Strong Converse for Hypothesis Testing Against Independence over a Two-Hop Network

TL;DR

This paper establishes a strong converse for hypothesis testing against independence over a two-hop network, enhancing previous results by combining advanced proof techniques to strengthen the theoretical understanding of communication constraints.

Contribution

The paper introduces a novel proof approach that combines two recent strong converse techniques, applicable to multiterminal hypothesis testing problems.

Findings

Proves a strong converse for the two-hop network hypothesis testing problem.

Demonstrates the applicability of combined techniques to other multiterminal testing scenarios.

Strengthens the theoretical limits of hypothesis testing under communication constraints.

Abstract

By proving a strong converse, we strengthen the weak converse result by Salehkalaibar, Wigger and Wang (2017) concerning hypothesis testing against independence over a two-hop network with communication constraints. Our proof follows by judiciously combining two recently proposed techniques for proving strong converse theorems, namely the strong converse technique via reverse hypercontractivity by Liu, van Handel, and Verd\'u (2017) and the strong converse technique by Tyagi and Watanabe (2018), in which the authors used a change-of-measure technique and replaced hard Markov constraints with soft information costs. The techniques used in our paper can also be applied to prove strong converse theorems for other multiterminal hypothesis testing against independence problems.