The Noisy Quantitative Group Testing Problem
Information Theory
2026-04-21 v2 math.IT
Abstract
In this paper, we study the problem of quantitative group testing (QGT) and analyze the performance of three models: the noiseless model, the additive Gaussian noise model, and the noisy Z-channel model. For each model, we analyze two algorithmic approaches: a linear estimator based on correlation scores, and a least squares estimator (LSE). We derive upper bounds on the number of tests required for exact recovery with vanishing error probability, and complement these results with information-theoretic lower bounds. In the additive Gaussian noise setting, our lower and upper bounds match in order.
Cite
@article{arxiv.2601.11797,
title = {The Noisy Quantitative Group Testing Problem},
author = {Tenghao Li and Neha Sangwan and Xiaxin Li and Arya Mazumdar},
journal= {arXiv preprint arXiv:2601.11797},
year = {2026}
}