Less noisy domination by symmetric channels
Name
isit17_lessnoisy.pdf
Description
Accepted version
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370.05 KB
Format
Adobe PDF
Checksum (MD5)
7d242253280581061fbe53e976503b4a
Author(s)
Makur, Anuran
Polyanskiy, Yury
Date Issued
June 2017
Journal
2017 IEEE International Symposium on Information Theory (ISIT)
Publisher
IEEE
Citation
Makur, Anuran and Yury Polyanskiy. "Less Noisy Domination by Symmetric Channels." 2017 IEEE International Symposium on Information Theory (ISIT), Aachen, Germany, 25-30 June 2017.
Version
Author's final manuscript
Abstract
Consider the family of all q-ary symmetric channels (q-SCs) with capacities decreasing from log(q) to 0. This paper addresses the following question: what is the member of this family with the smallest capacity that dominates a given channel V in the 'less noisy' preorder sense. When the q-SCs are replaced by q-ary erasure channels, this question is known as the 'strong data processing inequality.' We provide several equivalent characterizations of the less noisy preorder in terms of x2-divergence, Lowner (PSD) partial order, and spectral radius. We then illustrate a simple criterion for domination by a q-SC based on degradation, and mention special improvements for the case where V is an additive noise channel over an Abelian group of order q. Finally, as an application, we discuss how logarithmic Sobolev inequalities for q-SCs, which are well-studied, can be transported to an arbitrary channel V.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution 3.0 unported license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1109/isit.2017.8006972
