## 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 ≤ 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.

Original language | English |
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Article number | 8827291 |

Pages (from-to) | 5775-5784 |

Number of pages | 10 |

Journal | IEEE Transactions on Signal Processing |

Volume | 67 |

Issue number | 22 |

DOIs | |

Publication status | Published - 15 Nov 2019 |

## Keywords

- Compressed sensing
- error probability
- parameter estimation
- sparse matrices