2024/01/10 by Junren Chen, Jonathan Scarlett, Chen, Junren +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Medicine · #Advanced biosensing and bioanalysis techniques #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Privacy-Preserving Technologies in Data #Probability (math.PR) #SARS-CoV-2 detection and testing #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2401.04884
openalex publication_date 2024/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In recent years, the mathematical limits and algorithmic bounds for probabilistic group testing have become increasingly well-understood, with exact asymptotic thresholds now being known in general scaling regimes for the noiseless setting. In the noisy setting where each test outcome is flipped with constant probability, there have been similar developments, but the overall understanding has lagged significantly behind the noiseless setting. In this paper, we substantially narrow this gap by deriving exact asymptotic thresholds for the noisy setting under two widely-studied random test designs: i.i.d. Bernoulli and near-constant tests-per-item. These thresholds are established by combining components of an existing information-theoretic threshold decoder with a novel analysis of maximum-likelihood decoding (upper bounds), and deriving a novel set of impossibility results by analyzing certain failure events for optimal maximum-likelihood decoding (lower bounds).