Hypothesis Testing Over the Two-hop Relay Network

TL;DR

This paper develops coding schemes for binary hypothesis testing over two-hop relay networks, achieving optimal error exponents and simplifying the coding process under certain Markov chain conditions.

Contribution

It introduces cascade source coding schemes with decision-forwarding and proves their optimality in various testing scenarios, including testing against conditional independence.

Findings

Decoupled schemes attain optimal error exponents in specific Markov chain cases.

Decision-forwarding simplifies the coding process without performance loss.

Analysis of existing binning schemes for point-to-point hypothesis testing included.

Abstract

Coding and testing schemes and the corresponding achievable type-II error exponents are presented for binary hypothesis testing over two-hop relay networks. The schemes are based on cascade source coding techniques and {unanimous decision-forwarding}, the latter meaning that a terminal decides on the null hypothesis only if all previous terminals have decided on the null hypothesis. If the observations at the transmitter, the relay, and the receiver form a Markov chain in this order, then, without loss in performance, the proposed cascade source code can be replaced by two independent point-to-point source codes, one for each hop. The decoupled scheme (combined with decision-forwarding) is shown to attain the optimal type-II error exponents for various instances of "testing against conditional independence." The same decoupling is shown to be optimal also for some instances of "testing against independence," when the observations at the transmitter, the receiver, and the relay form a Markov chain in this order, and when the relay-to-receiver link is of sufficiently high rate. For completeness, the paper also presents an analysis of the Shimokawa-Han-Amari binning scheme for the point-to-point hypothesis testing setup.