Optimality of Binning for Distributed Hypothesis Testing

TL;DR

This paper investigates the optimality of binning strategies in distributed hypothesis testing, demonstrating that binning is optimal for testing against conditional independence and providing bounds for more general cases.

Contribution

It proves binning's optimality in a specific hypothesis testing setting and extends the analysis to broader problem classes with outer bounds.

Findings

Binning is optimal for testing against conditional independence.

An outer bound is derived for more general distributed hypothesis testing problems.

Binning performance may be limited by errors in the process, but remains optimal in certain scenarios.

Abstract

We study a hypothesis testing problem in which data is compressed distributively and sent to a detector that seeks to decide between two possible distributions for the data. The aim is to characterize all achievable encoding rates and exponents of the type 2 error probability when the type 1 error probability is at most a fixed value. For related problems in distributed source coding, schemes based on random binning perform well and often optimal. For distributed hypothesis testing, however, the use of binning is hindered by the fact that the overall error probability may be dominated by errors in binning process. We show that despite this complication, binning is optimal for a class of problems in which the goal is to "test against conditional independence." We then use this optimality result to give an outer bound for a more general class of instances of the problem.