Mathematical Foundations of Information Theory (Dover Books on Mathematics)

Khinchin, A. Ya.

ISBN 10: 0486604349 / ISBN 13: 9780486604343

Published by Dover Publications Inc., New York, 2003

About this Item

VG in glossy illustrated wrappers. Paperbound. Covers lightly shelf-rubbed, creased. Spine slightly cocked, tight, uncreased. Inside front cover has name of prior owner in ink.Text sunned, clean. No marks.

Seller Inventory # 14909

Bibliographic Details

• Title: Mathematical Foundations of Information Theory (Dover Books on Mathematics)
• Publisher: Dover Publications Inc., New York
• Publication Date: 2003
• Language: English
• ISBN 10: 0486604349
• ISBN 13: 9780486604343
• Binding: Soft cover
• Condition: Very Good

About this title

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.