Stochastic Modelling and Applied Probability

By: H. Koga (Translator), Te Sun Han

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Hardcover | 8 October 2002

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Hardcover
564 Pages

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24.13 x 16.51 x 3.18

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This book opens a novel dimension in the 50 year history of mathematical theory of "information" since the birth of Shannon theory. First of all, it introduces, in place of the traditional notion of entropy and mutual information, the completely new and highly unconventional approach of "information-spectrum" as a basic but powerful tool for constructing the general theory of information. Reconstructing step-by-step all the essential major topics in information theory from the viewpoint of such an "information-spectrum", this comprehensive work provides an accessible introduction to the new type of mathematical theory of information that focuses mainly on general nonstationary and /or nonergodic sources and channels, in clear contrast with the traditional theories of information. This book is a new non-traditional theoretical reference for communication professionals and statisticians specializing in information theory.

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MATHEMATICAL REVIEWS

"This book nicely complements the existing literature on information and coding theory by concentrating on arbitrary nonstationary and/or nonergodic sources and channels with arbitrarily large alphabets. Even with such generality the authors have managed to successfully reach a highly unconventional but very fertile exposition rendering new insights into many problems."

"This book proposes a generalization of information theory in the sense of Shannon to a situation with sources and channels being possibly nonstationary and/or nonergodic. ... This book presents useful and important concepts in information theory arising from original ideas of the author ... ." (A. Akutowicz, Zentralblatt MATH, Vol. 1010, 2003)

"This book nicely complements the existing literature on information and coding theory by concentrating on arbitrary nonstationary and/or nonergodic sources and channels with arbitrarily large alphabets. Even with such generality the authors have managed to successfully reach a highly unconventional but very fertile exposition rendering new insights into many problems. The book establishes a unified general treatment for a collection of results ... . The book contains a considerable number of historical remarks together with a rather extensive list of references ... ." (Andrei Kelarev, Mathematical Reviews, 2003 i)

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Source Coding	p. 1
Source Coding: Fixed-Length Codes	p. 1
Source Coding: Variable-Length Codes	p. 8
Coding for General Sources: Fixed-Length Codes	p. 14
Fixed-Length Coding for Mixed Sources	p. 20
Strong Converse Theorem for Source Coding	p. 34
e-Source Coding	p. 38
Coding for General Sources: Variable-Length Codes	p. 43
Coding for General Source: Weak Variable-Length Codes	p. 51
Source Coding and Large Deviation: Decoding Error Probability	p. 63
Source Coding and Large Deviation: Probability of Correct Decoding	p. 85
Reliability Functions of the General Source with Variable-Length Coding	p. 96
Information Spectrum and Invariancy	p. 97
Random Number Generation	p. 103
Random Number Generation	p. 103
Resolvability and Intrinsic Randomness	p. 118
Strong Converse Theorem for Random Number Generation	p. 124
d-Random Number Generation	p. 128
Variable-Length Intrinsic Randomness	p. 141
Random Number Generation and Source Coding	p. 154
Channel Coding	p. 169
Channel Coding: Stationary Memoryless Channel	p. 169
Coding for General Channel	p. 176
Coding for Mixed Channels	p. 190
e-Channel Coding	p. 210
Strong Converse Theorem on Channel Coding	p. 218
Channel Capacity with Cost Constraint	p. 225
Strong Converse Property of Channel with Cost Constraint	p. 232
Joint Source-Channel Coding	p. 247
Separation Theorems of the Traditional Type	p. 263
Hypothesis Testing	p. 269
Hypothesis Testing	p. 269
e-Hypothesis Testing	p. 279
Strong Converse Theorem for Hypothesis Testing	p. 283
Hypothesis Testing and Large Deviation Probability of Testing Error	p. 286
Hypothesis Testing and Large Deviation: Probability of Correct Testing	p. 308
Generalized Hypothesis Testing	p. 319
Hypothesis Testing and Source Coding	p. 320
Rate-Distortion Theory	p. 325
Coding Subject to Distortion Criterion	p. 325
Rate-Distortion Theory for Stationary Memoryless Sources	p. 325
General Rate-Distortion Theory	p. 333
Rate-Distortion Function R_fm(D X)	p. 340
Rate-Distortion Function R_fa(D X)	p. 343
Rate-Distortion Function R_vm(D X)	p. 348
Rate-Distortion Function R_va(D X)	p. 357
Rate-Distortion for Stationary Memoryless Sources Revisited	p. 369
Rate-Distortion for Stationary Ergodic Sources	p. 376
Rate-Distortion Function for Mixed Sources	p. 380
Identification Code and Channel Resolvability	p. 395
Identification Code and Channel Resolvability	p. 395
Identification Coding	p. 396
Channel Resolvability	p. 404
Identification Capacity Theorem and Channel Resolvability Theorem	p. 413
Identification Capacity with Cost Constraint	p. 421
Channel Resolvability with Cost Constraint	p. 422
Identification Capacity and Resolvability of Continuous Input Channels	p. 425
Identification-Transmission Codes	p. 435
Multi-Terminal Information Theory	p. 453
What Is Multi-Terminal Information Theory?	p. 453
The Slepian-Wolf Source Coding System	p. 454
Slepian-Wolf Source Coding for Mixed Sources	p. 464
e-Source Coding for Slepian-Wolf Source Coding System	p. 471
Strong Converse Theorem for Slepian-Wolf Source Coding System	p. 477
Multiple-Access Channel Coding Systems	p. 481
General Capacity Region Theorem for Multiple-Access Channels	p. 483
Stationary Memoryless Multiple-Access Channels	p. 487
Mixed Multiple-Access Channels	p. 495
Proof of Theorem 7.7.1	p. 500
e-Coding for Multiple-Access Channel	p. 509
Strong Converse Theorem for Multiple-Access Channels	p. 513
Multiple-Access Channels with Cost Constraint	p. 520
References	p. 527
Index	p. 533
Table of Contents provided by Publisher. All Rights Reserved.

Stochastic Modelling and Applied Probability

At a Glance

Hardcover

Industry Reviews

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