Yet Another Proof of the Entropy Power Inequality

TL;DR

This paper presents a new, straightforward proof of the entropy power inequality that simplifies previous methods, avoiding complex integrations and inequalities, and clearly addresses the equality case.

Contribution

It introduces a simple, dimension-independent proof of the entropy power inequality that bypasses traditional complex techniques.

Findings

Provides a simple, dimension-independent proof of the entropy power inequality.

Avoids integration over Gaussian perturbation paths and Young's inequality with sharp constants.

Easily characterizes the equality case in the inequality.

Abstract

Yet another simple proof of the entropy power inequality is given, which avoids both the integration over a path of Gaussian perturbation and the use of Young's inequality with sharp constant or R\'enyi entropies. The proof is based on a simple change of variables, is formally identical in one and several dimensions, and easily settles the equality case.