Title :
A Strengthened Entropy Power Inequality for Log-Concave Densities
Author :
Toscani, Giuseppe
Author_Institution :
Dept. of Math., Univ. of Pavia, Pavia, Italy
Abstract :
We show that Shannon´s entropy-power inequality admits a strengthened version in the case in which the densities are log-concave. In such a case, in fact, one can extend the Blachman-Stam argument to obtain a sharp inequality for the second derivative of Shannon´s entropy functional with respect to the heat semigroup.
Keywords :
entropy; Blachman-Stam argument; Shannon entropy functional; heat semigroup; log-concave densities; strengthened entropy power inequality; Convex functions; Covariance matrices; Entropy; Heating; Mathematical model; Random variables; Yttrium; Entropy; Stam’s Fisher information inequality; Stam???s Fisher information inequality; entropy-power inequality; information measure; information theory;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2015.2495302
