The Noisy Quantitative Group Testing Problem
Provides theoretical performance bounds for quantitative group testing, a problem relevant to biological and communication systems.
The paper studies quantitative group testing under noiseless, additive Gaussian noise, and noisy Z-channel models, deriving matching upper and lower bounds on the number of tests required for exact recovery in the Gaussian case.
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.