The Noisy Quantitative Group Testing Problem

Tenghao Li; Neha Sangwan; Xiaxin Li; Arya Mazumdar

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arXiv · 2601.11797

The Noisy Quantitative Group Testing Problem

Tenghao Li·Neha Sangwan·Xiaxin Li·Arya Mazumdar

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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.

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Tenghao Li, Neha Sangwan, Xiaxin Li, Arya Mazumdar. 2026-01-16. The Noisy Quantitative Group Testing Problem. https://arxiv.org/abs/2601.11797

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