Math @ Duke

Publications [#337696] of Henry Pfister
Papers Published
 Reeves, G; Pfister, HD; Dytso, A, Mutual Information as a Function of Matrix SNR for Linear Gaussian Channels,
Ieee International Symposium on Information Theory Proceedings, vol. 2018June
(August, 2018),
pp. 17541758, IEEE, ISBN 9781538647806 [doi]
(last updated on 2019/04/18)
Abstract: © 2018 IEEE. This paper focuses on the mutual information and minimum meansquared error (MMSE) as a function a matrixvalued signaltonoise ratio (SNR) for a linear Gaussian channel with arbitrary input distribution. As shown by Lamarca, the mutualinformation 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 informationtheoretic 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 freelyindependent matrices can be characterized succinctly via free convolution.


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