Gradient of mutual information in linear vector Gaussian channels

This paper considers a general linear vector Gaussian channel with arbitrary signaling and pursues two closely related goals: i) closed-form expressions for the gradient of the mutual information with respect to arbitrary parameters of the system, and ii) fundamental connections between information...

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Vydáno v:	IEEE transactions on information theory Ročník 52; číslo 1; s. 141 - 154
Hlavní autoři:	Palomar, D.P., Verdu, S.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York, NY IEEE 01.01.2006 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	Applied sciences Channels Closed-form solution Covariance matrix De Bruijn's identity Derivatives divergence Electrical engineering Estimation theory Exact sciences and technology Exact solutions Gaussian Gaussian channels Gaussian noise Information theory Information, signal and communications theory Joints Mathematical analysis Mathematical models minimum mean-square error (MMSE) multiple-input multiple-output (MIMO) channels Mutual information nonlinear estimation precoder optimization Robustness Signal to noise ratio Signaling Systems, networks and services of telecommunications Telecommunications Telecommunications and information theory Transmission and modulation (techniques and equipments) Vectors Vectors (mathematics) MIMO system Non linear estimation precoder optimization Gaussian channel Transmission channel Linear channel nonlinear estimation minimum mean-square error (MMSE) Optimization Mean square error divergence Gaussian noise multiple-input multiple- output (MIMO) channels De Bruijn's identity Mutual information Information theory
ISSN:	0018-9448, 1557-9654
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Popis
Shrnutí:	This paper considers a general linear vector Gaussian channel with arbitrary signaling and pursues two closely related goals: i) closed-form expressions for the gradient of the mutual information with respect to arbitrary parameters of the system, and ii) fundamental connections between information theory and estimation theory. Generalizing the fundamental relationship recently unveiled by Guo, Shamai, and Verdu/spl acute/, we show that the gradient of the mutual information with respect to the channel matrix is equal to the product of the channel matrix and the error covariance matrix of the best estimate of the input given the output. Gradients and derivatives with respect to other parameters are then found via the differentiation chain rule.
Bibliografie:	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23
ISSN:	0018-9448 1557-9654
DOI:	10.1109/TIT.2005.860424