Joint sparse graph over GF(q) for code division multiple access systems

Low-density signature code division multiple access (LDS-CDMA) and low-density parity-check (LDPC) code can both be represented by a single sparse graph. In this study, the authors propose a joint sparse graph (JSG) over GF(q) which combines LDS-CDMA and non-binary LDPC codes, namely JSG-CDMA. On the JSG, multiple accessing and channel coding are well-linked together, in addition, joint detection and decoding are performed by message passing algorithm. Two schedules for message updating on the JSG, that is, flooding and serial schedules, are, respectively, presented. To predict the convergence behaviour of the joint detection and decoding, they depict the iterative structure of the JSG-CDMA receiver and analyse its extrinsic information transfer chart. Key factors of JSG-CDMA include message passing schedule, maximum iteration number and Galois field order. Simulation results show that JSG-CDMA performs much better than conventional CDMA, in addition, compared with LDS-CDMA and turbo structured LDS-CDMA, at a bit error rate of 3 × 10^-4, JSG-CDMA brings about 1.9 and 1.1 dB gain, respectively.