A Generalization of Costa's Entropy Power Inequality

Luca Tamanini

doi:10.1109/TIT.2022.3159132

A Generalization of Costa's Entropy Power Inequality

Luca Tamanini^*

^*Corresponding author

Research output: Contribution to journal › Article

Abstract

Aim of this short note is to study Shannon's entropy power along entropic interpolations, thus generalizing Costa's concavity theorem. We shall provide two proofs of independent interest: the former by G-calculus, hence applicable to more abstract frameworks; the latter with an explicit remainder term, reminiscent of Villani (IEEE Trans. Inf. Theory, 2006), allowing us to characterize the case of equality.

Original language	English
Pages (from-to)	4224-4229
Number of pages	6
Journal	IEEE Transactions on Information Theory
Volume	68
DOIs	https://doi.org/10.1109/TIT.2022.3159132
Publication status	Published - 2022

Keywords

Entropy
Schrodinger problem
entropy power
heat equation
information theory

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10.1109/TIT.2022.3159132

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title = "A Generalization of Costa's Entropy Power Inequality",

abstract = "Aim of this short note is to study Shannon's entropy power along entropic interpolations, thus generalizing Costa's concavity theorem. We shall provide two proofs of independent interest: the former by G-calculus, hence applicable to more abstract frameworks; the latter with an explicit remainder term, reminiscent of Villani (IEEE Trans. Inf. Theory, 2006), allowing us to characterize the case of equality.",

keywords = "Entropy, Schrodinger problem, entropy power, heat equation, information theory, Entropy, Schrodinger problem, entropy power, heat equation, information theory",

author = "Luca Tamanini",

year = "2022",

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PY - 2022

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AB - Aim of this short note is to study Shannon's entropy power along entropic interpolations, thus generalizing Costa's concavity theorem. We shall provide two proofs of independent interest: the former by G-calculus, hence applicable to more abstract frameworks; the latter with an explicit remainder term, reminiscent of Villani (IEEE Trans. Inf. Theory, 2006), allowing us to characterize the case of equality.

KW - Entropy

KW - Schrodinger problem

KW - entropy power

KW - heat equation

KW - information theory

KW - Entropy

KW - Schrodinger problem

KW - entropy power

KW - heat equation

KW - information theory

UR - http://hdl.handle.net/10807/232464

U2 - 10.1109/TIT.2022.3159132

DO - 10.1109/TIT.2022.3159132

M3 - Article

SN - 0018-9448

VL - 68

SP - 4224

EP - 4229

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

ER -

A Generalization of Costa's Entropy Power Inequality

Abstract

Keywords

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