The Capacity of Adaptive Group Testing

TL;DR

This paper introduces a theoretical framework for the capacity of adaptive group testing, deriving bounds for noisy models and analyzing the limits of noiseless and erasure testing using information theory.

Contribution

It defines the capacity for adaptive group testing and provides new bounds, improving upon previous results and analyzing the limits of existing algorithms.

Findings

Derived capacity bounds for noisy group testing models.

Proved a tighter lower bound for noiseless adaptive group testing.

Analyzed the capacity of erasure group testing models.

Abstract

We define capacity for group testing problems and deduce bounds for the capacity of a variety of noisy models, based on the capacity of equivalent noisy communication channels. For noiseless adaptive group testing we prove an information-theoretic lower bound which tightens a bound of Chan et al. This can be combined with a performance analysis of a version of Hwang's adaptive group testing algorithm, in order to deduce the capacity of noiseless and erasure group testing models.