A Strengthened Entropy Power Inequality for Log-Concave Densities

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 r...

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Bibliographic Details
Published in:IEEE transactions on information theory 2015-12, Vol.61 (12), p.6550-6559
Main Author: Toscani, Giuseppe
Format: Article
Language:English
Subjects:
Convex functions
Covariance matrices
Entropy
entropy-power inequality
Heating
information measure
Information theory
Mathematical model
Random variables
Stam's Fisher information inequality
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Summary: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.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2015.2495302