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Mathematical Foundations of Information Theory

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Mathematical Foundations of Information Theory Cover

 

Synopses & Reviews

Publisher Comments:

The first comprehensive introduction to information theory, this text explores the work begun by Shannon and continued by McMillan, Feinstein, and Khinchin. Its rigorous treatment addresses the entropy concept in probability theory and fundamental theorems as well as ergodic sources, the martingale concept, anticipation and memory, and other subjects. 1957 edition. 

Synopsis:

First comprehensive introduction to information theory explores the work of Shannon, McMillan, Feinstein, and Khinchin. Topics include the entropy concept in probability theory, fundamental theorems, and other subjects. 1957 edition. 

Synopsis:

Comprehensive, rigorous introduction to work of Shannon, McMillan, Feinstein, and Khinchin. Translated by R. A. Silverman and M. D. Friedman.

Table of Contents

The Entropy Concept In Probability Theory

1. Entropy of Finite Schemes

2. The Uniqueness Theorem

3. Entropy of Markov chains

4. Fundamental Theorems

5. Application to Coding Theory

On the Fundamental Theorems of Information Theory

INTRODUCTION

CHAPTER I. Elementary Inequalities

  1. Two generalizations of Shannon's inequality

  2. Three inequalities of Feinstein

CHAPTER II. Ergodic Sources

  3. Concept of a source. Stationarity. Entropy

  4. Ergodic Sources

  5. The E property. McMillan's theorem.

  6. The martingale concept. Doob's theorem.

  7. Auxillary propositions

  8. Proof of McMillan's theorem.

CHAPTER III. Channels and the sources driving them

  9. Concept of channel. Noise. Stationarity. Anticipation and memory

  10. Connection of the channel to the source

  11. The ergodic case

CHAPTER IV. Feinstein's Fundamental Lemma

  12. Formulation of the problem

  13. Proof of the lemma

CHAPTER V. Shannon's Theorems

  14. Coding

  15. The first Shannon theorem

  16. The second Shannon theorem

CONCLUSION

REFERENCES

Product Details

ISBN:
9780486604343
Author:
Khinchin, Alexander I.
Author:
Khinchin, Aleksandr Iakovlevich
Author:
Khinchin, A. I.
Author:
Khinchin, A. Ya.
Author:
Khinchin, A. Ya
Author:
Mathematics
Publisher:
Dover Publications
Subject:
General
Subject:
Mathematics
Subject:
Statistics
Subject:
Philosophy & Social Aspects
Subject:
Probability
Subject:
Probabilities
Subject:
Information Theory
Subject:
General Mathematics
Subject:
Applied
Subject:
Science Reference-Philosophy of Science
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Publication Date:
19570631
Binding:
TRADE PAPER
Language:
English
Pages:
128
Dimensions:
8.5 x 5.38 in 0.34 lb

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Engineering » Communications » Information Theory
Reference » Science Reference » Philosophy of Science
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Mathematical Foundations of Information Theory New Trade Paper
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Product details 128 pages Dover Publications - English 9780486604343 Reviews:
"Synopsis" by ,
First comprehensive introduction to information theory explores the work of Shannon, McMillan, Feinstein, and Khinchin. Topics include the entropy concept in probability theory, fundamental theorems, and other subjects. 1957 edition. 
"Synopsis" by ,
Comprehensive, rigorous introduction to work of Shannon, McMillan, Feinstein, and Khinchin. Translated by R. A. Silverman and M. D. Friedman.

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