Transportation proofs of Rényi entropy power inequalities

Olivier Rioul 1, 2
1 COMNUM - Communications Numériques
LTCI - Laboratoire Traitement et Communication de l'Information
Abstract : A framework for deriving Rényi entropy-power inequalities (EPIs) is presented that uses linearization and an inequality of Dembo, Cover, and Thomas. Simple arguments are given to recover the previously known Rényi EPIs and derive new ones, by unifying a multiplicative form with con- stant c and a modification with exponent α of previous works. An information-theoretic proof of the Dembo-Cover-Thomas inequality—equivalent to Young’s convolutional inequality with optimal constants—is provided, based on properties of Rényi conditional and relative entropies and using transportation ar- guments from Gaussian densities. For log-concave densities, a transportation proof of a sharp varentropy bound is presented.
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https://hal.telecom-paristech.fr/hal-02300781
Contributor : Olivier Rioul <>
Submitted on : Sunday, September 29, 2019 - 8:27:41 PM
Last modification on : Thursday, October 17, 2019 - 12:36:59 PM

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  • HAL Id : hal-02300781, version 1

Citation

Olivier Rioul. Transportation proofs of Rényi entropy power inequalities. IEEE Information Theory and Applications Workshop (ITA 2019), Feb 2019, San Diego, United States. ⟨hal-02300781⟩

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