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

Authors:
Miquel Payaró;Daniel P. Palomar
Affiliations:
Centre Tecnològic de Telecomunicacions de Catalunya, Barcelona, Spain and Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Clear Water Bay, K ...;Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
Venue:
IEEE Transactions on Information Theory
Year:
2009

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Abstract

Within the framework of linear vector Gaussian channels with arbitrary signaling, 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, the Hessian of the mutual information and the entropy are derived. These expressions are then used to assess the concavity properties of mutual information and entropy under different channel conditions and also to derive a multivariate version of an entropy power inequality due to Costa.