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A vector generalization of Costa entropy-power inequality and applications

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4 Author(s)
Ruoheng Liu ; Department of Electrical Engineering, Princeton University, NJ 08544, USA ; Tie Liu ; H. Vincent Poor ; Shlomo Shamai

This paper considers an entropy-power inequality (EPI) of Costa and presents a natural vector generalization with a real positive semidefinite matrix parameter. This new inequality is proved using a perturbation approach via a fundamental relationship between the derivative of mutual information and the minimum mean-square error (MMSE) estimate in linear vector Gaussian channels. As an application, a new extremal entropy inequality is derived from the generalized Costa EPI and then used to establish the secrecy capacity regions of the degraded vector Gaussian broadcast channel with layered confidential messages.

Published in:

2009 IEEE International Symposium on Information Theory

Date of Conference:

June 28 2009-July 3 2009