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2018•IEEE Transactions on Information TheoryOpen access

On the Entropy Power Inequality for the Rényi Entropy of Order [0, 1]

Arnaud Marsiglietti, James Melbourne

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Abstract

Using a sharp version of the reverse Young inequality, and a Rényi entropy comparison result due to Fradelizi, Madiman, and Wang (2016), the authors derive Rényi entropy power inequalities for log-concave random vectors when Rényi parameters belong to [0, 1]. Furthermore, the estimates are shown to be sharp up to absolute constants.

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What this paper is about

Using a sharp version of the reverse Young inequality, and a Rényi entropy comparison result due to Fradelizi, Madiman, and Wang (2016), the authors derive Rényi entropy power inequalities for log-concave random vectors when Rényi parameters belong to [0, 1]. Furthermore, the estimates are shown to be sharp up to absolute constants.

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Available abstract

Using a sharp version of the reverse Young inequality, and a Rényi entropy comparison result due to Fradelizi, Madiman, and Wang (2016), the authors derive Rényi entropy power inequalities for log-concave random vectors when Rényi parameters belong to [0, 1]. Furthermore, the estimates are shown to be sharp up to absolute constants.

Key concepts: Rényi entropy, Mathematics, Entropy power inequality, Min entropy, Entropy (arrow of time), Inequality, Maximum entropy probability distribution, Statistical physics

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