Group Testing in the High Dilution Regime

TL;DR

This paper studies non-adaptive group testing under dilution noise, analyzing the number of tests needed and providing bounds, revealing that appropriate test design can offset noise effects in high noise regimes.

Contribution

It introduces a new analysis of dilution noise in group testing, deriving bounds and showing noise-level-dependent test design effectiveness.

Findings

Matching achievability and converse bounds in high noise regimes

Dilution noise can be offset by suitable Bernoulli test design

Provides an algorithm-independent converse bound

Abstract

Non-adaptive group testing refers to the problem of inferring a sparse set of defectives from a larger population using the minimum number of simultaneous pooled tests. Recent positive results for noiseless group testing have motivated the study of practical noise models, a prominent one being dilution noise. Under the dilution noise model, items in a test pool have an i.i.d. probability of being diluted, meaning their contribution to a test does not take effect. In this setting, we investigate the number of tests required to achieve vanishing error probability with respect to existing algorithms and provide an algorithm-independent converse bound. In contrast to other noise models, we also encounter the interesting phenomenon that dilution noise on the resulting test outcomes can be offset by choosing a suitable noise-level-dependent Bernoulli test design, resulting in matching achievability and converse bounds up to order in the high noise regime.