On the Reliability Function of Distributed Hypothesis Testing Under Optimal Detection

TL;DR

This paper investigates the reliability function in distributed hypothesis testing with full side-information, deriving bounds for error exponents using optimal detection and connecting it to channel coding theory.

Contribution

It introduces a novel reduction of the hypothesis testing problem to channel coding, deriving single-letter bounds for the reliability function with optimal detection.

Findings

Derived a hierarchical ensemble-based random-coding bound.

Established a single-letter expurgated bound.

Conjectured the ensemble-tightness of the random-coding bound.

Abstract

The distributed hypothesis testing problem with full side-information is studied. The trade-off (reliability function) between the two types of error exponents under limited rate is studied in the following way. First, the problem is reduced to the problem of determining the reliability function of channel codes designed for detection (in analogy to a similar result which connects the reliability function of distributed lossless compression and ordinary channel codes). Second, a single-letter random-coding bound based on a hierarchical ensemble, as well as a single-letter expurgated bound, are derived for the reliability of channel-detection codes. Both bounds are derived for a system which employs the optimal detection rule. We conjecture that the resulting random-coding bound is ensemble-tight, and consequently optimal within the class of quantization-and-binning schemes.