Comparison of channels: criteria for domination by a symmetric channel
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1609.06877.pdf
Description
Submitted version
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718.82 KB
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Author(s)
Makur, Anuran
Polyanskiy, Yury
Date Issued
May 2018
Journal
IEEE Transactions on Information Theory
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Makur, Anuran, and Yury Polyanskiy, "Comparison of channels: criteria for domination by a symmetric channel." IEEE Transactions on Information Theory 64, 8 (Aug. 2018): p. 5704-25; doi: 10.1109/TIT.2018.2839743 ©2018 Author(s)
Version
Original manuscript
Abstract
This paper studies the basic question of whether a given channel V can be dominated (in the precise sense of being more noisy) by a q-ary symmetric channel. The concept of less noisy relation between channels originated in network information theory (broadcast channels) and is defined in terms of mutual information or Kullback-Leibler divergence. We provide an equivalent characterization in terms of χ²-divergence. Furthermore, we develop a simple criterion for domination by a q-ary symmetric channel in terms of the minimum entry of the stochastic matrix defining the channel V. The criterion is strengthened for the special case of additive noise channels over finite Abelian groups. Finally, it is shown that domination by a symmetric channel implies (via comparison of Dirichlet forms) a logarithmic Sobolev inequality for the original channel. ©2018 Keywords: less noisy; degradation; q-ary symmetric channel; additive noise channel; Dirichlet form; logarithmic Sobolev inequalities
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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DOI of Published Version
https://doi.org/10.1109/TIT.2018.2839743
