The study in group testing aims to develop strategies to identify a small set of defective items among a large population using a few pooled tests. The established techniques have been highly beneficial in a broad spectrum of applications ranging from channel communication to identifying COVID-19-infected individuals efficiently. Despite significant research on group testing and its variants since the 1940s, testing strategies robust to deletion noise have yet to be studied. Many practical systems exhibit deletion errors, for instance, in wireless communication and data storage systems. Such deletions of test outcomes lead to asynchrony between the tests, which the current group testing strategies cannot handle. In this work, we initiate the study of non-adaptive group testing strategies resilient to deletion noise. We characterize the necessary and sufficient conditions to successfully identify the defective items even after the adversarial deletion of certain test outputs. We also provide constructions of testing matrices along with an efficient recovery algorithm.

翻译：群测试研究旨在开发通过少量混合测试，从大量个体中识别出少量缺陷个体的策略。自20世纪40年代以来，已建立的该类技术在从信道通信到高效识别COVID-19感染个体的广泛应用中发挥了重要作用。尽管关于群测试及其变体的研究已开展多年，但针对删除噪声鲁棒的测试策略尚未得到研究。许多实际系统（例如无线通信和数据存储系统）存在删除错误。此类测试结果的删除会导致测试之间的非同步性，而当前的群测试策略无法处理该问题。本文首次开展了对抵抗删除噪声的非自适应群测试策略的研究。我们刻画了即使在测试输出遭受恶意删除后，成功识别缺陷个体所需满足的必要和充分条件。同时，我们提供了测试矩阵的构造方法以及高效恢复算法。