Covering Codes as Near-Optimal Quantizers for Distributed Testing Against Independence

TL;DR

This paper investigates the use of binary linear codes as near-optimal quantizers for distributed hypothesis testing against independence, providing bounds, algorithms, and numerical validation for their effectiveness.

Contribution

It introduces an alternating optimization algorithm to identify optimal binary linear codes for hypothesis testing, and characterizes their error performance with bounds and exponents.

Findings

Binary linear codes with optimal covering radius perform near-optimally.

The proposed algorithm effectively minimizes error probabilities.

Error bounds and exponents are derived for large code lengths.

Abstract

We explore the problem of distributed Hypothesis Testing (DHT) against independence, focusing specifically on Binary Symmetric Sources (BSS). Our investigation aims to characterize the optimal quantizer among binary linear codes, with the objective of identifying optimal error probabilities under the Neyman-Pearson (NP) criterion for short code-length regime. We define optimality as the direct minimization of analytical expressions of error probabilities using an alternating optimization (AO) algorithm. Additionally, we provide lower and upper bounds on error probabilities, leading to the derivation of error exponents applicable to large code-length regime. Numerical results are presented to demonstrate that, with the proposed algorithm, binary linear codes with an optimal covering radius perform near-optimally for the independence test in DHT.