Distributed Source Coding

SHUANG WANG, University of California, San Diego, USA YONG FANG, Northwest A&F University, China SAMUEL CHENG, University of Oklahoma, USA

Preface xiii


Acknowledgment xv


About the Companion Website xvii


1 Introduction 1


1.1 What is Distributed Source Coding? 2


1.2 Historical Overview and Background 2


1.3 Potential and Applications 3


1.4 Outline 4


Part I Theory of Distributed Source Coding 7


2 Lossless Compression of Correlated Sources 9


2.1 Slepian–Wolf Coding 10


2.1.1 Proof of the SWTheorem 15


Achievability of the SWTheorem 16


Converse of the SWTheorem 19


2.2 Asymmetric and Symmetric SWCoding 21


2.3 SWCoding of Multiple Sources 22


3 Wyner–Ziv Coding Theory 25


3.1 Forward Proof ofWZ Coding 27


3.2 Converse Proof of WZ Coding 29


3.3 Examples 30


3.3.1 Doubly Symmetric Binary Source 30


Problem Setup 30


A Proposed Scheme 31


Verify the Optimality of the Proposed Scheme 32


3.3.2 Quadratic Gaussian Source 35


Problem Setup 35


Proposed Scheme 36


Verify the Optimality of the Proposed Scheme 37


3.4 Rate Loss of theWZ Problem 38


Binary Source Case 39


Rate loss of General Cases 39


4 Lossy Distributed Source Coding 41


4.1 Berger–Tung Inner Bound 42


4.1.1 Berger–Tung Scheme 42


Codebook Preparation 42


Encoding 42


Decoding 43


4.1.2 Distortion Analysis 43


4.2 Indirect Multiterminal Source Coding 45


4.2.1 Quadratic Gaussian CEO Problem with Two Encoders 45


Forward Proof of Quadratic Gaussian CEO Problem with Two Terminals 46


Converse Proof of Quadratic Gaussian CEO Problem with Two Terminals 48


4.3 Direct Multiterminal Source Coding 54


4.3.1 Forward Proof of Gaussian Multiterminal Source Coding Problem with Two Sources 55


4.3.2 Converse Proof of Gaussian Multiterminal Source Coding Problem with Two Sources 63


Bounds for R1 and R2 64


Collaborative Lower Bound 66


–sum Bound 67


Part II Implementation 75


5 Slepian–Wolf Code Designs Based on Channel Coding 77


5.1 Asymmetric SWCoding 77


5.1.1 Binning Idea 78


5.1.2 Syndrome–based Approach 79


Hamming Binning 80


SWEncoding 80


SWDecoding 80


LDPC–based SWCoding 81


5.1.3 Parity–based Approach 82


5.1.4 Syndrome–based Versus Parity–based Approach 84


5.2 Non–asymmetric SWCoding 85


5.2.1 Generalized Syndrome–based Approach 86


5.2.2 Implementation using IRA Codes 88


5.3 Adaptive Slepian–Wolf Coding 90


5.3.1 Particle–based Belief Propagation for SWCoding 91


5.4 Latest Developments and Trends 93


6 Distributed Arithmetic Coding 97


6.1 Arithmetic Coding 97


6.2 Distributed Arithmetic Coding 101


6.3 Definition of the DAC Spectrum 103


6.3.1 Motivations 103


6.3.2 Initial DAC Spectrum 104


6.3.3 Depth–i DAC Spectrum 105


6.3.4 Some Simple Properties of the DAC Spectrum 107


6.4 Formulation of the Initial DAC Spectrum 107


6.5 Explicit Form of the Initial DAC Spectrum 110


6.6 Evolution of the DAC Spectrum 113


6.7 Numerical Calculation of the DAC Spectrum 116


6.7.1 Numerical Calculation of the Initial DAC Spectrum 117


6.7.2 Numerical Estimation of DAC Spectrum Evolution 118


6.8 Analyses on DAC Codes with Spectrum 120


6.8.1 Definition of DAC Codes 121


6.8.2 Codebook Cardinality 122


6.8.3 Codebook Index Distribution 123


6.8.4 Rate Loss 123


6.8.5 Decoder Complexity 124


6.8.6 Decoding Error Probability 126


6.9 Improved Binary DAC Codec 130


6.9.1 Permutated BDAC Codec 130


Principle 130


Proof of SWLimit Achievability 131


6.9.2 BDAC Decoder withWeighted Branching 132


6.10 Implementation of the Improved BDAC Codec 134


6.10.1 Encoder 134


Principle 134


Implementation 135


6.10.2 Decoder 135


Principle 135


Implementation 136


6.11 Experimental Results 138


Effect of Segment Size on Permutation Technique 139


Effect of Surviving–Path Number onWB Technique 139


Comparison with LDPC Codes 139


Application of PBDAC to Nonuniform Sources 140


6.12 Conclusion 141


7 Wyner–Ziv Code Design 143


7.1 Vector Quantization 143


7.2 Lattice Theory 146


7.2.1 What is a Lattice? 146


Examples 146


Dual Lattice 147


Integral Lattice 147


Lattice Quantization 148


7.2.2 What is a Good Lattice? 149


Packing Efficiency 149


Covering Efficiency 150


Normalized Second Moment 150


Kissing Number 150


Some Good Lattices 151


7.3 Nested Lattice Quantization 151


Encoding/decoding 152


Coset Binning 152


Quantization Loss and Binning Loss 153


SW Coded NLQ 154


7.3.1 Trellis Coded Quantization 154


7.3.2 Principle of TCQ 155


Generation of Codebooks 156


Generation of Trellis from Convolutional Codes 156


Mapping of Trellis Branches onto Sub–codebooks 157


Quantization 157


Example 158


7.4 WZ Coding Based on TCQ and LDPC Codes 159


7.4.1 Statistics of TCQ Indices 159


7.4.2 LLR of Trellis Bits 162


7.4.3 LLR of Codeword Bits 163


7.4.4 Minimum MSE Estimation 163


7.4.5 Rate Allocation of Bit–planes 164


7.4.6 Experimental Results 166


Part III Applications 167


8 Wyner–Ziv Video Coding 169


8.1 Basic Principle 169


8.2 Benefits of WZ Video Coding 170


8.3 Key Components of WZ Video Decoding 171


8.3.1 Side–information Preparation 171


Bidirectional Motion Compensation 172


8.3.2 Correlation Modeling 173


Exploiting Spatial Redundancy 174


8.3.3 Rate Controller 175


8.4 Other Notable Features of Miscellaneous WZ Video Coders 175


9 Correlation Estimation in DVC 177


9.1 Background to Correlation Parameter Estimation in DVC 177


9.1.1 Correlation Model inWZ Video Coding 177


9.1.2 Offline Correlation Estimation 178


Pixel Domain Offline Correlation Estimation 178


Transform Domain Offline Correlation Estimation 180


9.1.3 Online Correlation Estimation 181


Pixel Domain Online Correlation Estimation 182


Transform Domain Online Correlation Estimation 184


9.2 Recap of Belief Propagation and Particle Filter Algorithms 185


9.2.1 Belief Propagation Algorithm 185


9.2.2 Particle Filtering 186


9.3 Correlation Estimation in DVC with Particle Filtering 187


9.3.1 Factor Graph Construction 187


9.3.2 Correlation Estimation in DVC with Particle Filtering 190


9.3.3 Experimental Results 192


9.3.4 Conclusion 197


9.4 Low Complexity Correlation Estimation using Expectation Propagation 199


9.4.1 System Architecture 199


9.4.2 Factor Graph Construction 199


Joint Bit–plane SWCoding (Region II) 200


Correlation Parameter Tracking (Region I) 201


9.4.3 Message Passing on the Constructed Factor Graph 202


Expectation Propagation 203


9.4.4 Posterior Approximation of the Correlation Parameter using Expectation Propagation 204


Moment Matching 205


9.4.5 Experimental Results 206


9.4.6 Conclusion 211


10 DSC for Solar Image Compression 213


10.1 Background 213


10.2 RelatedWork 215


10.3 Distributed Multi–view Image Coding 217


10.4 Adaptive Joint Bit–plane WZ Decoding of Multi–view Images with Disparity Estimation 217


10.4.1 Joint Bit–planeWZ Decoding 217


10.4.2 Joint Bit–planeWZ Decoding with Disparity Estimation 219


10.4.3 Joint Bit–planeWZ Decoding with Correlation Estimation 220


10.5 Results and Discussion 221


10.6 Summary 224


11 Secure Distributed Image Coding 225


11.1 Background 225


11.2 System Architecture 227


11.2.1 Compression of Encrypted Data 228


11.2.2 Joint Decompression and Decryption Design 230


11.3 Practical Implementation Issues 233


11.4 Experimental Results 233


11.4.1 Experiment Setup 234


11.4.2 Security and Privacy Protection 235


11.4.3 Compression Performance 236


11.5 Discussion 239


12 Secure Biometric Authentication Using DSC 241


12.1 Background 241


12.2 RelatedWork 243


12.3 System Architecture 245


12.3.1 Feature Extraction 246


12.3.2 Feature Pre–encryption 248


12.3.3 SeDSC Encrypter/decrypter 248


12.3.4 Privacy–preserving Authentication 249


12.4 SeDSC Encrypter Design 249


12.4.1 Non–asymmetric SWCodes with Code Partitioning 250


12.4.2 Implementation of SeDSC Encrypter using IRA Codes 251


12.5 SeDSC Decrypter Design 252


12.6 Experiments 256


12.6.1 Dataset and Experimental Setup 256


12.6.2 Feature Length Selection 257


12.6.3 Authentication Accuracy 257


Authentication Performances on Small Feature Length (i.e., N = 100) 257


Performances on Large Feature Lengths (i.e., N ≥ 300) 258


12.6.4 Privacy and Security 259


12.6.5 Complexity Analysis 261


12.7 Discussion 261


A Basic Information Theory 263


A.1 Information Measures 263


A.1.1 Entropy 263


A.1.2 Relative Entropy 267


A.1.3 Mutual Information 268


A.1.4 Entropy Rate 269


A.2 Independence and Mutual Information 270


A.3 Venn Diagram Interpretation 273


A.4 Convexity and Jensen’s Inequality 274


A.5 Differential Entropy 277


A.5.1 Gaussian Random Variables 278


A.5.2 Entropy Power Inequality 278


A.6 Typicality 279


A.6.1 Jointly Typical Sequences 282


A.7 Packing Lemmas and Covering Lemmas 284


A.8 Shannon’s Source CodingTheorem 286


A.9 Lossy Source Coding—Rate–distortionTheorem 289


A.9.1 Rate–distortion Problem with Side Information 291


B Background on Channel Coding 293


B.1 Linear Block Codes 294


B.1.1 Syndrome Decoding of Block Codes 295


B.1.2 Hamming Codes, Packing Bound, and Perfect Codes 295


B.2 Convolutional Codes 297


B.2.1 Viterbi Decoding Algorithm 298


B.3 Shannon’s Channel CodingTheorem 301


B.3.1 Achievability Proof of the Channel CodingTheorem 303


B.3.2 Converse Proof of Channel CodingTheorem 305


B.4 Low–density Parity–check Codes 306


B.4.1 A Quick Summary of LDPC Codes 306


B.4.2 Belief Propagation Algorithm 307


B.4.3 LDPC Decoding using BP 312


B.4.4 IRA Codes 314


C Approximate Inference 319


C.1 Stochastic Approximation 319


C.1.1 Importance SamplingMethods 320


C.1.2 Markov Chain Monte Carlo 321


Markov Chains 321


Markov Chain Monte Carlo 321


C.2 Deterministic Approximation 322


C.2.1 Preliminaries 322


Exponential Family 322


Kullback–Leibler Divergence 323


Assumed–density Filtering 324


C.2.2 Expectation Propagation 325


Relationship with BP 326


C.2.3 Relationship with Other Variational Inference Methods 328


D Multivariate Gaussian Distribution 331


D.1 Introduction 331


D.2 Probability Density Function 331


D.3 Marginalization 332


D.4 Conditioning 333


D.5 Product of Gaussian pdfs 334


D.6 Division of Gaussian pdfs 337


D.7 Mixture of Gaussians 337


D.7.1 Reduce the Number of Components in Gaussian Mixtures 338


Which Components to Merge? 340


How to Merge Components? 341


D.8 Summary 342


Appendix: Matrix Equations 343


Bibliography 345


Index 357