Proving Information Inequalities by Gaussian Elimination

TL;DR

This paper introduces a symbolic computation method for proving information inequalities under linear constraints, avoiding linear programming and its numerical errors, resulting in more efficient proofs.

Contribution

The paper presents a novel symbolic computation approach that completely eliminates the need for linear programming in proving information inequalities.

Findings

The method avoids numerical errors associated with LP-based algorithms.

It is more computationally efficient than existing LP-based methods.

Successfully proves information inequalities without linear programming.

Abstract

The proof of information inequalities and identities under linear constraints on the information measures is an important problem in information theory. For this purpose, ITIP and other variant algorithms have been developed and implemented, which are all based on solving a linear program (LP). In this paper, we develop a method with symbolic computation. Compared with the known methods, our approach can completely avoids the use of linear programming which may cause numerical errors. Our procedures are also more efficient computationally.