An Efficient Algorithm for Capacity-Approaching Noisy Adaptive Group Testing

TL;DR

This paper introduces a computationally efficient four-stage adaptive group testing algorithm for noisy environments that nearly achieves the theoretical minimum number of tests, approaching the capacity limit in low-sparsity scenarios.

Contribution

The paper presents a novel four-stage adaptive testing algorithm that approaches the information-theoretic bounds for noisy group testing with computational efficiency.

Findings

Number of tests close to the information-theoretic bound

Approaches capacity-based converse in low-sparsity regime

Efficient algorithm with practical implementation

Abstract

In this paper, we consider the group testing problem with adaptive test designs and noisy outcomes. We propose a computationally efficient four-stage procedure with components including random binning, identification of bins containing defective items, 1-sparse recovery via channel codes, and a "clean-up" step to correct any errors from the earlier stages. We prove that the asymptotic required number of tests comes very close to the best known information-theoretic achievability bound (which is based on computationally intractable decoding), and approaches a capacity-based converse bound in the low-sparsity regime.