Transportation Proof of an inequality by Anantharam, Jog and Nair

TL;DR

This paper provides a brief proof of a recent entropic inequality that generalizes key inequalities in information theory and mathematics using optimal transport methods.

Contribution

It offers a new proof of an important entropic inequality that unifies the Shannon-Stam and Brascamp-Lieb inequalities through optimal transport.

Findings

The inequality generalizes classical entropy power and Brascamp-Lieb inequalities.

Optimal transport provides an elegant proof technique.

The result unifies multiple fundamental inequalities in information theory.

Abstract

Anantharam, Jog and Nair recently put forth an entropic inequality which simultaneously generalizes the Shannon-Stam entropy power inequality and the Brascamp-Lieb inequality in entropic form. We give a brief proof of their result based on optimal transport.