Fourier-Motzkin Elimination Software for Information Theoretic Inequalities

TL;DR

This paper introduces MATLAB software that performs Fourier-Motzkin elimination for information theory inequalities, efficiently removing redundant constraints using Shannon-type inequalities to simplify rate region analysis.

Contribution

It presents an open-source MATLAB tool that automates FME and incorporates Shannon-type inequalities to eliminate redundant constraints in information theoretic problems.

Findings

Software effectively simplifies rate regions by removing inactive constraints.

Incorporating Shannon-type inequalities improves the accuracy of constraint elimination.

The tool demonstrates practical utility in information theory problem-solving.

Abstract

We provide open-source software implemented in MATLAB, that performs Fourier-Motzkin elimination (FME) and removes constraints that are redundant due to Shannon-type inequalities (STIs). The FME is often used in information theoretic contexts to simplify rate regions, e.g., by eliminating auxiliary rates. Occasionally, however, the procedure becomes cumbersome, which makes an error-free hand-written derivation an elusive task. Some computer software have circumvented this difficulty by exploiting an automated FME process. However, the outputs of such software often include constraints that are inactive due to information theoretic properties. By incorporating the notion of STIs (a class of information inequalities provable via a computer program), our algorithm removes such redundant constraints based on non-negativity properties, chain-rules and probability mass function factorization. This newsletter first illustrates the program's abilities, and then reviews the contribution of STIs to the identification of redundant constraints.