Communications, Information and Network Security pp 333-359 | Cite as

# On Entropy, Information Inequalities, and Groups

## Abstract

There has been significant progress in the study of entropy functions and information inequalities in the past 10 years. The set-theoretic structure of Shannon’s information measures has been established, and machineproving of most information inequalities known to date (Shannon-type inequalities) has become possible. Most importantly, the recent discovery of a few so-called non-Shannon-type inequalities reveals the existence of information inequalities which cannot be proved by techniques known during the first 50 years of information theory. In this expository paper, the essence of this fundamental subject is explained, a number of applications of the results are given, and their implications in information theory, probability theory, and group theory are discussed.

## Keywords

Mutual Information Conditional Independence Markov Random Field Network Security Entropy Function## Preview

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