Mathematical Foundations of Information Theory

Overview

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. 

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Mathematical Foundations of Information Theory

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Overview

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. 

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Product Details

  • ISBN-13: 9780486604343
  • Publisher: Dover Publications
  • Publication date: 6/1/1957
  • Series: Dover Books on Mathematics Series
  • Pages: 128
  • Sales rank: 499,793
  • Product dimensions: 5.74 (w) x 7.86 (h) x 0.30 (d)

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
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