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

作者：Liu Ruoheng^*; Liu Tie; Poor H Vincent; Shamai Shlomo

来源：IEEE Transactions on Information Theory, 2010, 56(4): 1865-1879.

DOI：10.1109/TIT.2010.2040879

• Entropy-power inequality (EPI)
• extremal entropy inequality
• information-theoretic security
• mutual information and minimum mean-square error (MMSE) estimate
• vector Gaussian broadcast channel

This paper considers an entropy-power inequality (EPI) of Costa and presents a natural vector generalization with a real positive semidefinite matrix parameter. The 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.

• 出版日期2010-4