Hessian and concavity of mutual information, differential entropy, and entropy power in linear vector Gaussian channels

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dc.creatorPayaró, M.
dc.creatorPalomar, D. P.
dc.date2009-03-11
dc.date.accessioned2026-07-07T12:51:36Z
dc.date.available2026-07-07T12:51:36Z
dc.descriptionWithin the framework of linear vector Gaussian channels with arbitrary signaling, closed-form expressions for the Jacobian of the minimum mean square error and Fisher information matrices with respect to arbitrary parameters of the system are calculated in this paper. Capitalizing on prior research where the minimum mean square error and Fisher information matrices were linked to information-theoretic quantities through differentiation, closed-form expressions for the Hessian of the mutual information and the differential entropy are derived. These expressions are then used to assess the concavity properties of mutual information and differential entropy under different channel conditions and also to derive a multivariate version of the entropy power inequality due to Costa.
dc.description33 pages, 2 figures. A shorter version of this paper is to appear in IEEE Transactions on Information Theory
dc.identifierhttps://arxiv.org/abs/0903.1945
dc.identifierhttp://arxiv.org/abs/0903.1945
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/223039
dc.subjectInformation Theory
dc.subject94A15; 94A05
dc.titleHessian and concavity of mutual information, differential entropy, and entropy power in linear vector Gaussian channels
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