The Noisy Quantitative Group Testing Problem
🤖 AI Summary
This work addresses the problem of quantitative group testing in noisy environments, with a focus on exact signal recovery under three noise models, including additive Gaussian noise and the Z-channel. By integrating a correlation-score-based linear estimator with a least-squares estimator and complementing the approach with information-theoretic analysis, the study derives an upper bound on the number of tests required to achieve vanishing error probability. The key contribution lies in establishing, for the first time, an order-wise matching between this upper bound and the information-theoretic lower bound in the additive Gaussian noise model. This result yields a tight information-theoretic limit, providing a fundamental theoretical benchmark for quantitative group testing under noise.
Application Category
📝 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.
Problem
Research questions and friction points this paper is trying to address.
Quantitative Group Testing
Noisy Group Testing
Additive Gaussian Noise
Z-channel
Exact Recovery
Innovation
Methods, ideas, or system contributions that make the work stand out.
Quantitative Group Testing
Additive Gaussian Noise
Least Squares Estimator
Information-Theoretic Bounds
Exact Recovery
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