Strong Converse using Change of Measure Arguments

TL;DR

This paper introduces a general method using change of measure arguments to prove strong converses in information theory, applicable to distributed problems and resolving several open cases.

Contribution

It develops a unified, simple recipe for strong converse proofs in distributed settings, extending previous methods and solving previously open problems.

Findings

Proved strong converse for Wyner-Ziv problem.

Established strong converse theorems for interactive function computation, common randomness, and secret key agreement.

Provided a new proof technique applicable to various distributed information theory problems.

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.