# A Joint Detection and Decoding Scheme for PC-SCMA System Based on Pruning Iteration
## 1 Introduction
### Related Work  
Non-orthogonal multiple access has become the focus of current research, in order to meet the demand of the next generation of mobile communication for large capacity, massive connection, low latency, etc., SCMA is an air interface technology designed in response to the demand of 5G [22; 23; 24]. SCMA can be jointly designed with channel coding and obtain a joint performance gain. However, the decoding delay and complexity will increase since the joint detection and decoding requires feedback iteration. Therefore, improving the error performance of a joint system while reducing the delay and complexity of decoding has become a key research topic. Most of the current research mainly focuses on the turbo code and LDPC code combined with SCMA [25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38]. The authors of [25] first proposed the iterative detection and decoding (IDD) algorithm, and the proposed 'Turbo principles' has been widely applied in joint source and channel decoding [26], and multiuser detection [27; 28]. However, the scheme cannot take full advantage of the SCMA iterative structure and suffers high complexity and decoding delay. In [29], the authors adopted IDD to a turbo coded SCMA system and proposed an iterative scheme based on information reliability to correct external information to reduce error information. In [30], a joint detection and decoding JDD algorithm for the Turbo-SCMA system was proposed, and the Log-JDD algorithm was used to transform the complicated exponential operation into the max operation, which effectively reduced the computational complexity. Additionally, the fully parallel mode FP-JDD scheme proposed by the author can validly improve data throughput. The authors of [31; 32; 33; 34] adopted a JDD scheme to the joint system, which combines LDPC with different technologies. In [35], the authors employed a JDD scheme to the LDPC coded SCMA system and proposed an improved iterative detection and decoding scheme. MPA algorithm was divided into the inherent part and the prior part from the perspective of solving edge functions, and MPA algorithm based on the logarithmic form was derived as an approximate algorithm of MAP, which effectively reduced the computational complexity. The authors of [36] combined RNs, joint user nodes (UNs), and check nodes into a joint factor graph to update messages among the three types of nodes. At the same time, the computation complexity was effectively reduced by the Jacobi approximation algorithm. In [37], the minimum mean square error parallel interference elimination algorithm was proposed, and MPA algorithm based on sphere decoding was used for partial decoding. In [38], the authors ensured ideal system error performance by minimizing the upper limit of the worst performance threshold for decoding. The authors of [39] proposed a joint sparse graph based on the subgraph of the LDPC-SCMA system, and performed joint detection and decoding through message passing between the subsparse graph and LDPC sparse graph. The polar code can achieve Shannon capacity in a specific channel while maintaining ideal computational complexity by using the channel polarization. Therefore, it has a great significance to study how to improve the performance of a PC-SCMA system with different code lengths and reduce the delay and complexity of the receiver. In recent years, more and more attention has been paid to the research on the PC-SCMA system. The authors of [40] proposed a joint detection and decoding algorithm based on the hard decision feedback. This scheme did not fully utilize the soft information in the decoding process of the polar factor graph. Although SCL decoding algorithm has a good BER performance when the search width L is large enough, the decoding delay and complexity have a great space for improvement. In [16], MPA algorithm and BP algorithm were used to detect and decode the polar-SCMA system which significantly improved the system throughput by spreading the soft message in parallel, but the BP algorithm suffers high complexity.