Variants of the Entropy Power Inequality

TL;DR

This paper extends the entropy power inequality to Rényi entropy for arbitrary independent variables in ^n, establishing a new inequality involving Re9nyi entropy powers for certain powers .

Contribution

It introduces a generalized entropy power inequality for Re9nyi entropy with arbitrary independent summands and specific power conditions.

Findings

Established a new inequality for Re9nyi entropy powers.

Extended the classical entropy power inequality to a broader Re9nyi entropy context.

Applicable to independent variables in ^n for certain powers .

Abstract

An extension of the entropy power inequality to the form $N_r^\alpha(X+Y) \geq N_r^\alpha(X) + N_r^\alpha(Y)$ with arbitrary independent summands $X$ and $Y$ in $\mathbb{R}^n$ is obtained for the R\'enyi entropy and powers $\alpha \geq (r+1)/2$.