Mathematical Foundations of Information Theory (eBook)

A. Ya. Khinchin (Autor)

eBook Download: EPUB

2013
128 Seiten
Dover Publications (Verlag)
978-0-486-31844-8 (ISBN)

Infos

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.

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The first comprehensive introduction to information theory, this book places the work begun by Shannon and continued by McMillan, Feinstein, and Khinchin on a rigorous mathematical basis. For the first time, mathematicians, statisticians, physicists, cyberneticists, and communications engineers are offered a lucid, comprehensive introduction to this rapidly growing field.In his first paper, Dr. Khinchin develops the concept of entropy in probability theory as a measure of uncertainty of a finite “scheme,” and discusses a simple application to coding theory. The second paper investigates the restrictions previously placed on the study of sources, channels, and codes and attempts “to give a complete, detailed proof of both … Shannon theorems, assuming any ergodic source and any stationary channel with a finite memory.”Partial Contents: I. The Entropy Concept in Probability Theory — Entropy of Finite Schemes. The Uniqueness Theorem. Entropy of Markov chains. Application to Coding Theory. II. On the Fundamental Theorems of Information Theory — Two generalizations of Shannon’s inequality. Three inequalities of Feinstein. Concept of a source. Stationarity. Entropy. Ergodic sources. The E property. The martingale concept. Noise. Anticipation and memory. Connection of the channel to the source. Feinstein’s Fundamental Lemma. Coding. The first Shannon theorem. The second Shannon theorem.

Inhalt

The Entropy Concept In Probability Theory1. Entropy of Finite Schemes2. The Uniqueness Theorem3. Entropy of Markov chains4. Fundamental Theorems5. Application to Coding TheoryOn the Fundamental Theorems of Information TheoryINTRODUCTIONCHAPTER I. Elementary Inequalities 1. Two generalizations of Shannon's inequality 2. Three inequalities of FeinsteinCHAPTER 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 caseCHAPTER IV. Feinstein's Fundamental Lemma 12. Formulation of the problem 13. Proof of the lemmaCHAPTER V. Shannon's Theorems 14. Coding 15. The first Shannon theorem 16. The second Shannon theoremCONCLUSIONREFERENCES

Produkt-Details

• Erscheint lt. Verlag: 9.4.2013
• Reihe/Serie: Dover Books on Mathematics
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik
• ISBN-10: 0-486-31844-3 / 0486318443
• ISBN-13: 978-0-486-31844-8 / 9780486318448