Distributed Source Coding
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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
