Generalized Mutual Information
Information Theory
2019-07-15 v1 math.IT
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.
Cite
@article{arxiv.1907.05484,
title = {Generalized Mutual Information},
author = {Zhiyi Zhang},
journal= {arXiv preprint arXiv:1907.05484},
year = {2019}
}