1. Hypothesis Test for Bounds on the Size of Random Defective Set.
- Author
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D'yachkov, Arkadii, Polyanskii, Nikita, Shchukin, Vladislav, and Vorobyev, Ilya
- Subjects
RANDOM sets ,ERROR probability ,DECODING algorithms ,RANDOM numbers ,HYPOTHESIS ,SPARSE matrices - Abstract
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 $\leq s_1$ against the alternative hypothesis $H_1$ : the number of defectives $\geq s_2$. 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. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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