Group characterizable entropy functions

TL;DR

This paper explores entropy functions derived from groups and subgroups, revealing their information-theoretic properties and providing a method to establish outer bounds for these functions.

Contribution

It introduces a novel approach linking group theory with entropy functions and proposes an extension method to bound these functions.

Findings

Group-induced entropy functions have corresponding group-theoretic interpretations.

Many information-theoretic properties are mirrored in the group-theoretic context.

An extension method for deriving outer bounds on group-induced entropy functions.

Abstract

This paper studies properties of entropy functions that are induced by groups and subgroups. We showed that many information theoretic properties of those group induced entropy functions also have corresponding group theoretic interpretations. Then we propose an extension method to find outer bound for these group induced entropy functions.