TY - GEN

T1 - Proof of entropy power inequalities via MMSE

AU - Guo, Dongning

AU - Shamai, Shlomo

AU - Verdu, Sergio

PY - 2006/12/1

Y1 - 2006/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=39049117948&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=39049117948&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2006.261880

DO - 10.1109/ISIT.2006.261880

M3 - Conference contribution

AN - SCOPUS:39049117948

SN - 1424405041

SN - 9781424405046

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 1011

EP - 1015

BT - Proceedings - 2006 IEEE International Symposium on Information Theory, ISIT 2006

T2 - 2006 IEEE International Symposium on Information Theory, ISIT 2006

Y2 - 9 July 2006 through 14 July 2006

ER -