Strong Converses for Group Testing From Finite Blocklength Results

We prove new strong converse results in a variety of group testing settings, generalizing a result of Baldassini et al.. First, in the non-adaptive case, we mimic the hypothesis testing argument introduced in the finite blocklength channel coding regime by Polyanskiy et al., and using joint source-channel coding arguments of Kostina and Verdú. 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.