A generalization of the entropy power inequality with applications
Zamir, R.
Feder, M.
Dept. of Electr. Eng., Tel Aviv Univ.;
This paper appears in: Information Theory, IEEE Transactions on
Publication Date: Sep 1993
Volume: 39,
Issue: 5
On page(s): 1723-1728
ISSN: 0018-9448
References Cited: 14
CODEN: IETTAW
INSPEC Accession Number: 4627413
Digital Object Identifier: 10.1109/18.259666
Current Version Published: 2002-08-06
Abstract
The authors prove the following generalization of the entropy
power inequality: h(ax_)⩾h(Ax_) where h(·)
denotes (joint-) differential-entropy x_=x1...xn
, is a random vector with independent components,
x˜_=x˜...x˜n, is a Gaussian vector
with independent components such that h(x¯i)=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. They
also describe a dual generalization of the Fisher information inequality
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