Mathematical Foundations of Information Theory

✍ Scribed by A. Ya. Khinchin

• Publisher: Dover Publications
• Year: 1957
• Tongue: English
• Leaves: 125
• Series: Dover Books on Mathematics
• Edition: 1st Dover
• Category: Library

✦ 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.

✦ Subjects

Information Theory;Computer Science;Computers & Technology;Electrical & Electronics;Circuits;Digital Design;Electric Machinery & Motors;Electronics;Fiber Optics;Networks;Superconductivity;Engineering;Engineering & Transportation;History & Philosophy;Science & Math;Applied;Biomathematics;Differential Equations;Game Theory;Graph Theory;Linear Programming;Probability & Statistics;Statistics;Stochastic Modeling;Vector Analysis;Mathematics;Science & Math