Saddle Point in the Minimax Converse for Channel Coding
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mc_saddle.pdf
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296.7 KB
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Author(s)
Polyanskiy, Yury
Date Issued
May 2013
Journal
IEEE Transactions on Information Theory
Publisher
Institute of Electrical and Electronics Engineers
Citation
Polyanskiy, Yury. Saddle Point in the Minimax Converse for Channel Coding. IEEE Transactions on Information Theory 59, no. 5 (May 2013): 2576-2595.
Version
Author's final manuscript
Abstract
A minimax metaconverse has recently been proposed as a simultaneous generalization of a number of classical results and a tool for the nonasymptotic analysis. In this paper, it is shown that the order of optimizing the input and output distributions can be interchanged without affecting the bound. In the course of the proof, a number of auxiliary results of separate interest are obtained. In particular, it is shown that the optimization problem is convex and can be solved in many cases by the symmetry considerations. As a consequence, it is demonstrated that in the latter cases, the (multiletter) input distribution in information-spectrum (Verdú-Han) converse bound can be taken to be a (memoryless) product of single-letter ones. A tight converse for the binary erasure channel is rederived by computing the optimal (nonproduct) output distribution. For discrete memoryless channels, a conjecture of Poor and Verdú regarding the tightness of the information spectrum bound on the error exponents is resolved in the negative. Concept of the channel symmetry group is established and relations with the definitions of symmetry by Gallager and Dobrushin are investigated.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1109/TIT.2012.2236382
