Improved Bounds For Efficiently Decodable Probabilistic Group Testing With Unreliable Items

This work uses non-adaptive probabilistic group testing to find a set of L defective items out of n items. In contrast to traditional group testing, in the considered setup each item can hide itself (or become inactive) during any given test with probability 1-α and is active with probability α. The authors of [Cheraghchi et al.] proposed an efficiently decodable probabilistic group testing scheme which requires (L log (n)/α3) tests for the per-instance scenario (where the group testing matrix works for any arbitrary, but fixed, set of L defective items) and (equation presented) tests for the universal scenario (where the same group testing matrix works for all possible defective sets of L items). The contribution of this work is two-fold: (i) with a slight modification in the construction of the group testing matrix proposed by [Cheraghchi et al.], the corresponding bounds on the number of sufficient tests are improved to t(L log (n)/α2) and (equation presented) for the per-instance and universal scenarios respectively, while still using their efficient decoding method; and (ii) it is shown that the same bounds also hold for the fixed pool-size probabilistic group testing scenario, where in every test a fixed number of items are included for testing.