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Mathematical Foundations of - Paperback, by Khinchin A. Ya. - Very Good

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Book Title
Mathematical Foundations of Information Theory (Dover Books on Ma
ISBN
9780486604343
Kategorie

Über dieses Produkt

Product Identifiers

Publisher
Dover Publications, Incorporated
ISBN-10
0486604349
ISBN-13
9780486604343
eBay Product ID (ePID)
102907202

Product Key Features

Number of Pages
128 Pages
Language
English
Publication Name
Mathematical Foundations of Information Theory
Publication Year
1957
Subject
Information Theory, Probability & Statistics / General, Electrical, Applied
Type
Textbook
Subject Area
Mathematics, Computers, Technology & Engineering
Author
A. I. Khinchin
Series
Dover Books on Mathematics Ser.
Format
Trade Paperback

Dimensions

Item Weight
5.6 Oz
Item Length
8.5 in
Item Width
5.5 in

Additional Product Features

Intended Audience
College Audience
Table Of Content
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
Synopsis
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., 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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