Strong Converses using Typical Changes of Measures and Asymptotic Markov Chains

TL;DR

This paper introduces new, simplified proofs for strong converse bounds in information theory problems using change of measure techniques and asymptotic Markov chain analysis, covering source coding, channel coding, and hypothesis testing.

Contribution

It provides alternative, measure-based proofs for well-known bounds and introduces new strong converses for complex multi-terminal problems involving Markov chains.

Findings

New proofs for source and channel coding bounds

Strong converse for K-hop hypothesis testing

Strong converse for multi-terminal interactive compression

Abstract

The paper presents exponentially-strong converses for source-coding, channel coding, and hypothesis testing problems. More specifically, it presents alternative proofs for the well-known exponentially-strong converse bounds for almost lossless source-coding with side-information and for channel coding over a discrete memoryless channel (DMC). These alternative proofs are solely based on a change of measure argument on the sets of conditionally or jointly typical sequences that result in a correct decision, and on the analysis of these measures in the asymptotic regime of infinite blocklengths. The paper also presents a new exponentially-strong converse for the K-hop hypothesis testing against independence problem with certain Markov chains and a strong converse for the two-terminal Lround interactive compression problem with multiple distortion constraints that depend on both sources and both reconstructions. This latter problem includes as special cases the Wyner-Ziv problem, the interactive function computation problem, and the compression with lossy common reconstruction problem. These new strong converse proofs are derived using similar change of measure arguments as described above and by additionally proving that certain Markov chains involving auxiliary random variables hold in the asymptotic regime of infinite blocklengths. As shown in related publications, the same method also yields converse bounds under expected resource constraints.