Continuity of mutual entropy in the limiting signal-to-noise ratio regimes

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. © 2011 Springer-Verlag Berlin Heidelberg.