Simple Proof of the Concavity of the Entropy Power with Respect to Added Gaussian Noise.

摘要

Recently, Costa proved that the entropy power of Xt = X + N(O,tI) is concave in t, thus sharpening the original version of the entropy power inequality due to Shannon. A very simple proof of this result is derived as an immediate consequence of an inequality concerning Fisher information. Keywords: Entropy power; Fisher information; de-Bruijn identity; Reprints. (KT)