Gradient of mutual information in linear vector Gaussian channels

Daniel P. Palomar, Sergio Verdú

Research output: Contribution to journalArticle

238 Scopus citations

Abstract

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 Verdú, 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.

Original languageEnglish (US)
Pages (from-to)141-154
Number of pages14
JournalIEEE Transactions on Information Theory
Volume52
Issue number1
DOIs
StatePublished - Jan 1 2006

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

Keywords

  • De Bruijn's identity
  • Divergence
  • Gaussian noise
  • Minimum mean-square error (MMSE)
  • Multiple-input multiple-output (MIMO) channels
  • Mutual information
  • Nonlinear estimation
  • Precoder optimization

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