Ensemble Average Analysis of Non-Adaptive Group Testing with Sparse Pooling Graphs

TL;DR

This paper provides a combinatorial ensemble average analysis of false alarm and misdetection probabilities in non-adaptive group testing with sparse pooling graphs, focusing on specific detection algorithms.

Contribution

It introduces a novel ensemble average approach to analyze FA/MD probabilities in non-adaptive group testing with sparse graphs, applicable to orthogonal matching pursuit and defective detection algorithms.

Findings

The analysis accurately predicts FA/MD probabilities in numerical examples.

The technique characterizes the performance of group testing schemes with sparse pooling graphs.

Abstract

A combinatorial analysis of the false alarm (FA) and misdetection (MD) probabilities of non-adaptive group testing with sparse pooling graphs is developed. The analysis targets the combinatorial orthogonal matching pursuit and definite defective detection algorithms in the noiseless, non-quantitative setting. The approach follows an ensemble average perspective, where average FA/MD probabilities are computed for pooling graph ensembles with prescribed degree distributions. The accuracy of the analysis is demonstrated through numerical examples, showing that the proposed technique can be used to characterize the performance of non-adaptive group testing schemes based on sparse pooling graphs.