Mutual Information as a Function of Matrix SNR for Linear Gaussian Channels

Published

Conference Paper

© 2018 IEEE. This paper focuses on the mutual information and minimum mean-squared error (MMSE) as a function a matrix-valued signal-to-noise ratio (SNR) for a linear Gaussian channel with arbitrary input distribution. As shown by Lamarca, the mutual-information is a concave function of a positive semidefinite matrix, which we call the matrix SNR. This implies that the mapping from the matrix SNR to the MMSE matrix is decreasing monotone. Building upon these functional properties, we start to construct a unifying framework that provides a bridge between classical information-theoretic inequalities, such as the entropy power inequality, and interpolation techniques used in statistical physics and random matrix theory. This framework provides new insight into the structure of phase transitions in coding theory and compressed sensing. In particular, it is shown that the parallel combination of linear channels with freely-independent matrices can be characterized succinctly via free convolution.

Full Text

Duke Authors

Cited Authors

  • Reeves, G; Pfister, HD; Dytso, A

Published Date

  • August 15, 2018

Published In

Volume / Issue

  • 2018-June /

Start / End Page

  • 1754 - 1758

International Standard Serial Number (ISSN)

  • 2157-8095

International Standard Book Number 13 (ISBN-13)

  • 9781538647806

Digital Object Identifier (DOI)

  • 10.1109/ISIT.2018.8437326

Citation Source

  • Scopus