Group Testing in the High Dilution Regime


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.

Asterisk denotes equal contribution. In 2021 IEEE International Symposium on Information Theory (ISIT)