TY - JOUR

T1 - A Generalization of the Entropy Power Inequality with Applications

AU - Zamir, Ram

AU - Feder, Meir

N1 - Funding Information:
Manuscript received July 29, 1993; revised February 10, 1993. This work was supported in part by the Wolfson Research Awards administrated by the Israel Academy of Science and Humanities. This paper was presented in part at the International Symposium on Information Theory, San Antonio, TX, January 1993. The authors are with the Department of Electrical Engineering-Systems, Tel-Aviv University, Tel-Aviv 69978, Israel. IEEE Log Number 9211273.

PY - 1993/9

Y1 - 1993/9

N2 - We prove the following generalization of the Entropy Power Inequality: [formula omitted] where h(.) denotes (joint-) differential-entropy, x = x1…xnis a random vector with independent components, [formula omitted] is a Gaussian vector with independent components such that h(xi~) = h(xi), i = 1…n, and A is any matrix. This generalization of the entropy-power inequality is applied to show that a non-Gaussian vector with independent components becomes “closer” to Gaussianity after a linear transformation, where the distance to Gaussianity is measured by the information divergence. Another application is a lower bound, greater than zero, for the mutual-information between nonoverlapping spectral components of a non-Gaussian white process. Finally, we describe a dual generalization of the Fisher Information Inequality.

AB - We prove the following generalization of the Entropy Power Inequality: [formula omitted] where h(.) denotes (joint-) differential-entropy, x = x1…xnis a random vector with independent components, [formula omitted] is a Gaussian vector with independent components such that h(xi~) = h(xi), i = 1…n, and A is any matrix. This generalization of the entropy-power inequality is applied to show that a non-Gaussian vector with independent components becomes “closer” to Gaussianity after a linear transformation, where the distance to Gaussianity is measured by the information divergence. Another application is a lower bound, greater than zero, for the mutual-information between nonoverlapping spectral components of a non-Gaussian white process. Finally, we describe a dual generalization of the Fisher Information Inequality.

KW - Entropy power inequality

KW - Fisher information inequality

KW - divergence

KW - non-Gaussianity

UR - http://www.scopus.com/inward/record.url?scp=0027659563&partnerID=8YFLogxK

U2 - 10.1109/18.259666

DO - 10.1109/18.259666

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AN - SCOPUS:0027659563

SN - 0018-9448

VL - 39

SP - 1723

EP - 1728

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 5

ER -