Noisy group testing: An information theoretic perspective

The fundamental task of group testing is to recover a small distinguished subset of items from a large group while efficiently reducing the total number of tests (measurements). The key contribution of this paper is in adopting a new information-theoretic perspective on group testing problems. Establishing its connection to Shannon-coding theory, we formulate the group testing problem as a channel coding/decoding problem and derive a unifying result that reduces many of the interesting questions to computation of a mutual information expression. This result is fairly general; it allows us to verify existing bounds for some of the known scenarios and extend the analysis to many new interesting setups including noisy versions of group testing. Among the models we consider are the deterministic noise-free case, approximate reconstruction with bounded distortion, additive measurement noise, and dilution models.