Strong converses for group testing in the finite blocklength regime

We prove new strong converse results in a variety of group testing settings, generalizing a result of Baldassini, Johnson and Aldridge. First, in the non-adaptive case, we mimic the hypothesis testing argument introduced in the finite blocklength channel coding regime by Polyanskiy, Poor and Verdu, and using joint source–channel coding arguments of Kostina and Verdu. In the adaptive case, we combine this approach with a novel model formulation based on causal probability and directed information theory. 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.