Average Entropy Functions

TL;DR

This paper introduces a new approach to analyze entropy functions by mapping the complex set to a simpler n-dimensional region using averaging, which can be characterized by Shannon-type inequalities.

Contribution

It proposes a novel averaging method to simplify the characterization of entropy functions, reducing the problem to Shannon-type inequalities.

Findings

The mapping to Phi*n simplifies the entropy function analysis.

Phi*n can be fully characterized by Shannon-type inequalities.

The approach offers new insights into the structure of entropy functions.

Abstract

The closure of the set of entropy functions associated with n discrete variables, Gammar*n, is a convex cone in (2n-1)- dimensional space, but its full characterization remains an open problem. In this paper, we map Gammar*n to an n-dimensional region Phi*n by averaging the joint entropies with the same number of variables, and show that the simpler Phi*n can be characterized solely by the Shannon-type information inequalities