Strong Converses using Change of Measure and Asymptotic Markov Chains

TL;DR

This paper establishes a strong converse for distributed hypothesis testing in multi-hop networks, showing that achievable error exponents are independent of type-I error thresholds, using novel change of measure and Markov chain techniques.

Contribution

Introduces a new strong converse proof method for distributed hypothesis testing that avoids variational and blowing-up techniques, applicable to multi-hop scenarios.

Findings

Type-II error exponents are independent of type-I error probabilities.

The proof employs change of measure and asymptotic Markov chain analysis.

Method simplifies converse proofs in distributed hypothesis testing.

Abstract

The main contribution of this paper is a strong converse result for $K$-hop distributed hypothesis testing against independence with multiple (intermediate) decision centers under a Markov condition. Our result shows that the set of type-II error exponents that can simultaneously be achieved at all the terminals does not depend on the maximum permissible type-I error probabilities. Our strong converse proof is based on a change of measure argument and on the asymptotic proof of specific Markov chains. This proof method can also be used for other converse proofs, and is appealing because it does not require resorting to variational characterizations or blowing-up methods as in previous related proofs.