Less noisy domination by symmetric channels
Author(s)Makur, Anuran; Polyanskiy, Yury
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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.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
2017 IEEE International Symposium on Information Theory (ISIT)
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.
Author's final manuscript