TY - GEN
T1 - Proof of entropy power inequalities via MMSE
AU - Guo, Dongning
AU - Shamai, Shlomo
AU - Verdú, Sergio
PY - 2006
Y1 - 2006
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.
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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 -