Hypothesis Test for Bounds on the Size of Random Defective Set

The conventional model of disjunctive group testing assumes that there are several defective elements (or defectives) among a large population, and a group test yields the positive response if and only if the testing group contains at least one defective element. The basic problem is to find all defectives using a minimal possible number of group tests. However, when the number of defectives is unknown there arises an additional problem, namely: how to estimate the random number of defective elements. In this paper, we concentrate on testing the hypothesis H
₀
: the number of defectives ≤ s
₁
against the alternative hypothesis H
₁
: the number of defectives ≥ s
₂
. We introduce a new decoding algorithm based on the comparison of the number of tests having positive responses with an appropriate fixed threshold. For some asymptotic regimes on s
₁
and s
₂
, the proposed algorithm is shown to be order-optimal. Additionally, our simulation results verify the advantages of the proposed algorithm such as low complexity and a small error probability compared with known algorithms.