Non-Adaptive Group Testing in the Linear Regime: Strong Converse and Approximate Recovery
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In this paper, we consider the non-adaptive group testing problem in the linear sparsity regime. We prove a strong converse bound for exact recovery, showing that individual testing is asymptotically optimal for any non-zero target success probability, and strengthening the existing weak converse (Aldridge, 2019). To overcome this barrier, we additionally study an approximate recovery criterion. We demonstrate broad scenarios in which randomized test designs can improve on individual testing under this relaxed criterion, and provide a rate-distortion type converse.
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