|| Group Testing in the High Dilution Regime
||Gabriel Arpino, Nicolò Grometto, Afonso S. Bandeira, ETH Zurich, Switzerland|
||D4-S7-T3: Group Testing
||Friday, 16 July, 00:00 - 00:20
||Friday, 16 July, 00:20 - 00:40
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 a fixed probability of being independently 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.