Proof of entropy power inequalities via MMSE

Dongning Guo, Shlomo Shamai, Sergio Verdu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

29 Scopus citations

Abstract

The differential entropy of a random variable (or vector) can be expressed as the integral over signal-to-noise ratio (SNR) of the minimum mean-square error (MMSE) of estimating the variable (or vector) when observed in additive Gaussian noise. This representation sidesteps Fisher's information to provide simple and insightful proofs for Shannon's entropy power inequality (EPI) and two of its variations: Costa's strengthened EPI in the case in which one of the variables is Gaussian, and a generalized EPI for linear transformations of a random vector due to Zamir and Feder.

Original languageEnglish (US)
Title of host publicationProceedings - 2006 IEEE International Symposium on Information Theory, ISIT 2006
Pages1011-1015
Number of pages5
DOIs
StatePublished - Dec 1 2006
Event2006 IEEE International Symposium on Information Theory, ISIT 2006 - Seattle, WA, United States
Duration: Jul 9 2006Jul 14 2006

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8101

Other

Other2006 IEEE International Symposium on Information Theory, ISIT 2006
CountryUnited States
CitySeattle, WA
Period7/9/067/14/06

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

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