Analysis of Theoretical Bounds in Noisy Threshold Group Testing

The objective of this study was to describe a noisy threshold group testing model where positive and negative cases could occur depending on virus concentration in coronavirus disease 2019 (COVID-19) diagnosis with output results flipped due to measurement noise. We investigated lower bounds for successful reconstruction of a small set of defective samples in the noisy threshold group testing framework. To this end, using Fano’s inequality, we derived the minimum number of tests required to find unknown signals with defective samples. Our results showed that the minimum number of tests on probability of error for reconstruction of unknown signals was a function of the defective rate and noise probability. We obtained lower bounds for on performance of the noisy threshold group testing framework with respect to noise intervals. In addition, the relationship between defective rate of signals and sparsity of group matrices to design optimal noisy threshold group testing systems is presented. © 2022. The Korean Institute of Information Scientists and Engineers