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Introduction 1

Problems 12

Notes 13

Part one：Information theory 17

1 Entropy and mutual information 17

1.1 Discrete random variables 17

1.2 Discrete random vectors 33

1.3 Nondiscrete random variables and vectors 37

Problems 44

Notes 49

2 Discrete memoryless channels and their capacity-cost functions 50

2.1 The capacity-cost function 50

2.2 The channel coding theorem 58

Problems 68

Notes 73

3 Discrete memoryless sources and their rate-distortion functions 75

3.1 The rate-distortion function 75

3.2 The source coding theorem 84

Problems 91

Notes 93

4 The Gaussian channel and source 95

4.1 The Gaussian channel 95

4.2 The Gaussian source 99

Problems 105

Notes 110

5 The source-channel coding theorem 112

Problems 120

Notes 122

6 Survey of advanced topics for part one 123

6.1 Introduction 123

6.2 The channel coding theorem 123

6.3 The source coding theorem 131

Part two：Coding theory 139

7 Linear codes 139

7.1 Introduction：The generator and parity-check matrices 139

7.2 Syndrome decoding on q-ary symmetric channels 143

7.3 Hamming geometry and code performance 146

7.4 Hamming codes 148

7.5 Syndrome decoding on general q-ary channels 149

7.6 Weight enumerators and the MacWilliams identities 153

Problems 158

Notes 165

8 Cyclic codes 167

8.1 Introduction 167

8.2 Shift-register encoders for cyclic codes 181

8.3 Cyclic Hamming codes 195

8.4 Burst-error correction 199

8.5 Decoding burst-error correcting cyclic codes 215

Problems 220

Notes 228

9 BCH，Reed-Solomon，and related codes 230

9.1 Introduction 230

9.2 BCH codes as cyclic codes 234

9.3 Decoding BCH codes，Part one：the key equation 236

9.4 Euclid’s algorithm for polynomials 244

9.5 Decoding BCH codes，Part two：the algorithms 249

9.6 Reed-Solomon codes 253

9.7 Decoding when erasures are present 266

9.8 The（23，12）Golay code 277

Problems 282

Notes 292

10 Convolutional codes 293

10.1 Introduction 293

10.2 State diagrams，trellises，and Viterbi decoding 300

10.3 Path enumerators and error bounds 307

10.4 Sequential decoding 313

Problems 322

Notes 329

11 Variable-length source coding 330

11.1 Introduction 330

11.2 Uniquely decodable variable-length codes 331

11.3 Matching codes to sources 334

11.4 The construction of optimal UD codes（Huffman’s algorithm） 337

Problems 342

Notes 345

12 Survey of advanced topics for Part two 347

12.1 Introduction 347

12.2 Block codes 347

12.3 Convolutional codes 357

12.4 A comparison of block and convolutional codes 359

12.5 Source codes 363

Appendices 366

A Probability theory 366

B Convex functions and Jensen’s inequality 370

C Finite fields 375

D Path enumeration in directed graphs 380

References 384

1 General reference textbooks 384

2 An annotated bibliography of the theory of information and coding 384

3 Original papers cited in the text 386

Index of Theorems 388

Index 390