Strong converses for group testing in the finite blocklength regime

TL;DR

This paper establishes new strong converse bounds for group testing in finite blocklength settings, using information-theoretic methods for both adaptive and non-adaptive scenarios, extending previous asymptotic results.

Contribution

It introduces novel finite blocklength strong converse results for group testing, employing hypothesis testing and directed information approaches for adaptive and non-adaptive cases.

Findings

Strong converse bounds valid for finite-sized group testing problems.

Results generalize previous asymptotic capacity results.

Graphical illustrations demonstrate the bounds across models.

Abstract

We prove new strong converse results in a variety of group testing settings, generalizing a result of Baldassini, Johnson and Aldridge. These results are proved by two distinct approaches, corresponding to the non-adaptive and adaptive cases. In the non-adaptive case, we mimic the hypothesis testing argument introduced in the finite blocklength channel coding regime by Polyanskiy, Poor and Verd\'{u}. In the adaptive case, we combine a formulation based on directed information theory with ideas of Kemperman, Kesten and Wolfowitz from the problem of channel coding with feedback. In both cases, we prove results which are valid for finite sized problems, and imply capacity results in the asymptotic regime. These results are illustrated graphically for a range of models.