Sub-Graph Based Joint Sparse Graph for Sparse Code Multiple Access Systems

Sparse code multiple access (SCMA) is a promising air interface candidate technique for next-generation mobile networks, especially for massive machine-type communications. In this paper, we design a low-density parity-check (LDPC) coded SCMA detector by combining the sparse graphs of LDPC and SCMA into one joint sparse graph (JSG). In our proposed scheme, the SCMA sparse graph defined by small size indicator matrix is utilized to construct the JSG, which is termed as sub-graph-based JSG of SCMA (SG-JSG-SCMA). In this paper, we first study the binary-LDPC coded SG-JSG-SCMA system. To combine the SCMA variable node and LDPC variable node into one joint variable node, a non-binary LDPC (NB-LDPC) coded SG-JSG-SCMA is also proposed. Furthermore, to reduce the complexity of NB-LDPC coded SG-JSG-SCMA, a joint trellis representation (JTR) is introduced to represent the search space of NB-LDPC coded SG-JSG-SCMA. Based on JTR, a low complexity joint trellis-based detection and decoding algorithm is proposed to reduce the computational complexity of the NB-LDPC coded SG-JSG-SCMA system. According to the simulation results, SG-JSG-SCMA brings significant performance improvement compare with the conventional receiver using the disjoint approach, and it can also outperform a turbo-structured receiver with comparable complexity. Moreover, the joint approach also has advantages in terms of processing latency compare with the turbo approaches.