通过空间耦合的含噪分组测试
Noisy group testing via spatial coupling
AI总结：
研究含噪分组测试问题，提出SPARC算法以渐近最少测试数高概率将感染个体识别至$o(k)$误差内，并提出SPEX算法以匹配constant column design信息论下界的测试数精确识别感染个体。
摘要：
我们研究通过同时测试个体组来从规模为$n$的大量群体中识别一小批$k\sim n^θ$（$0<θ<1$）感染个体的问题。所有测试均并发进行，目标是最小化所需的总测试数。本文假设测试存在噪声，即包含感染个体的组可能以一定概率返回阴性结果，不包含感染个体的组可能返回阳性结果，且噪声不必对称。我们开发了名为SPARC的算法，能以高概率将感染个体集合正确识别至$o(k)$误差内，且使用渐近最少的测试数。此外，我们开发了名为SPEX的算法，能以高概率精确识别感染个体集合，其测试数与constant column design（一种强大且被广泛研究的测试设计）的信息论下界相匹配。
英文摘要：
We study the problem of identifying a small set $k\sim n^θ$, $0<θ<1$, of infected individuals within a large population of size $n$ by testing groups of individuals simultaneously. All tests are conducted concurrently. The goal is to minimise the total number of tests required. In this paper we make the (realistic) assumption that tests are noisy, i.e.\ that a group that contains an infected individual may return a negative test result or one that does not contain an infected individual may return a positive test results with a certain probability. The noise need not be symmetric. We develop an algorithm called SPARC that correctly identifies the set of infected individuals up to $o(k)$ errors with high probability with the asymptotically minimum number of tests. Additionally, we develop an algorithm called SPEX that exactly identifies the set of infected individuals w.h.p. with a number of tests that matches the information-theoretic lower bound for the constant column design, a powerful and well-studied test design.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
