This paper considers the problem of Quantitative Group Testing (QGT). Consider a set of N items among which K items are defective. The QGT problem is to identify (all or a sufficiently large fraction of) the defective items, where the result of a test reveals the number of defective items in the tested group. In this work, we propose a non-adaptive QGT scheme using sparse graph codes over bi-regular bipartite graphs and binary t-error-correcting BCH codes. The proposed scheme provides exact recovery with probabilistic guarantee, i.e. recovers all the defective items with high probability. In particular, we show that for the sub-linear regime where K N vanishes as K, N → ∞, the proposed scheme requires at most m ≈ 1.19K log 2 4.74 N K tests to recover all the defective items with probability approaching one as K, N → ∞. This bound can be achieved by t = 2. The testing and recovery algorithms of the proposed scheme for any t ≤ 4 have the computational complexity of O(K log 2 N K ) and O(K log N K ), respectively. Our simulation results also show that the proposed scheme significantly outperforms a non-adaptive semi-quantitative group testing scheme recently proposed by Abdalla et al. in terms of the required number of tests for identifying all the defective items with high probability.
Recently, in REF , we proposed the first nonadaptive QGT scheme for the sub-linear regime that requires m ≈ 1.19K log 4.74 N K tests to recover all the defective items with probability approaching 1.
Sparse Graph Codes for Non-adaptive Quantitative Group Testing
2019 IEEE Information Theory Workshop (ITW)
2019 IEEE Information Theory Workshop (ITW)
Mathematics Computer Science