# A Joint Detection and Decoding Scheme for PC-SCMA System Based on Pruning Iteration
## 1 Introduction
As a parallel confidence propagation algorithm, SCAN has lower computational complexity and faster convergence speed while maintaining ideal error performance. Furthermore, SCAN only needs a few iterations to achieve the same performance results as BP [15]. The authors of [17] proposed a JIDD, where messages are updated through the external iteration between the MPA and SCAN algorithm, and it improved the convergence speed and efficiently reduced the computational complexity. JIDD provides a good foundation for the design of PC-SCMA joint receiver. However, its error performance and computational complexity still have great room for improvement. In [18], a serial JIDD algorithm S-JIDD is proposed to accelerate the convergence speed by updating the messages serially, and reduce the computational complexity effectively without losing the error performance. The serial algorithm changes the messaging pattern of the factor graph, but the redundant information during the update process is not taken into account, and the S-JIDD treats all transmitted information as equally important. However, during the message passing process of the factor graph, different branches converge at different rates, and not all messages are equally useful to convergence for the JIDD. Furthermore, its performance can be further improved [19]. In this paper, a joint detection and decoding scheme PI-JDD based on the pruning iteration is proposed. During each iteration, branches to update messages are selected according to the confidence stability of the resource node (RN), before the next iteration, the system factor graph is dynamically updated, and the branches with large deviation in adjacent iterations are propagated in priority which ensures that the unreliable messages are propagated first. Furthermore, the branches closest to convergence are pruned and external messages transmitted reduce as the iteration progresses, which can accelerate the decoding convergence and effectively reduce the computational complexity. Secondly, too low SNR might lead to a convergence error during the iteration process [20; 21]. In order to avoid the decoding deviation and further reduce the BER, we add a cyclic redundancy check (CRC) early stopping condition at the end of the joint detection and decoding process to lock the correct codeword timely, and quit the decoding iteration process once the check passes. Finally, the joint algorithm PIC-JDD which combines the PI-JDD and CRC early stopping condition can effectively improve the joint detection and decoding performance with a lower computation complexity. Simulation results show that the proposed joint optimization algorithm achieves significant BER performance gain when the code lengths are 256 and 1024, respectively. Compared with the traditional S-JIDD algorithm, the PIC-JDD algorithm can use five iterations to reach the same error performance of traditional algorithm in seven iterations. Further, in terms of the computational complexity, the PIC-JDD can reduce about 50% addition and 24% multiplication operations when the number of iterations is seven. The main structure of this paper is stated as follows. Firstly, the system model of the PC-SCMA is introduced. Secondly, the three optimization schemes proposed are described in detail, which are also the main contributions of this paper, including joint detection and decoding scheme based on pruning iteration PI-JDD, the C-JIDD scheme with CRC termination mechanism, and the joint optimization scheme PIC-JDD. Thirdly, the simulation results and performance analysis of the three schemes are presented, respectively. Finally, we summarize the paper and look forward to the future work.