Continuity of mutual entropy in the large signal-to-noise ratio limit

TL;DR

This paper investigates the continuity of mutual entropy in Gaussian channels and discusses conditions under which the entropy power inequality remains valid, focusing on the large signal-to-noise ratio limit.

Contribution

It provides a detailed analysis of the continuity properties of mutual entropy and clarifies the assumptions necessary for the entropy power inequality to hold.

Findings

Mutual entropy exhibits specific continuity properties in high SNR regimes.

Certain assumptions are crucial for the validity of the entropy power inequality.

The paper clarifies the conditions under which EPI holds in additive memoryless channels.

Abstract

This article addresses the issue of the proof of the entropy power inequality (EPI), an important tool in the analysis of Gaussian channels of information transmission, proposed by Shannon. We analyse continuity properties of the mutual entropy of the input and output signals in an additive memoryless channel and discuss assumptions under which the entropy-power inequality holds true.