Name
Abstract | ||
|---|---|---|
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 semi-definite 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. |
Year | Venue | Keywords |
|---|---|---|
2018 | 2018 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT) | I-MMSE, entropy power inequality, conditional central limit theorem, random matrix theory, compressed sensing, Gaussian logarithmic Sobolev inequality |
Field | DocType | Citations |
Entropy power inequality,Discrete mathematics,Free convolution,Matrix (mathematics),Computer science,Positive-definite matrix,Interpolation,Concave function,Algorithm,Mutual information,Random matrix | Conference | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Galen Reeves | 1 | 60 | 9.34 |
| Henry D. Pfister | 2 | 227 | 25.28 |
| Alex Dytso | 3 | 45 | 20.03 |