Information theoretic inequalities
Dembo, A.
Cover, T.M.
Thomas, J.A.
Stanford Univ., CA;
This paper appears in: Information Theory, IEEE Transactions on
Publication Date: Nov 1991
Volume: 37,
Issue: 6
On page(s): 1501-1518
ISSN: 0018-9448
References Cited: 40
CODEN: IETTAW
INSPEC Accession Number: 4083981
Digital Object Identifier: 10.1109/18.104312
Current Version Published: 2002-08-06
Abstract
The role of inequalities in information theory is reviewed, and
the relationship of these inequalities to inequalities in other branches
of mathematics is developed. The simple inequalities for differential
entropy are applied to the standard multivariate normal to furnish new
and simpler proofs of the major determinant inequalities in classical
mathematics. The authors discuss differential entropy inequalities for
random subsets of samples. These inequalities when specialized to
multivariate normal variables provide the determinant inequalities that
are presented. The authors focus on the entropy power inequality
(including the related Brunn-Minkowski, Young's, and Fisher information
inequalities) and address various uncertainty principles and their
interrelations
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