Sublinear decoding schemes for non-adaptive group testing with inhibitors

Identification of up to $d$ defective items and up to $h$ inhibitors in a set of $n$ items is the main task of non-adaptive group testing with inhibitors. To efficiently reduce the cost of this Herculean task, a subset of the $n$ items is formed and then tested. This is called \textit{group testing}. A test outcome on a subset of items is positive if the subset contains at least one defective item and no inhibitors, and negative otherwise. We present two decoding schemes for efficiently identifying the defective items and the inhibitors in the presence of $e$ erroneous outcomes in time $\mathsf{poly}(d, h, e, \log_2{n})$, which is sublinear to the number of items $n$. This decoding complexity significantly improves the state-of-the-art schemes in which the decoding time is linear to the number of items $n$, i.e., $\mathsf{poly}(d, h, e, n)$. Moreover, each column of the measurement matrices associated with the proposed schemes can be nonrandomly generated in polynomial order of the number of rows. As a result, one can save space for storing them. Simulation results confirm our theoretical analysis. When the number of items is sufficiently large, the decoding time in our proposed scheme is smallest in comparison with existing work. In addition, when some erroneous outcomes are allowed, the number of tests in the proposed scheme is often smaller than the number of tests in existing work.