Generalized Mutual Information

Zhiyi Zhang

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arXiv · 1907.05484

Generalized Mutual Information

Zhiyi Zhang

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Abstract

Mutual information is one of the essential building blocks of information theory. Yet, it is only finitely defined for distributions with fast decaying tails on a countable joint alphabet of two random elements. The unboundedness of mutual information over the general class of all distributions on a joint alphabet prevents its potential utility to be fully realized. This is in fact a void in the foundation of information theory that needs to be filled. This article proposes a family of generalized mutual information all of whose members 1) are finitely defined for each and every distribution of two random elements on a joint countable alphabet, except the one by Shannon, and 2) enjoy all utilities of a finite Shannon's mutual information.

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Zhiyi Zhang. 2019-07-11. Generalized Mutual Information. https://arxiv.org/abs/1907.05484

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