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Mathematical Foundations of Information Theoryby Alexander I. Khinchin
Synopses & ReviewsPublisher 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 ContentsThe 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 What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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