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Information Theory and Network Codingpdf电子书版本下载
- Raymond W. Yeung 著
- 出版社： Springer US
- ISBN：387792333
- 出版时间：2008
- 标注页数：582页
- 文件大小：58MB
- 文件页数：605页
- 主题词：
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图书目录
1 The Science of Information 1
Part Ⅰ Components of Information Theory 7
2 Information Measures 7
2.1 Independence and Markov Chains 7
2.2 Shannon’s Information Measures 12
2.3 Continuity of Shannon’s Information Measures for Fixed Finite Alphabets 18
2.4 Chain Rules 21
2.5 Informational Divergence 23
2.6 The Basic Inequalities 26
2.7 Some Useful Information Inequalities 28
2.8 Fano’sInequality 32
2.9 Maximum Entropy Distributions 36
2.10 Entropy Rate of a Stationary Source 38
Appendix 2.A：Approximation of Random Variables with Countably Infinite Alphabets by Truncation 41
Chapter Summary 43
Problems 45
Historical Notes 50
3 The I-Measure 51
3.1 Preliminaries 52
3.2 The I-Measure for Two Random Variables 53
3.3 Construction of the I-Measure μ 55
3.4 μ* Can Be Negative 59
3.5 Information Diagrams 61
3.6 Examples of Applications 67
Appendix 3.A：A Variation of the Inclusion-Exclusion Formula 74
Chapter Summary 76
Problems 78
Historical Notes 80
4 Zero-Error Data Compression 81
4.1 The Entropy Bound 81
4.2 Prefix Codes 86
4.2.1 Definition and Existence 86
4.2.2 Huffman Codes 88
4.3 Redundancy of Prefix Codes 93
Chapter Summary 97
Problems 98
Historical Notes 99
5 Weak Typicality 101
5.1 The Weak AEP 101
5.2 The Source Coding Theorem 104
5.3 Efficient Source Coding 106
5.4 The Shannon-McMillan-Breiman Theorem 107
Chapter Summary 109
Problems 110
Historical Notes 112
6 Strong Typicality 113
6.1 Strong AEP 113
6.2 Strong Typicality Versus Weak Typicality 121
6.3 Joint Typicality 122
6.4 An Interpretation of the Basic Inequalities 131
Chapter Summary 131
Problems 132
Historical Notes 135
7 Discrete Memoryless Channels 137
7.1 Definition and Capacity 141
7.2 The Channel Coding Theorem 149
7.3 The Converse 152
7.4 Achievability 157
7.5 A Discussion 164
7.6 Feedback Capacity 167
7.7 Separation of Source and Channel Coding 172
Chapter Summary 175
Problems 176
Historical Notes 181
8 Rate-Distortion Theory 183
8.1 Single-Letter Distortion Measures 184
8.2 The Rate-Distortion Function R（D） 187
8.3 The Rate-Distortion Theorem 192
8.4 The Converse 200
8.5 Achievability of RI （D） 202
Chapter Summary 207
Problems 208
Historical Notes 209
9 The Blahut-Arimoto Algorithms 211
9.1 Alternating Optimization 212
9.2 The Algorithms 214
9.2.1 Channel Capacity 214
9.2.2 The Rate-Distortion Function 219
9.3 Convergence 222
9.3.1 A Sufficient Condition 222
9.3.2 Convergence to the Channel Capacity 225
Chapter Summary 226
Problems 227
Historical Notes 228
10 Differential Entropy 229
10.1 Preliminaries 231
10.2 Definition 235
10.3 Joint Differential Entropy，Conditional （Differential） Entropy，and Mutual Information 238
10.4 The AEP for Continuous Random Variables 245
10.5 Informational Divergence 248
10.6 Maximum Differential Entropy Distributions 249
Chapter Summary 252
Problems 255
Historical Notes 256
11 Continuous-Valued Channels 257
11.1 Discrete-Time Channels 257
11.2 The Channel Coding Theorem 260
11.3 Proof of the Channel Coding Theorem 262
11.3.1 The Converse 262
11.3.2 Achievability 265
11.4 Memoryless Gaussian Channels 270
11.5 Parallel Gaussian Channels 272
11.6 Correlated Gaussian Channels 278
11.7 The Bandlimited White Gaussian Channel 280
11.8 The Bandlimited Colored Gaussian Channel 287
11.9 Zero-Mean Gaussian Noise Is the Worst Additive Noise 290
Chapter Summary 294
Problems 296
Historical Notes 297
12 Markov Structures 299
12.1 Conditional Mutual Independence 300
12.2 Full Conditional Mutual Independence 309
12.3 Markov Random Field 314
12.4 Markov Chain 317
Chapter Summary 319
Problems 320
Historical Notes 321
13 Information Inequalities 323
13.1 The Region Γ*n 325
13.2 Information Expressions in Canonical Form 326
13.3 A Geometrical Framework 329
13.3.1 Unconstrained Inequalities 329
13.3.2 Constrained Inequalities 330
13.3.3 Constrained Identities 332
13.4 Equivalence of Constrained Inequalities 333
13.5 The Implication Problem of Conditional Independence 336
Chapter Summary 337
Problems 338
Historical Notes 338
14 Shannon-Type Inequalities 339
14.1 The Elemental Inequalities 339
14.2 A Linear Programming Approach 341
14.2.1 Unconstrained Inequalities 343
14.2.2 Constrained Inequalities and Identities 344
14.3 A Duality 345
14.4 Machine Proving - ITIP 347
14.5 Tackling the Implication Problem 351
14.6 Minimality of the Elemental Inequalities 353
Appendix 14.A：The Basic Inequalities and the Polymatroidal Axioms 356
Chapter Summary 357
Problems 358
Historical Notes 360
15 Beyond Shannon-Type Inequalities 361
15.1 Characterizations of Γ*2，Γ*3，and Γ*n 361
15.2 A Non-Shannon-Type Unconstrained Inequality 369
15.3 A Non-Shannon-Type Constrained Inequality 374
15.4 Applications 380
Chapter Summary 383
Problems 383
Historical Notes 385
16 Entropy and Groups 387
16.1 Group Preliminaries 388
16.2 Group-Characterizable Entropy Functions 393
16.3 A Group Characterization of Γn 398
16.4 Information Inequalities and Group Inequalities 401
Chapter Summary 405
Problems 406
Historical Notes 408
Part Ⅱ Fundamentals of Network Coding 411
17 Introduction 411
17.1 The Butterfly Network 412
17.2 Wireless and Satellite Communications 415
17.3 Source Separation 417
Chapter Summary 418
Problems 418
Historical Notes 419
18 The Max-Flow Bound 421
18.1 Point-to-Point Communication Networks 421
18.2 Examples Achieving the Max-Flow Bound 424
18.3 A Class of Network Codes 427
18.4 Proof of the Max-Flow Bound 429
Chapter Summary 431
Problems 431
Historical Notes 434
19 Single-Source Linear Network Coding：Acyclic Networks 435
19.1 Acyclic Networks 436
19.2 Linear Network Codes 437
19.3 Desirable Properties of a Linear Network Code 443
19.3.1 Transformation of a Linear Network Code 447
19.3.2 Implementation of a Linear Network Code 448
19.4 Existence and Construction 449
19.5 Generic Network Codes 460
19.6 Static Network Codes 468
19.7 Random Network Coding：A Case Study 473
19.7.1 How the System Works 474
19.7.2 Model and Analysis 475
Chapter Summary 478
Problems 479
Historical Notes 482
20 Single-Source Linear Network Coding：Cyclic Networks 485
20.1 Delay-Free Cyclic Networks 485
20.2 Convolutional Network Codes 488
20.3 Decoding of Convolutional Network Codes 498
Chapter Summary 503
Problems 503
Historical Notes 504
21 Multi-source Network Coding 505
21.1 The Max-Flow Bounds 505
21.2 Examples of Application 508
21.2.1 Multilevel Diversity Coding 508
21.2.2 Satellite Communication Network 510
21.3 A Network Code for Acyclic Networks 511
21.4 The Achievable Information Rate Region 512
21.5 Explicit Inner and Outer Bounds 515
21.6 The Converse 516
21.7 Achievability 521
21.7.1 Random Code Construction 524
21.7.2 Performance Analysis 527
Chapter Summary 536
Problems 537
Historical Notes 539
Bibliography 541
Index 561
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