Optimal transportation to the entropy-power inequality

Olivier Rioul 1, 2
1 COMNUM - Communications Numériques
LTCI - Laboratoire Traitement et Communication de l'Information
Abstract :

We present a simple proof of the entropy-power inequality using an optimal transportation argument which takes the form of a simple change of variables. The same argument yields a reverse inequality involving a conditional differential entropy which has its own interest. It can also be generalized in various ways. The equality case is easily captured by this method and the proof is formally identical in one and several dimensions.

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Conference papers
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https://hal.telecom-paristech.fr/hal-02288488
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Submitted on : Saturday, September 14, 2019 - 6:52:58 PM
Last modification on : Monday, September 16, 2019 - 1:09:45 AM

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  • HAL Id : hal-02288488, version 1

Citation

Olivier Rioul. Optimal transportation to the entropy-power inequality. IEEE Information Theory and Applications Workshop (ITA 2017), Feb 2017, San Diego, United States. ⟨hal-02288488⟩

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