The Construction of Disjunct Matrix for Non-Adaptive Group Testing

Grant-Free Transmission by LDPC Matrix Mapping and Integrated Cover-MPA Detector

“…Inspired by [21], again, active user identification is regarded as a group testing problem in this paper. But its performance is improved by us through two aspects: a) instead of disjunct matrices [22], [23], the protocol sequence used in the cover decoder which is obtained from a properly constructed LDPC parity-check matrix; b) not only the cover decoder but also the belief propagation (BP) decoder are employed in group testing procedure, where the later enable the receiver to iteratively update S based on the feedbacks from data decoder.…”

“…Spreading matrix optimization in the background of cover decoder applications has been studied in [22], [23], where it was also termed the non-adaptive group testing (GT) problem.…”

“…Moreover, in these studies, a noiseless case where Î = I is assumed in the optimization process of the spreading matrix. It was proved in [22], [23] that in order to minimize the active user identification error, which could be quantified by | Ûa ac (I) − U a ac |, spreading matrix has to be a disjunct matrix. With the aid of the disjunct matrix based design of spreading matrix, error-free active user identification becomes possible.…”

“…Proposing such a solution of GT problem in [22], [23] is owing to an underlying constraint that they have to accomplish active user identification in once chance, i.e. only through the cover decoder.…”

“…How to coordinate the channel access patterns of all the coexisted users for supporting more simultaneously activated users is still an important open problem [22], [23]. In [24], a more radical solution was proposed, which even did not have an explicit active user identification stage.…”