Entropy and Information Theory
By: by Robert M. Gray
Publisher: Springer New York
Published: 1990
Place of publication: New York, NY
Language: eng
Format: [electronic resource] /
Number of pages: 332
ISBN-13: 9781475739848; 9781475739824
Subjects: Engineering; Engineering mathematics; Distribution (Probability theory)
Description: This book is devoted to the theory of probabilistic information measures and their application to coding theorems for information sources and noisy channels. The eventual goal is a general development of Shannon's mathematical theory of communication, but much of the space is devoted to the tools and methods required to prove the Shannon coding theorems. These tools form an area common to ergodic theory and information theory and comprise several quantitative notions of the information in random variables, random processes, and dynamical systems. Examples are entropy, mutual information, conditional entropy, conditional information, and discrimination or relative entropy, along with the limiting normalized versions of these quantities such as entropy rate and information rate. Much of the book is concerned with their properties, especially the long term asymptotic behavior of sample information and expected information. This is the only up-to-date treatment of traditional information theory emphasizing ergodic theory.
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Table of contents: title: Contents: Information Sources; title: Entropy and Information; title: The Entropy Ergodic Theorem; title: Information Rates I; title: Relative Entropy; title: Information Rates II; title: Relative Entropy Rates; title: Ergodic Theorems for Densities; title: Channels and Codes; title: Distortion; title: Source Coding Theorems; title: Coding for Noisy Channels; title: Bibliography; title: Index.