On Sub-optimality of Random Binning for Distributed Hypothesis Testing

TL;DR

This paper analyzes the limitations of the random binning approach in distributed hypothesis testing and introduces a sequential scheme that outperforms the traditional SHA scheme for certain binary sources.

Contribution

It provides new tools to evaluate the critical rate of the SHA scheme and proposes an improved sequential scheme for binary symmetric sources.

Findings

The SHA scheme has sub-optimal critical rates for certain sources.

A new sequential scheme surpasses SHA in specific binary source scenarios.

Tools are developed to evaluate the performance limits of binning schemes.

Abstract

We investigate the quantize and binning scheme, known as the Shimokawa-Han-Amari (SHA) scheme, for the distributed hypothesis testing. We develop tools to evaluate the critical rate attainable by the SHA scheme. For a product of binary symmetric double sources, we present a sequential scheme that improves upon the SHA scheme.