/1 Blocking 2/1 1/1 4/1 Jerkiness or Unnatural Motion 1/3 1/4 1/1 The contents of Table 25 are converted to the matrix below: 1.0 0.5000 3.0 2.0 1.0 4.0 0.3333 0.2500 1.0 ! "# "# "# $% The weights of the criteria can determined by computing the eigenvector [Triantaphyllou, 1996 #302]of the matrix above. Other methods of computing the weights of the criteria include logarithmic least squares [Triantaphyllou, 1996 #302], goal programming[Bryson, 1995 #303] and fuzzy programming [Mikhailov, 1999 #304] methods. In this example, we will use 100 the eigenvector method. The matrix is successively squared and its eigenvector is computed. 2 1.0 0.5000 3.0 3.0 1.75 8.0 2.0 1.0 4.0 5.3332 3.0 14.0 0.3333 0.2500 1.0 1.1666 0.6667 3.0 ! ! "#" # = "#" # "#" # $%$ % The eigenvector is computed by normalizing the sum of the rows: Sum of row 1 = (3.0 + 1.75 + 8.0) = 12.75 Sum of row 2 = (5.3332 + 3.0 + 14.0) = 22.3332 Sum of row 3 = ( 1.1666 + 0.6667 + 3.0) = 4.8333 Sum of row totals: 39.9165 The eigenvector is obtained by normalizing each row total (dividing by 39.9165) = 0.3194 0.5595 0.1211 ,- ,- ,- This process is repeated until the eigenvector does not change significantly between iterations. The final eigenvector is: 0.3196 0.5584 0.1220 ,- ,- ,- 101 The elements in the eigenvector represent the rankings of each criterion. This means that (in this example) blocking is the most important criteria, blurring is the second most important, and jerkiness is the least important. The elements of the eigenvector serve as weights to be input to the cost function. 102 Figure 10 Ranking of Evaluation Criteria Phase 3: Assign a composite score to each alternative. The same process will now be performed for each alternative (candidate code). The process begins by performing pairwise comparisons of each alternative (candidate code) relative to the blocking, blurring and Maintain User-Specified Level of Perceptual Quality 1.0 General 0.3196 Videoconference 0.5584 Television 0.1220 Code1 Code 2 Code 3 Code 4 Code1 Code 2 Code 3 Code 4 Code1 Code 2 Code 3 Code 4 103 jerkiness metrics. Table 26 contains a set of rankings relative to the blurring metric. Table 26 Alternative Rankings Relative to Blurring Metric Code 1 Code 2 Code 3 Code 4 Code 1 1/1 1/4 4/1 1/6 Code 2 4/1 1/1 4/1 1/4 Code 3 1/4 1/4 1/1 1/5 Code 4 6/1 4/1 5/1 1/1 The rankings of the four alternatives relative to blurriness were extracted from the eigenvector associated with Table 26 above: Table 27 Ranking of Alternatives Using Eigenvector Method Alternative Eigenvector Code 1 0.1160 Code 2 0.2470 Code 3 0.0600 Code 4 0.5770 104 For economy of space, assume that the alternative ranking process resulted in eigenvectors that generated the results in Figure 11. Figure 11 Ranking of Code Alternatives Maintain Perceptual Quality 1.0 General 0.3196 Videoconference 0.5584 Television 0.1220 Code1 = 0.1160 Code 2 = 0.2470 Code 3 = 0.0600 Code 4 = 0.5770 Code1 = 0.3790 Code 2 = 0.2900 Code 3 = 0.0740 Code 4 = 0.2570 Code1 = 0.3010 Code 2 = 0.2390 Code 3 = 0.2120 Code 4 = 0.2480 105 The final ranking of the candidate codes for a given set of channel conditions can now be determined by multiplying the matrices below. Table 28 Numerical Ranking of Candidate Codes General Videoconference Television Criteria ranking eigenvector Code 1 .1160 .3790 .3010 0.3196 blurring Code 2 .2470 .2900 .2390 * 0.5584 blocking Code 3 .0600 .0740 .2120 0.1220 jerkiness Code 4 .5770 .2570 .2480 106 Table 29 Final Ranking of Candidate Codes Code 1 .3060 Code 2 .2720 Code 3 .0940 Code 4 .3280 Note that all of the matrices have a constant form – with the exception of the matrix that rates each evaluation criterion relative to the others. Depending upon the set of evaluation criteria, its values may change as a result of channel conditions, user preferences or bandwidth allocations. For example if delay, text and chromaticity were included in the evaluation criteria, the user might prefer the ability to read text to a degradation in chromaticity. A vision or hearing-impaired user may have a different set of preferences. These examples highlight the need for an adaptive mechanism that is flexible enough to support the perceptual quality requirements associated with several user types. 5.3 Fuzzy Analytic Hierarchy Process The previous section described how the Analytic Hierarchy Process provides a methodology for selecting an alternative based upon multiple Highest ranking alternative 107 evaluation criteria. The success of the approach is strongly tied to the ability of the user to accurately quantify his/her (dis)satisfaction with the quality of a video clip. It is more natural for human beings to use linguistic terms to articulate their preferences. The difficulty associated with precisely specifying human perceptual preferences suggests the need for imprecise or fuzzy decision-making methods. Saaty’s AHP has been expanded to include fuzzy data in [Boender, 1989 #307][Buckley, 1985 #308][McCahon, 1990 #309]. Fuzzy Numbers A fuzzy number represents an imprecise, rather than a precise quantity, as is the case with conventional, single-valued numbers. A fuzzy number is a function whose domain is a set of real numbers whose range spans a subset of non-negative real numbers [Yen, 1998 #315]. The components of the triangular fuzzy number associated with the Fuzzy AHP represent the minimum, mode and maximum values associated with a linguistic term describing the user’s preference for a pair of alternatives. Each value in the domain is mapped to corresponding value in the domain; this value specifies the membership grade of the fuzzy number. A fuzzy number is denoted (l,m,u) where l and u represent the lower and upper values while m represents the model value. The membership mapping function can be described as [Triantaphyllou, 1996 #302]: 108 [] [] 1 1 , x , 1 1 ( ) , x , 0 otherwise m x l m m l m l x x m u m u m u µ ( = ( Linguistic Variables A linguistic variable assumes qualitative as well as quantitative values. For example a variable called picture quality could assume values poor, fair and excellent. The membership function corresponding to picture quality provides a mapping between its universe of discourse (poor, fair, excellent) and the interval [0,1] which represents the degree of membership. Figure 12 below illustrates this concept. The values corresponding to the linguistic variable picture quality in the figure are described by the Gaussian membership function. The symmetric Gaussian function has two parameters and c as described by: 2 2 ( ) 2 ( ; , ) x c f x c e = 109 Figure 12 Membership Functions - Picture Quality We now have the tools to implement the Fuzzy Analytic Hierarchy Process. Recall that the AHP involves the following steps: Phase 1: Specification of the problem hierarchy Phase 2: Pairwise comparison of the criteria Phase 3: Assign a composite score to each alternative. The sections below will describe the ‘fuzzification’ of these steps. 110 Figure 13 Multicriteria Decision Model Provide Optimal Video Quality Network Conditions Bandwidth Efficiency Video Impairments BER FER SNR estimate Code rate Code structure Spectral Efficiency blocking blurring overall 111 Figure 13 depicts a hierarchical, multicriteria model in which each criterion is decomposed into three sub-criteria. The overarching goal is to provide optimal video quality given a set of user-defined performance requirements (criteria). Each code will be evaluated relative to its performance in combating the prevailing channel conditions, satisfying the bandwidth requirements and providing the best perceptual video quality given these constraints. 5.3.2 Comparison of Alternatives Step 2 of the AHP process is accomplished by performing a pairwise comparison of the criteria as well as the sub-criteria relative to the alternatives. Gulcin’s linguistic weighting set will be used to obtain a more accurate description of the user’s preferences. 112 Table 30 Linguistic Descriptors Linguistic Descriptors English Interpretation Membership Function JE Just Equal – Items are identical o JE 1, x=1 = 0, otherwise µ ALI Absolutely Less Important ALI SMI 1 µ µ = VSLI Very Strongly Less Important VSLI VSMI 1 µ µ = SLI Slightly Less Important SLI SMI 1 µ µ = WLI Weakly Less Important LI MI 1 µ µ = EI Equally Important EI 1 2 1 for 1 2 3 2 3 for 1 x 2 0, otherwise x x x µ ++ = + ++ 113 Table 30 Continued Linguistic Descriptors English Interpretation Membership Function WMI Weakly More Important WMI 3 2( 1) for 2 2 3 2 4 for x 2 2 0, otherwise x x x µ ++ = + ++ SMI Strongly More Important SMI 3 2 3 for 2 2 5 2 5 for 2 x 2 0, otherwise x x x µ ++ = + ++ VSMI Very Strongly More Important VSMI 5 2( 2) for 2 2 5 2( 3) for x 3 2 0, otherwise x x x µ ++ = + + AMI Absolutely More Important AMI 5 2 5 for 3 2 7 2 7 for 3 x 2 0, otherwise x x x µ ++ = + ++ 114 These linguistic terms are used to determine the relative importance of the criteria and sub-criteria; they are also used to rate the candidate codes. As an example Code 3 may be rated strongly more important than Code 1 under certain criteria. The membership function for each criteria/subcriteria captures the correlation between the linguistic weights and numerical values. Membership functions may be modeled by a variety of functions. The interested reader is referred to {Yen, 1998 #315}{Jang, 1997 #350} for a thorough discussion of this topic. The triangular membership function will be used in this problem. The triangular membership function is specified by three parameters (a,b,c) as follows {Yen, 1998 #315}: 0 x<a (x-a) a x b (b-a) triangle(x:a,b,c) (c-x) b x c (c-b) 0 x>c ++ = ++ 115 The triangular membership function is applied to the linguistic descriptors as described in Table 31. Table 31 Membership Functions of Linguistic Descriptors Linguistic Descriptors Membership Function Triangular Membership Function JE JE 1, x=1 = 0, otherwise µ ( ) 1,1,1 EI EI 1 2 1 for 1 2 3 2 3 for 1 x 2 0, otherwise x x x µ ++ = + ++ 1 3 ,1, 2 2 ! "# $% WMI WMI 3 2( 1) for 2 2 3 2 4 for x 2 2 0, otherwise x x x µ ++ = + ++ 3 1, , 2 2 ! "# $% 116 Table 31 Continued Linguistic Descriptors Membership Function Triangular Membership Function VSMI 5 2( 2) for 2 2 5 2( 3) for x 3 2 0, otherwise x x x µ ++ = + + 5 2, ,3 2 ! "# $% AMI AMI 5 2 5 for 3 2 7 2 7 for 3 x 2 0, otherwise x x x µ ++ = + ++ 5 7 ,3, 2 2 ! "# $% ALI ALI SMI 1 µ µ = 2 1 , , 2 7 3 ! "# $% VSLI VSLI VSMI 1 µ µ = 1 2 1 , , 3 5 2 ! "# $% SLI SLI SMI 1 µ µ = 2 1 2 , , 5 2 3 ! "# $% WLI LI MI 1 µ µ = 2 ,1, 2 3 ! "# $% 117 The triangular membership functions for the values of each linguistic descriptor are depicted in Figure 13. Figure 14 User Preference Membership Functions Because of the inverse nature of the membership functions, the table only depicts half of the descriptors. For the purpose of illustration, Figure 14 illustrates the relationship between two inverse descriptors: Weakly More Important and Weakly Less Important. 118 Figure 15 Inverse Membership Functions We will now demonstrate the remainder of the process for comparing the criteria and subcriteria as they relate to three candidate codes. We will 119 now demonstrate our approach using a scenario in which the user used fuzzy linguistic descriptors to express his/her preferences. The preferences are not based on an evaluation by human viewers – such an undertaking is too ambitious for this study. For simplicity, this contrived example parallels that described in {Yen, 1998 #315}. Table 32 Relative Performance of Main Criteria NC BW VI Network Conditions (NC) JE EI WMI Bandwidth Efficiency(BW) EI JE WMI Video Impairments (VI) WLI WLI JE Table 33 Relative Importance of Sub-Criteria Associated with Network Conditions Network Condition Sub- Criteria BER FER fade BER JE EI WMI FER EI JE WMI fade WLI WLI JE Table 34 Relative Importance of Sub-Criteria Associated with Bandwidth Efficiency Bandwidth Efficiency Sub-Criteria code rate code structure spectral efficiency 120 code rate JE EI WMI code structure EI JE WMI spectral efficiency WLI WLI JE Table 35 Relative Importance of Sub-Criteria Associated with Video Impairments Video Impairment Sub-Criteria blurring blocking overall blurring JE WMI WMI blocking WLI JE EI overall WLI EI JE The rankings in Tables 32 thru 35 must now be converted to fuzzy numbers. The fuzzy evaluation matrix with respect to each objective is defined in the Tables 36 thru 45. Table 36 Fuzzy Quantification of Relative Performance of Main Criteria Network Conditions Bandwidth Efficiency Video Impairments Network Conditions (1,1,1) 1 3 ,1, 2 2 ! "# $% 3 1, , 2 2 ! "# $% Bandwidth Efficiency 2 ,1, 2 3 ! "# $% (1,1,1) 3 1, , 2 2 ! "# $% Video Impairments 1 2 , ,1 2 3 ! "# $% 1 2 , ,1 2 3 ! "# $% (1,1,1) 121 Table 37 Fuzzy Quantification of Alternatives Relative to BER Code 1 Code 2 Code 3 W BER Code 1 (1,1,1) 1 2 , ,1 2 3 ! "# $% 5 2, ,3 2 ! "# $% 0.43 Code 2 3 1, , 2 2 ! "# $% (1,1,1) 5 2, ,3 2 ! "# $% 0.57 Code 3 1 2 1 , , 3 5 2 ! "# $% 1 2 1 , , 3 5 2 ! "# $% (1,1,1) 0.0 Table 38 Fuzzy Quantification of Alternatives Relative to FER Code 1 Code 2 Code 3 W FER Code 1 (1,1,1) 1 2 1 , , 3 5 2 ! "# $% 3 1, , 2 2 ! "# $% 0.0 Code 2 5 2, ,3 2 ! "# $% (1,1,1) 5 2, ,3 2 ! "# $% 1.0 Code 3 1 2 , ,1 2 3 ! "# $% 1 2 1 , , 3 5 2 ! "# $% (1,1,1) 0.0 122 Table 39 Fuzzy Quantification of Alternatives Relative to Network Fading Code 1 Code 2 Code 3 W fade Code 1 (1,1,1) 2 1 2 , , 5 2 3 ! "# $% 1 2 , ,1 2 3 ! "# $% 0.1 Code 2 3 5 , 2, 2 2 ! "# $% (1,1,1) 3 1, , 2 2 ! "# $% 0.56 Code 3 3 1, , 2 2 ! "# $% 1 2 , ,1 2 3 ! "# $% (1,1,1) 0.34 Table 40 Fuzzy Quantification of Alternatives Relative to Code Rate Code 1 Code 2 Code 3 W code rate Code 1 (1,1,1) 1 2 , ,1 2 3 ! "# $% 3 1, , 2 2 ! "# $% 0.34 Code 2 3 1, , 2 2 ! "# $% (1,1,1) 3 5 , 2, 2 2 ! "# $% 0.56 Code 3 1 2 , ,1 2 3 ! "# $% 2 1 2 , , 5 2 3 ! "# $% (1,1,1) 0.1 Table 41 Fuzzy Ranking of Alternatives Relative to Code Structure Code 1 Code 2 Code 3 W structure Code 1 (1,1,1) 2 1 2 , , 5 2 3 ! "# $% 1 3 ,1, 2 2 ! "# $% 0.16 Code 2 3 5 , 2, 2 2 ! "# $% (1,1,1) 3 5 , 2, 2 2 ! "# $% 0.61 Code 3 2 ,1, 2 3 ! "# $% 2 1 2 , , 5 2 3 ! "# $% (1,1,1) 0.23 123 Table 42 Fuzzy Ranking of Alternatives Relative to Spectral Efficiency Code 1 Code 2 Code 3 W spectral eff Code 1 (1,1,1) 1 2 , ,1 2 3 ! "# $% 1 2 , ,1 2 3 ! "# $% 0.21 Code 2 3 1, , 2 2 ! "# $% (1,1,1) 3 1, , 2 2 ! "# $% 0.45 Code 3 3 1, , 2 2 ! "# $% 1 2 , ,1 2 3 ! "# $% (1,1,1) 0.34 Table 43 Fuzzy Ranking of Alternatives Relative to Blurring Metric Code 1 Code 2 Code 3 W blur Code 1 (1,1,1) 1 3 ,1, 2 2 ! "# $% 3 5 , 2, 2 2 ! "# $% 0.46 Code 2 2 ,1, 2 3 ! "# $% (1,1,1) 3 5 , 2, 2 2 ! "# $% 0.46 Code 3 2 1 2 , , 5 2 3 ! "# $% 2 1 2 , , 5 2 3 ! "# $% (1,1,1) 0.09 Table 44 Fuzzy Ranking of Alternatives Relative to Blocking Metric Code 1 Code 2 Code 3 W block Code 1 (1,1,1) 1 3 ,1, 2 2 ! "# $% 3 1, , 2 2 ! "# $% 0.38 Code 2 2 ,1, 2 3 ! "# $% (1,1,1) 3 1, , 2 2 ! "# $% 0.38 Code 3 1 2 , ,1 2 3 ! "# $% 1 2 , ,1 2 3 ! "# $% (1,1,1) 0.24 124 Table 45 Fuzzy Ranking of Alternatives Relative to Overall Perceptual Quality Code 1 Code 2 Code 3 W overall Code 1 (1,1,1) 1 3 ,1, 2 2 ! "# $% 3 5 , 2, 2 2 ! "# $% 0.46 Code 2 2 ,1, 2 3 ! "# $% (1,1,1) 3 5 , 2, 2 2 ! "# $% 0.46 Code 3 2 1 2 , , 5 2 3 ! "# $% 2 1 2 , , 5 2 3 ! "# $% (1,1,1) 0.09 The fuzzy equivalent of the addition, division and comparison operations will be performed to rank these values in a manner analogous to that performed as part of the crisp AHP described in Section 5.2. These operations are described below. Assume that A and B are fuzzy numbers represented by the triads A= (l 1,m 1,u 1) and B = (l 2,m 2,u 2). Fuzzy Addition: A+B =(l 1,m 1,u 1) + (l 2,m 2,u 2) = (l 1+l 2,m 1+m 2,u 1+u 2) Fuzzy Multiplication: A.B=(l 1,m 1,u 1) · (l 2,m 2,u 2)= (l 1·l 2,m 1·m 2,u 1·u 2) Fuzzy Inverse: (l 1,m 1,u 1) -1 =(1/u 1,1.m 1,1/l 1) 125 Articulating the preference of alternatives relative to each other as well as to the evaluation criteria is more difficult to perform using fuzzy numbers. The ranking of alternatives relative to a goal set is performed using extent analysis [Chang, others]. Extent analysis is the analog of the comparison operation in the fuzzy domain. Suppose that the problem consists of C={C1,…,Cn}, the set of criteria, and set A={A1,…,Am}, the set of alternatives. Chang’s extent analysis defines an extent analysis metric, M, for each alternative relative to each goal. Extent analysis is performed as follows: Step 1: Let represent the relative importance of alternative j relative to criterion i. ( is a triangular fuzzy number) Determine ( 1.. ) for each alternative. i i i j C j C j C M M M j m = 1 1 1 1 Step 2: Compute the synthetic extent for each alternative as follows: i i m m n j j i C C j i j S M M == = = ,- 3 126 1 1 1 1 2 2 2 2 2 2 2 2 1 1 1 1 Step3:Compare the fuzzy preferences by computing the degree of possibility: For two fuzzy numbers, ( , , ) and ( , , ), the degree of possibility of M =( , , ) ( , , ) is defin M l m u M l m u l m u M l m u == = %% 2 1 2 1 1 2 1 2 2 2 1 1 ed as: 1 if V(M M ) 0 if otherwise ( ) ( ) m m l u l u m u m l = %% The degree of possibility is similar to the concept of probability in the crisp number domain. The interested reader may refer to {Buyukozkan, 2004 #360} for a detailed discussion. Following this procedure, the synthetic extent for each criterion is: 127 1 1 1 (2.5,3.5, 4.5) ( , , ) (0.2,0.39,0.63) 12.5 9.33 7.1 1 1 1 (2.67,3.5,5.0) ( , , ) (0.21,0.39,0.7) 12.5 9.33 7.1 1 1 1 (2.0,2.33,3.0) ( , , ) (0.16,0.26,0.42) 12.5 9.33 7.1 NC BW VI S S S = = = = = = Recall that the first vector represents the row sums. The second vector represents the inverse of the column sums. These vectors are used to compute the degree of probability: ( ) 1.0 ( ) 1.0 ( ) 1.0 ( ) 0.63 ( ) 0.62 '( ) ( , ) min(1.0,1.0) 1.0 '( ) ( ) min(1.0,1.0) 1.0 '( ) ( ) min(0.62,0.63) 0.62 NC BW NC VI BW NC BW VI VI BW NC BW VI BW NC VI VI BW NC V S S V S S V S S V S S V S S d NC V S S S d BW V S S S d VI V S S S = = = = = = == = == = == Note that d’(alternative) represents the relative preference of each alternative. The weight vector is therefore W’=(1.0, 1.0, 0.62). These values are normalized to allow the values to be analogous to weights. After normalization, the weight vector of the object with respect to each criterion is: T objective W =(0.38,0.38,0.24) (4.6) 128 Note that d'(alternative) represents the relative preference of each alternative. The weight vector is therefore ' (1.0,1.0, 0.62) These values are normalized in order to allow the values to be analog W = T objective ous to weights. After normalization, the weight vectors of the object with respect to each criteria is: W =(0.38,0.38,0.24) The process is repeated for each set of subcriteria. The results are presented in Tables 46 thru 50. Table 46 Ranking of Evaluation (Sub) Criteria MAIN CRITERIA LOCAL WEIGHTS SUB-CRITERIA LOCAL WEIGHTS BER 0.38 FER 0.38 Channel Conditions 0.38 Fade 0.24 Code Rate 0.38 Code Structure 0.38 Bandwidth Efficiency 0.38 Spectral Efficiency 0.24 Blurring 0.43 Blocking 0.27 Video Impairments 0.24 Overall 0.30 129 Table 47 Ranking of Code Weight Criterion ALTERNATIVE W code rate W code rate W code rate Priority Weight Code 1 0.43 0.16 0.21 0.24 Code 2 0.57 0.61 0.45 0.55 Code 3 0.10 0.23 0.34 0.21 Table 48 Ranking of Picture Quality Subcriteria ALTERNATIVE W blur W block W overall Priority Weight Code 1 0.46 0.38 0.46 0.44 Code 2 0.46 0.38 0.46 0.44 Code 3 0.09 0.24 0.09 0.12 Table 49 Final Ranking of Criteria ALTERNATIVE W channel condition W BW EFF W video imp Final Weight Code 1 0.19 0.24 0.44 0.27 Code 2 0.73 0.55 0.44 0.59 best alternative Code 3 0.08 0.21 0.12 0.14 130 5.4 Fuzzy Preference Programming The dynamic nature of our problem demands the use of a methodology capable of addressing inconsistencies in the optimization matrix. Conventional linear programming problems can be expressed as: 0 , max subject to a x Ax b 4 A conventional linear programming problem can be converted to its fuzzy counterpart by replacing the crisp parameters with symmetric triangular fuzzy numbers as follows {Carlsson, 2002 #316}: 1 1 ( , ) ( , ) ( , ) ... ( , ) ( , ), i=0,...,m ij i j ij i j i i n n i i a a b b d a x a x b d = = ++ % % 131 Fuzzy preference programming can be performed by making a list that describes what should happen during the decision process. This description can take the form of rules. A sample set might be: Rule 1: If the picture quality is excellent and the network condition is benign, then the system should apply weak quality control. Rule 2: If the picture quality is excellent and the network condition is typical, then the system should apply weak quality control. Rule 3: If the picture quality is excellent and the network condition is hostile, then the system should apply strong quality control. Rule 4: If the picture quality is fair and the network condition is benign, then the system should apply weak quality control. Rule 4: If the picture quality is fair and the network condition is typical, then the system should apply weak quality control. Table 50 contains a complete set of rules for our system. 132 Table 50 PerFEC Rules for Fuzzy Inference System network PQ benign typical hostile excellent weak weak strong fair weak weak strong blurry average average strong blocky average average strong poor strong strong strong The next step in the process is to map the linguistic variables to their respective membership functions; these are depicted in Figures 16 thru 18. 133 Figure 16 Membership Function - Picture Quality 134 Figure 17 Membership Function - Network Conditions 135 Figure 18 Membership Function - Degree of Protection We can now generate a 3-dimensional representation of the fuzzy solution surface corresponding to this problem. This approach allows us to perform sensitivity analysis in order to gain insight into how subtle changes in preference values or evaluation metrics impact the solution domain. Figure 18 below depicts the fuzzy solution surface corresponding to this problem. 136 Figure 19 Fuzzy Inference System Solution Surface 137 5.5 Summary This chapter described a methodology that allows engineers from disparate disciplines to articulate design goals in a common linguistic framework. Fuzzy reasoning was used to aggregate the preferences of multiple experts. The methodology was specifically applied to the problem of adaptively adjusting perceptual video or multimedia quality to a pre- defined level specified by a group of end-users. This approach allows the simulation designer to map the fuzzy linguistic descriptor ‘hostile network’ to the appropriate parameter settings for the Doppler coefficients, phases and frequencies described in Chapter 3. Similarly, a mapping can readily be developed between the perceptual quality metrics described in Chapter 4 and the phrase ‘poor video quality’. It is also possible to create fuzzy variables that correspond to each of the impairments generated by VQM’s Root Cause Analysis module. The visual representation of the solution surface provides insight into how nuances in the description vocabulary affect performance. The decision algorithm is flexible enough to consider any number of perceptual evaluation metrics. It can also be readily adapted to a variety of fixed and mobile wireless environments. 138 CHAPTER VI APPLICATION OF PERFEC TO WiMAX ENVIRONMENT 6.1 WiMAX Overview This chapter will explore the application of the PerFEC methodology to WiMAX, the Worldwide Interoperability for Microwave Access air interface standard (http://www.wimaxforum.org). The methodology will begin with an overview of the transmission environments and applications that the system architecture should support. WiMax is designed to support a variety of transmission scenarios: theme parks, campus connectivity, rural areas, military battlefields, distance education and entertainment networks {Forum, 2005 #357} WiMAX service classes include interactive gaming, VoIP, videoconferencing, streaming media, web browsing, instant messaging and store and forward networking {Forum, 2005 #357}. Table 51 presents the models recommended to simulate WiMAX transmission environments {Forum, 2006 #358}. Table 52 describes the WiMAX code structures. WiMAX provides quality of service (QoS) based on the Service Level Agreement (SLA) between the service provider and the end user {Forum, 2005 #357}.The WiMAX business model provides the flexibility to provide different SLA’s to different subscribers or even to different users within the 139 same Subscriber Station. Channel State Information (CSI) is communicated by the user terminal to the base station scheduler via a Channel Quality Indicator (CQI) {Forum, 2006 #356}. Table 51 WiMAX Transmission Environments Channel Model # of Paths Speed Doppler PSD # Users per Sector Model A 1 3 km/hr Jakes 3 (30%) Model B 3 10 km/hr Jakes 3 (30%) Model C 2 30 km/hr Jakes 2 (20%) Model D 1 120 km/hr Jakes 1 (10%) Model E 1 0 f Doppler =1.5Hz Rician K-Factor =10dB 1 (10%) Total Users Per Sector = 10 Total Users Per Cell = 30 140 Table 52 WiMAX Code Configuration and Transmission Characterization 5 MHz Channel 10 MHz Channel Modulation Type Code Type/Rate Downlink Rate (Mbps) Uplink Rate (Mbps) Downlink Rate (Mbps) Uplink Rate (Mbps) ½ CTC 0.53 0.38 1.06 0.78 ½ CTC 0.79 0.57 1.58 1.18 ½ CTC 1.58 1.14 3.17 2.35 ½ CTC 3.17 2.28 6.34 4.7 QPSK ¾ CTC 4.75 3.43 9.5 7.06 ½ CTC 6.34 4.57 12.67 9.41 16-QAM ¾ CTC 9.5 6.85 19.01 14.11 ½ CTC 9.5 6.85 19.01 14.11 2/3 CTC 12.67 9.14 25.34 18.82 ¾ CTC 14.26 10.28 28.51 21.17 64-QAM 5/6 CTC 15.84 11.42 31.68 23.52 141 6.2 Systems Engineering Process Figure 20 WiMAX Problem Hierarchy The systems engineer would use the information above to develop perceptual quality performance goals as described in Chapters 4 and 5. The first step would be to collect and analyze the perceptual preferences of the consumer and service provider stakeholders. This process would result in the definition of the problem hierarchy; Figure 19 presents a possible hierarchy. A pairwise comparison of the evaluation criteria and alternatives would then be performed using the Fuzzy Analytical Hierarchy Process Provide Optimal Video Quality Network Conditions Bandwidth Efficiency Video Impairments BER FER SNR estimate Code rate Code structure Spectral Efficiency blocking blurring overall 142 described in Chapter 5. The responses would be used to develop appropriate Service Level Agreements (SLA’s). The next phase involves the selection of codes that deliver the appropriate level of perceptual quality. Table 53 contains the codes for consideration. Table 53 WiMAX Error Correction Code Trade Space Modulation Code Structure ½ Convolutional Turbo Code QPSK ¾ Convolutional Turbo Code ½ Convolutional Turbo Code 16-QAM ¾ Convolutional Turbo Code Simulation of the performance of these codes indicates that they will not deliver the desired performance. This is probably due to the error floor characteristic of convolutional turbo codes (CTC); under the most favorable conditions, they do not provide bit error performance that exceeds 10 -8 {Divsalar, 1995 #82}. Table 54 displays the perceptual quality performance of the candidate codes. Although these codes may be capable of delivering satisfactory quality-of-service, they cannot satisfy perceptual quality requirements. 143 The author wishes to emphasize that simulation performance results are affected by clip length, the number or simulation runs, the cyclic nature of random number generators, etc. Table 54 Performance of Rate ½ Convolutional Code BER=10 -7 Developer General PSNR Television Videoconference 93.47 FAIL 79.53 FAIL 91.80 FAIL 89.39 FAIL 60.44 FAIL Root Cause Analysis Blurring = 55% Jerky or Unnatural Motion = 48% 100% = perceived as a primary artifact by all viewers 50% = perceived as a secondary artifact 0% = artifact not perceived Blurring = 65% Jerky or Unnatural Motion = 8% Global Noise = 29% Block Distortion = 61% 100% = perceived as a primary artifact by all viewers 50% = perceived as a secondary artifact 0% = artifact not perceived N/A Blurring = 16% Jerky or Unnatural Motion = 22% Global Noise = 100% Block Distortion = 66% Error Blocks = 61% 100% = perceived as a primary artifact by all viewers 50% = perceived as a secondary artifact 0% = artifact not perceived Blurring = 37% Jerky or Unnatural Motion = 22% Block Distortion = 33% 100% = perceived as a primary artifact by all viewers 50% = perceived as a secondary artifact 0% = artifact not perceived 144 6.3 Alternative Design The system engineering team is faced with the dilemma of considering another code architecture or by implementing design features that compensate for the effects of multipath fading. Low Density Parity Check (LDPC) offer excellent performance without the limitations of an error floor {MacKay, 1996 #359}. Table 55 displays performance results for the rate 0.76 (1024, 821) Reed-Solomon based code defined over Galois Field (2 5 ). Table 55 Performance of (1024, 821) Low Density Parity Check Code BER Developer General PSNR Television Videoconference 0 0 0 0 0 Root Cause Analysis Blurring = 0% Jerky or Unnatural Motion = 0% 100% = perceived as a primary artifact by all viewers 50% = perceived as a secondary artifact 0% = artifact not perceived Blurring = 0% Jerky or Unnatural Motion = 0% 100% = perceived as a primary artifact by all viewers 50% = perceived as a secondary artifact 0% = artifact not perceived N/A Blurring = 0% Jerky or Unnatural Motion = 0% 100% = perceived as a primary artifact by all viewers 50% = perceived as a secondary artifact 0% = artifact not perceived Blurring = 0% Jerky or Unnatural Motion = 0% 100% = perceived as a primary artifact by all viewers 50% = perceived as a secondary artifact 0% = artifact not perceived 145 6.4 Conclusion This chapter demonstrated the application of the PerFEC methodology to the WiMAX system. The systems engineering team would have to draft questionnaires for the consumers as well as for the service provider. The analysis and processing of their responses would facilitate the definition of Service Level Agreements (SLA’s). Simulation of the perceptual quality performance of the candidate codes could then be performed. This step suggested that the candidate code structures would be unsuitable for this application. Low Density Parity Check Codes were proposed as an alternate design choice. 146 CHAPTER VII FUTURE DIRECTIONS The topic of this thesis involves several disciplines: communication system analysis, signal and image processing, wireless networking, discrete event simulation and visual communications. Time did not permit the exploration of the derivative issues encountered during this project. The chapter provides an overview of the future projects and planned journal submissions resulting from this study as follows: Integrate Fuzzy Controller in the Partially Observable Markov Decision Process: The POMDP methodology described in Chapter 4 could be enhanced by the integration of a Fuzzy Controller. Weights would be assigned to the evaluation criteria and the policy iteration algorithm would be fuzzified. PerFEC Fuzzy Controller: The PerFEC fuzzy controller could be enhanced by 1) exploring methods for aggregating user preferences and by developing a methodology for selecting the appropriate membership function for the linguistic variables. 147 Fuzzy Simulation Methods: The fuzzy simulation methodology could be expanded by the development of possibilistic parameterization of communication channel parameterization. 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The Video Quality Model software tool {Pinson, #348} and a video test sequence generated by the Video Quality Experts Group was used as test data (src6_ref_625.yuv from ftp://ftp.crc.ca/crc/vqeg/TestSequences/Reference). Section 1 describes the error modeling techniques used to induce errors in the test sequences. Section 2 uses perceptual quality metrics to evaluate the effectiveness of PerFEC in protecting the video sequences from impairments. 1.0 Error Source Modeling The test sequence used was 9 seconds in duration and required 182MB of storage space. The format of the sequences is as follows: 625@50Hz 260 frames in length 720 pixels per horizontal line 4:2:2 Interlaced, Abekas files The wireless channel model described in Chapter 2 was expanded to include the ability to generate random and burst errors. This was particularly important due to the short length of the test sequence. The use of a longer test sequence was computationally prohibitive; depending upon the coding 178 scheme, it took 10-14 hours to encode, corrupt and decode the test sequence on a Pentium (4) 4 CPU running at 3 GHz. In addition, the cyclic nature of random number generators affected the ability to develop a truly random simulation. {Turin, 2004 #212} describes the use of alternating renewal process models to simulate fading processes. The approach used to model the error process is based on the theory, algorithms and Matlab code presented in {Turin, 2004 #212}. An alternating renewal process is a semi-Markov model with two states. The states alternate with different interval distributions. Error bursts occur independently with fixed probability b p . An error burst of length l occurs with probability ( ) b P l within each burst. An errored bit occurs with probabilty1 . The model does not allow for the probability of a bit error outside of an error burst. The model is a semi-Markov process with the following transition probability matrix: b b b b q p P q p ! = "# $% (4.7) The state holding time distributions are as follows: 11 (1) 1 w = (4.8) 179 22 ( ) ( ) b w l P l = (4.9) Turin shows that the burst-length distribution is matrix geometric and can therefore be described as a Hidden Markov Model (HMM). Since the distribution of the burst-length is geometric: 1 ( ) (1 ) l b P l g g = (4.10) The transition distributions are also geometric: 1 12 ( ) l b b f l p q = (4.11) 1 12 ( ) l b b f l p q = (4.12) where b b q gq p =+ . This is Gilbert’s Model with matrix 1 b b q p P q q ! = "# $%

Abstract (if available)

Abstract The global telecommunications system has evolved into a ubiquitous, integrated network capable of delivering video teleconferencing, videotelephony, high definition television (HDTV), multiple viewpoint video, video on demand (VoD), distance learning and telemedical applications. The reliable delivery of these services requires the use of flexible protocols that consider human perceptual issues. Legacy protocols are based on traditional network design objectives such as bit-error-rate (BER), cell loss rates, and peak-signal-to-noise-ratio (PSNR).

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Creator Boadi, Antonia Marie (author)

Core Title PerFEC: perceptually sensitive forward error control

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering (Computer Networks)

Publication Date 08/09/2009

Defense Date 04/12/2007

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag OAI-PMH Harvest,perceptual video quality,quality-of-service,turbo codes,video quality metrics

Language English

Advisor Silvester, John (committee chair), Khoshnevis, Behrokh (committee member), Ortega, Antonio (committee member)

Creator Email boadi@sbcglobal.net

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m782

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