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  信息论基础
  ￥78.21元
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  信息论基础
  ￥22.91元

　　本书作者现为香港中文大学网络编码研究所主任，是网络编码理论的提出者之一。本书原版自2002年出版以来，被哥伦比亚大学、康奈尔大学、麻省理工学院、斯坦福大学 等美国著名学府所采用，是信息理论方面的重要教材。本书首先介绍了信息论的经典内容，然后全面详细地论述了I-度量、网络编码、Shannon型与非Shannon型信息不等式等理论，以及熵函数与群论之间的关系。书中配有大量的实例、插图和习题，适合作为通信、电子信息、计算机等专业的高年级本科生和研究生的教材，也可供相关领域的科研人员参考。
　　Reprint from English language edition: A First Course in Information Theory by Raymond W. Yeung. Copyright2002, Springer US.
　　Springer US is a part of Springer Science+Business Media. All Rights Reserved.
　　This reprint has been authorized by Springer Science & Business Media for distribution in China Mainland only and not for export therefrom.本影印版由施普林格科学商业媒体授权仅在中国大陆境内发行，不得出口。

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• Contents
  1. THE SCIENCE OF INFORMATION 1
  2. INFORMATION MEASURES 5
  2.1 Independence and Markov Chains 5
  2.2 Shannon’s Information Measures 10
  2.3 Continuity of Shannon’s Information Measures 16
  2.4 Chain Rules 17
  2.5 Informational Divergence 19
  2.6 The Basic Inequalities 23
  2.7 Some Useful Information Inequalities 25
  2.8 Fano’s Inequality 28
  2.9 Entropy Rate of Stationary Source 32
  Problems 36
  Historical Notes 39
  3. ZERO-ERROR DATA COMPRESSION 41
  3.1 The Entropy Bound 42
  3.2 Prefix Codes 45
  3.2.1 Definition and Existence 45
  3.2.2 Huffman Codes 48
  3.3 Redundancy of Prefix Codes 54
  Problems 58
  Historical Notes 59
  4. WEAK TYPICALITY 61
  4.1 The Weak AEP 61
  4.2 The Source Coding Theorem 64
  4.3 Efficient Source Coding 66
  4.4 The Shannon-McMillan-Breiman Theorem 68
  Problems 70
  Historical Notes 71
  STRONG TYPICALITY 73
  5.1 Strong AEP 73
  5.2 Strong Typicality Versus Weak Typicality 81
  5.3 Joint Typicality 82
  5.4 An Interpretation of the Basic Inequalities 92
  Problems 93
  Historical Notes 94
  THE I-MEASURE 95
  6.1 Preliminaries 96
  6.2 The I-Measure for Two Random Variables 97
  6.3 Construction of the /-Measure u* 100
  6.4 u* Can be Negative 103
  6.5 Information Diagrams 105
  6.6 Examples of Applications 112
  Appendix 6. A: A Variation of the Inclusion-Exclusion Formula 119
  Problems 121
  Historical Notes 124
  MARKOV STRUCTURES 125
  7.1 Conditional Mutual Independence 126
  7.2 Full Conditional Mutual Independence 135
  7.3 Markov Random Field 140
  7.4 Markov Chain 143
  Problems 146
  Historical Notes 147
  CHANNEL CAPACITY 149
  8.1 Discrete Memoryless Channels 153
  8.2 The Channel Coding Theorem 158
  8.3 The Converse 160
  8.4 Achievability of the Channel Capacity 166
  8.5 A Discussion 171
  8.6 Feedback Capacity 174
  8.7 Separation of Source and Channel Coding 180
  Problems 183
  Historical Notes 186
  9. RATE-DISTORTION THEORY 187
  9.1 Single-Letter Distortion Measures 188
  9.2 The Rate-Distortion Function R(D) 191
  9.3 The Rate-Distortion Theorem 196
  9.4 The Converse 204
  9.5 Achievability of Ri(D) 206
  Problems 212
  Historical Notes 214
  10. THE BLAHUT-ARIMOTO ALGORITHMS 215
  10.1 Alternating Optimization 216
  10.2 The Algorithms 218
  10.2.1 Channel Capacity 218
  10.2.2 The Rate-Distortion Function 223
  10.3 Convergence 226
  10.3.1 A Sufficient Condition 227
  10.3.2 Convergence to the Channel Capacity 230
  Problems 231
  Historical Notes 231
  11. SINGLE-SOURCE NETWORK CODING 233
  11.1 A Foint-to-Point Network 234
  11.2 What is Network Coding? 236
  11.3 A Network Code 240
  11.4 The Max-Flow Bound 242
  11.5 Achievability of the Max-Flow Bound 245
  11.5.1 Acyclic Networks 246
  11.5.2 Cyclic Networks 251
  Problems 259
  Historical Notes 262
  12. INFORMATION INEQUALITIES 263
  12.1 The Region T*n 265
  12.2 Information Expressions in Canonical Form 267
  12.3 A Geometrical Framework 269
  12.3.1 Unconstrained Inequalities 269
  12.3.2 Constrained Inequalities 270
  12.3.3 Constrained Identities 272
  12.4 Equivalence of Constrained Inequalities 273
  12.5 The Implication Problem of Conditional Independence 276
  Problems 277
  Historical Notes 278
  13. SHANNON-TYPE INEQUALITIES 279
  13.1 The Elemental Inequalities 279
  13.2 A Linear Programming Approach 281
  13.2.1 Unconstrained Inequalities 283
  13.2.2 Constrained Inequalities and Identities 284
  13.3 A Duality 285
  13.4 Machine Proving - ITIP 287
  13.5 Tackling the Implication Problem 291
  13.6 Minimality of the Elemental Inequalities 293
  Appendix 13.A: The Basic Inequalities and the Polymatroidal Axioms 297
  Problems 298
  Historical Notes 300
  14. BEYOND SHANNON-TYPE INEQUALITIES 301
  14.1 Characterizations of r^, and r* 302
  14.2 A Non-Shannon-Type Unconstrained Inequality 310
  14.3 A Non-Shannon-Type Constrained Inequality 315
  14.4 Applications 321
  Problems 324
  Historical Notes 325
  15. MULTI-SOURCE NETWORK CODING 327
  15.1 Two Characteristics 328
  15.1.1 The Max-Flow Bounds 328
  15.1.2 Superposition Coding 330
  15.2 Examples of Application 335
  15.2.1 Multilevel Diversity Coding 335
  15.2.2 Satellite Communication Network 336
  15.3 A Network Code for Acyclic Networks 337
  15.4 An Inner Bound 340
  15.5 An Outer Bound 342
  15.6 The LP Bound and Its Tightness 346
  15.7 Achievability of Rin 350
  Appendix 15.A: Approximation of Random Variables with Infinite Alphabets 360
  Problems 361
  Historical Notes 364
  16. ENTROPY AND GROUPS 365
  16.1 Group Preliminaries 366
  16.2 Group-Characterizable Entropy Functions 372
  16.3 A Group Characterization of * 377
  16.4 Information Inequalities and Group Inequalities 380
  Problems 384
  Historical Notes 387
  Bibliography 389
  Index 403