Strong Converse Using Change of Measure Arguments

Tyagi, H and Watanabe, S (2020) Strong Converse Using Change of Measure Arguments. In: IEEE Transactions on Information Theory, 66 (2). pp. 689-703.

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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.

Item Type:	Journal Article
Publication:	IEEE Transactions on Information Theory
Publisher:	IEEE
Additional Information:	Copyright of this article belongs to IEEE
Keywords:	Errors, Function computations; measure change; Secret key agreement; Strong converse; Wire-tap channels, Computation theory
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	13 Feb 2020 08:15
Last Modified:	13 Feb 2020 08:15
URI:	http://eprints.iisc.ac.in/id/eprint/64514

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