Distributed Hypothesis Testing Over Discrete Memoryless Channels

TL;DR

This paper investigates the fundamental limits of distributed binary hypothesis testing over discrete memoryless channels, proposing coding schemes and characterizing error exponents for different scenarios, including testing against independence.

Contribution

It introduces new bounds and schemes for distributed hypothesis testing over DMCs, including a joint coding approach that outperforms separation in certain cases.

Findings

Single-letter lower bounds on error exponents are derived.

Exact characterization for testing against conditional independence is provided.

Joint coding scheme can outperform separate schemes in specific scenarios.

Abstract

A distributed binary hypothesis testing (HT) problem involving two parties, one referred to as the observer and the other as the detector is studied. The observer observes a discrete memoryless source (DMS) and communicates its observations to the detector over a discrete memoryless channel (DMC). The detector observes another DMS correlated with that at the observer, and performs a binary HT on the joint distribution of the two DMS's using its own observed data and the information received from the observer. The trade-off between the type I error probability and the type II error-exponent of the HT is explored. Single-letter lower bounds on the optimal type II error-exponent are obtained by using two different coding schemes, a separate HT and channel coding scheme and a joint HT and channel coding scheme based on hybrid coding for the matched bandwidth case. Exact single-letter characterization of the same is established for the special case of testing against conditional independence, and it is shown to be achieved by the separate HT and channel coding scheme. An example is provided where the joint scheme achieves a strictly better performance than the separation based scheme.