Group Testing in the High Dilution Regime
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2021
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Conference Paper
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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 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.
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2021 IEEE International Symposium on Information Theory (ISIT)
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1955 - 1960
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IEEE
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2021 IEEE International Symposium on Information Theory (ISIT 2021)
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09679 - Bandeira, Afonso / Bandeira, Afonso