A simple proof of the entropy-power inequality

Sergio Verdú; Dongning Guo

doi:10.1109/TIT.2006.872978

A simple proof of the entropy-power inequality

Sergio Verdú
, Dongning Guo

Research output: Contribution to journal › Article › peer-review

103 Scopus citations

Abstract

This correspondence gives a simple proof of Shannon's entropy-power inequality (EPI) using the relationship between mutual information and minimum mean-square error (MMSE) in Gaussian channels.

Original language	English (US)
Pages (from-to)	2165-2166
Number of pages	2
Journal	IEEE Transactions on Information Theory
Volume	52
Issue number	5
DOIs	https://doi.org/10.1109/TIT.2006.872978
State	Published - May 2006

All Science Journal Classification (ASJC) codes

Information Systems
Computer Science Applications
Library and Information Sciences

Keywords

Differential entropy
Entropy-power inequality (EPI)
Minimum mean-square error (MMSE)

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10.1109/TIT.2006.872978

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title = "A simple proof of the entropy-power inequality",

abstract = "This correspondence gives a simple proof of Shannon's entropy-power inequality (EPI) using the relationship between mutual information and minimum mean-square error (MMSE) in Gaussian channels.",

keywords = "Differential entropy, Entropy-power inequality (EPI), Minimum mean-square error (MMSE)",

author = "Sergio Verd{\'u} and Dongning Guo",

note = "Funding Information: Manuscript received July 13, 2005. This work was supported in part by the National Science Foundation under Grants NCR-0074277 and CCR-0312879. S. Verd{\'u} is with the Department of Electrical Engineering, Princeton University, Princeton, NJ 08544 USA (e-mail: [email protected]). D. Guo is with the Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL 60208 USA (e-mail: [email protected]). Communicated by Y. Steinberg, Associate Editor for Shannon Theory. Digital Object Identifier 10.1109/TIT.2006.872978 1For convenience, throughout this correspondence we assume that all logarithms are natural.",

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doi = "10.1109/TIT.2006.872978",

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T1 - A simple proof of the entropy-power inequality

AU - Verdú, Sergio

AU - Guo, Dongning

N1 - Funding Information: Manuscript received July 13, 2005. This work was supported in part by the National Science Foundation under Grants NCR-0074277 and CCR-0312879. S. Verdú is with the Department of Electrical Engineering, Princeton University, Princeton, NJ 08544 USA (e-mail: [email protected]). D. Guo is with the Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL 60208 USA (e-mail: [email protected]). Communicated by Y. Steinberg, Associate Editor for Shannon Theory. Digital Object Identifier 10.1109/TIT.2006.872978 1For convenience, throughout this correspondence we assume that all logarithms are natural.

PY - 2006/5

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N2 - This correspondence gives a simple proof of Shannon's entropy-power inequality (EPI) using the relationship between mutual information and minimum mean-square error (MMSE) in Gaussian channels.

AB - This correspondence gives a simple proof of Shannon's entropy-power inequality (EPI) using the relationship between mutual information and minimum mean-square error (MMSE) in Gaussian channels.

KW - Differential entropy

KW - Entropy-power inequality (EPI)

KW - Minimum mean-square error (MMSE)

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JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 5

ER -

A simple proof of the entropy-power inequality

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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