A Low-Complexity SCMA Detector Based on Discretization

As a new multiple access technique, sparse code multiple access (SCMA) combines quadrature amplitude modulation mapper and spreading together and thus significantly improves spectral efficiency. However, the computation complexity of most existing detection algorithms increases exponentially with $d_{f}$ (the degree of the resource nodes). The parameter $d_{f}$ must be designed to be very small, which largely limits the choice of codebooks. Even if the codebooks are designed to have low density, the detection still takes considerable time. In this paper, a new detection algorithm is proposed by discretizing the probability density functions (PDFs) in the layer nodes. Actually, the PDFs are updated according to the constraints in the factor graph after discretization. Compared with the conventional message passing algorithm (MPA) detector, the proposed detector only takes polynomial time to update one message in resource nodes instead of exponential time with negligible performance loss. In particular, it only needs near-linear time, if the real part is independent with the imaginary part in SCMA system. Furthermore, this paper presents a new design for codebooks by greedy strategy and exhaustive search in each step. The search is feasible with the help of discretization, and the resulting codebooks have good performance in the proposed detection algorithm, as well as in the conventional MPA.