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.
|Original language||English (US)|
|Title of host publication||2023 IEEE Information Theory Workshop, ITW 2023|
|Publisher||Institute of Electrical and Electronics Engineers Inc.|
|Number of pages||6|
|State||Published - 2023|
|Event||2023 IEEE Information Theory Workshop, ITW 2023 - Saint-Malo, France|
Duration: Apr 23 2023 → Apr 28 2023
|Name||2023 IEEE Information Theory Workshop, ITW 2023|
|Conference||2023 IEEE Information Theory Workshop, ITW 2023|
|Period||4/23/23 → 4/28/23|
Bibliographical noteFunding Information:
This research was supported in part by the U.S. National Science Foundation under Grant CCF-1907785. The authors would also like to thank Dr. M. Cheraghchi for discussing the improved bound, and his encouragement to submit this work.
© 2023 IEEE.