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CORR
2007
Springer

A Simple Proof of the Entropy-Power Inequality via Properties of Mutual Information

13 years 11 months ago
A Simple Proof of the Entropy-Power Inequality via Properties of Mutual Information
— While most useful information theoretic inequalities can be deduced from the basic properties of entropy or mutual information, Shannon’s entropy power inequality (EPI) seems to be an exception: available information theoretic proofs of the EPI hinge on integral representations of differential entropy using either Fisher’s information (FI) or minimum mean-square error (MMSE). In this paper, we first present a unified view of proofs via FI and MMSE, showing that they are essentially dual versions of the same proof, and then fill the gap by providing a new, simple proof of the EPI, which is solely based on the properties of mutual information and sidesteps both FI or MMSE representations.
Olivier Rioul
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2007
Where CORR
Authors Olivier Rioul
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