Strong Converse Using Change of Measure Arguments
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Publication:5211628
DOI10.1109/TIT.2019.2953877zbMATH Open1440.94022arXiv1805.04625OpenAlexW2989712406MaRDI QIDQ5211628
Publication date: 28 January 2020
Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)
Abstract: The strong converse for a coding theorem shows that the optimal asymptotic rate possible with vanishing error cannot be improved by allowing a fixed error. Building on a method introduced by Gu and Effros for centralized coding problems, we develop a general and simple recipe for proving strong converse that is applicable for distributed problems as well. Heuristically, our proof of strong converse mimics the standard steps for proving a weak converse, except that we apply those steps to a modified distribution obtained by conditioning the original distribution on the event that no error occurs. A key component of our recipe is the replacement of the hard Markov constraints implied by the distributed nature of the problem with a soft information cost using a variational formula introduced by Oohama. We illustrate our method by providing a short proof of the strong converse for the Wyner-Ziv problem and strong converse theorems for interactive function computation, common randomness and secret key agreement, and the wiretap channel; the latter three strong converse problems were open prior to this work.
Full work available at URL: https://arxiv.org/abs/1805.04625
wiretap channelsecret key agreementcommon randomnessWyner-Ziv probleminteractive function computationOohama variational formulasoft information coststrong converse for coding theorem
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