A Vector Generalization of Costa's Entropy-Power Inequality with Applications

Details A Vector Generalization of Costa's Entropy-Power Inequality with Applications A Vector Generalization of Costa's Entropy-Power Inequality with Applications

2009-03-17

arxiv.org/abs/0903.3024v1

Computer Science

Information Theory

Submitted to the IEEE Transactions on Information Theory

Scientific paper

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.

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