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

2009/03/11 by Miquel Payaró, M. Payaró, Daniel P. Palomar +3
Computer Science · Engineering · Mathematics · Physics and Astronomy · #94A05 #94A15 #FOS: Computer and information sciences #Information Theory (cs.IT) #Molecular Communication and Nanonetworks #Statistical Mechanics and Entropy #Wireless Communication Security Techniques #cs.IT #math.IT #msc:94A05 #msc:94A15

paper · pdf · doi:10.48550/arxiv.0903.1945

33 pages, 2 figures. A shorter version of this paper is to appear in IEEE Transactions on Information Theory

arxiv created 2009/03/11 · openalex publication_date 2009/03/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

Within 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.

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