Information Technology

Transmission, Processing and Storage

By: Raymond W. Yeung

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Hardcover | 16 June 2006

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440 Pages

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23.5 x 16.51 x 3.18

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Incepted halfway through the 20th century, information theory is a classical yet modern field which is more vibrant than ever before. In particular, there have been a number of major research results on the foundation of the theory during the 1990s. These results enable information theory to be understood and explored in a way which has not been possible before, and they open new dimensions in the theory. In short, the depth of information theory is far beyond what we used to know. This book is an integration of the most fundamental topics in information theory plus a few selected advanced topics. Results given include the theory of I-Me asure, Shannon-type and non-Shannon-type information inequalities, and network coding theory. Some important implications of information theory in probability theory and group theory are also explained in this book. ITIP, the software package that comes with the book, is the only software package of its kind which can prove all Shannon-type information inequalities.

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Published: 30th October 2012

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The Science of Information	p. 1
Information Measures	p. 5
Independence and Markov Chains	p. 5
Shannon's Information Measures	p. 10
Continuity of Shannon's Information Measures	p. 16
Chain Rules	p. 17
Informational Divergence	p. 19
The Basic Inequalities	p. 23
Some Useful Information Inequalities	p. 25
Fano's Inequality	p. 28
Entropy Rate of Stationary Source	p. 32
Problems	p. 36
Historical Notes	p. 39
Zero-Error Data Compression	p. 41
The Entropy Bound	p. 42
Prefix Codes	p. 45
Definition and Existence	p. 45
Huffman Codes	p. 48
Redundancy of Prefix Codes	p. 54
Problems	p. 58
Historical Notes	p. 59
Weak Typicality	p. 61
The Weak AEP	p. 61
The Source Coding Theorem	p. 64
Efficient Source Coding	p. 66
The Shannon-McMillan-Breiman Theorem	p. 68
Problems	p. 70
Historical Notes	p. 71
Strong Typicality	p. 73
Strong AEP	p. 73
Strong Typicality Versus Weak Typicality	p. 81
Joint Typicality	p. 82
An Interpretation of the Basic Inequalities	p. 92
Problems	p. 93
Historical Notes	p. 94
The I-Measure	p. 95
Preliminaries	p. 96
The I-Measure for Two Random Variables	p. 97
Construction of the I-Measure [mu]*	p. 100
[mu]* Can be Negative	p. 103
Information Diagrams	p. 105
Examples of Applications	p. 112
A Variation of the Inclusion-Exclusion Formula	p. 119
Problems	p. 121
Historical Notes	p. 124
Markov Structures	p. 125
Conditional Mutual Independence	p. 126
Full Conditional Mutual Independence	p. 135
Markov Random Field	p. 140
Markov Chain	p. 143
Problems	p. 146
Historical Notes	p. 147
Channel Capacity	p. 149
Discrete Memoryless Channels	p. 153
The Channel Coding Theorem	p. 158
The Converse	p. 160
Achievability of the Channel Capacity	p. 166
A Discussion	p. 171
Feedback Capacity	p. 174
Separation of Source and Channel Coding	p. 180
Problems	p. 183
Historical Notes	p. 186
Rate Distortion Theory	p. 187
Single-Letter Distortion Measures	p. 188
The Rate-Distortion Function R(D)	p. 191
The Rate-Distortion Theorem	p. 196
The Converse	p. 204
Achievability of R[subscript I](D)	p. 206
Problems	p. 212
Historical Notes	p. 214
The Blahut-Arimoto Algorithms	p. 215
Alternating Optimization	p. 216
The Algorithms	p. 218
Channel Capacity	p. 218
The Rate-Distortion Function	p. 223
Convergence	p. 226
A Sufficient Condition	p. 227
Convergence to the Channel Capacity	p. 230
Problems	p. 231
Historical Notes	p. 231
Single-Source Network Coding	p. 233
A Point-to-Point Network	p. 234
What is Network Coding?	p. 236
A Network Code	p. 240
The Max-Flow Bound	p. 242
Achievability of the Max-Flow Bound	p. 245
Acyclic Networks	p. 246
Cyclic Networks	p. 251
Problems	p. 259
Historical Notes	p. 262
Information Inequalities	p. 263
The Region [Gamma]*[subscript n]	p. 265
Information Expressions in Canonical Form	p. 267
A Geometrical Framework	p. 269
Unconstrained Inequalities	p. 269
Constrained Inequalities	p. 270
Constrained Identities	p. 272
Equivalence of Constrained Inequalities	p. 273
The Implication Problem of Conditional Independence	p. 276
Problems	p. 277
Historical Notes	p. 278
Shannon-Type Inequalities	p. 279
The Elemental Inequalities	p. 279
A Linear Programming Approach	p. 281
Unconstrained Inequalities	p. 283
Constrained Inequalities and Identities	p. 284
A Duality	p. 285
Machine Proving--ITIP	p. 287
Tackling the Implication Problem	p. 291
Minimality of the Elemental Inequalities	p. 293
The Basic Inequalities and the Polymatroidal Axioms	p. 297
Problems	p. 298
Historical Notes	p. 300
Beyond Shannon-Type Inequalities	p. 301
Characterizations of [Gamma][subscript 2], [Gamma][subscript 3], and [Gamma]*[subscript n]	p. 302
A Non-Shannon-Type Unconstrained Inequality	p. 310
A Non-Shannon-Type Constrained Inequality	p. 315
Applications	p. 321
Problems	p. 324
Historical Notes	p. 325
Multi-Source Network Coding	p. 327
Two Characteristics	p. 328
The Max-Flow Bounds	p. 328
Superposition Coding	p. 330
Examples of Application	p. 335
Multilevel Diversity Coding	p. 335
Satellite Communication Network	p. 336
A Network Code for Acyclic Networks	p. 337
An Inner Bound	p. 340
An Outer Bound	p. 342
The LP Bound and Its Tightness	p. 346
Achievability of R[subscript in]	p. 350
Approximation of Random Variables with Infinite Alphabets	p. 360
Problems	p. 361
Historical Notes	p. 364
Entropy and Groups	p. 365
Group Preliminaries	p. 366
Group-Characterizable Entropy Functions	p. 372
A Group Characterization of [Gamma]*[subscript n]	p. 377
Information Inequalities and Group Inequalities	p. 380
Problems	p. 384
Historical Notes	p. 387
Bibliography	p. 389
Index	p. 403
Table of Contents provided by Syndetics. All Rights Reserved.

Information Technology

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