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Mathematical Foundations of Information Theory by Alexander I. Khinchin

Mathematical Foundations of Information Theory

by Alexander I. Khinchin
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Book cover type: Paperback
  • ISBN13: 9780486604343
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Dover Publications
  • Publisher Imprint: Dover Publications
  • Publication Date:
  • Pages: 128
  • Original Price: USD 10.95
  • Language: English
  • Edition: N/A
  • Item Weight: 146 grams
  • BISAC Subject(s): Philosophy & Social Aspects and General

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.

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