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

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dc.creatorLiu, Ruoheng
dc.creatorLiu, Tie
dc.creatorPoor, H. Vincent
dc.creatorShamai, Shlomo
dc.date2009-03-17
dc.date.accessioned2026-07-07T12:53:13Z
dc.date.available2026-07-07T12:53:13Z
dc.descriptionThis 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.
dc.descriptionSubmitted to the IEEE Transactions on Information Theory
dc.identifierhttps://arxiv.org/abs/0903.3024
dc.identifierhttp://arxiv.org/abs/0903.3024
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/223550
dc.subjectInformation Theory
dc.titleA Vector Generalization of Costa's Entropy-Power Inequality with Applications
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