# A Joint Detection and Decoding Scheme for PC-SCMA System Based on Pruning Iteration
## 1 Introduction  
Polar code is a kind of channel coding theory that has been strictly proved to reach the Shannon capacity in the binary-discrete memoryless channel (B-DMC). As a standard control channel coding scheme which supports enhanced mobile broadband, polar code has excellent error correction performance and lower coding and decoding complexity than turbo code and low density parity check (LDPC) code [1]. Sparse code multiple access (SCMA) merges the high-dimensional modulation and sparse spreading spectrum during the transmission, and directly maps the encoded interleaved bits to a multidimensional codeword in the complex field preset in the codebook, so as to obtain a higher overload [2; 3]. At the receiver, the message passing algorithm (MPA) take the place of the traditional maximum a posterior probability (MAP) detection to obtain the approximate error performance with a lower complexity due to the sparsity of SCMA code [4; 5; 6]. Decoding methods of the polar code mainly have two categories: the first type is the soft-input hard-output (SIHO) decoding based on the traditional successive cancellation (SC) algorithm [7; 8], such as successive cancellation list (SCL) [9], successive cancellation stacking (SCS) [10], and successive cancellation hybrid (SCH) [11] algorithm. Additionally, the second type is the soft-input soft-output (SISO) decoding, such as belief propagation (BP) [12; 13] and soft cancellation (SCAN) [14; 15] algorithm. In practical applications, SCMA needs to combine with channel coding technology to obtain a better quality of service, which includes turbo code, LDPC code, and polar code. Polar code implementations are less complicated and more versatilethan turbo code for channels with relatively low throughput, but polar code lacks market maturity compared with turbo code and LDPC code, and faces greater challenges especially for high-throughput channels. The non-orthogonal resource allocation approach for SCMA scenarios can provide large scale connections and greater throughput. Previous studies have shown that SCMA and polar coding can be designed jointly, which has a significant effect on increasing system capacity and obtaining a certain joint performance gain. Therefore, the study of SCMA combined with polar code detection decoder has profound significance for the overall performance improvement of the communication system. In the existing research, polar code SCMA (PC-SCMA) receiver detection scheme includes separate and joint decoding schemes [15; 16; 17; 18]. The SCMA detection and polar decoding are carried out separately for the separate scheme, while the joint scheme iteratively updates the messages between the detector and decoder. At present, the proposed joint scheme mainly includes the joint algorithm which combines MPA and BP, the joint iterative detection and decoding algorithm (JIDD), and the serial joint algorithm S-JIDD. For the separate detection and decoding scheme, since the intermediate messages cannot be fully utilized, the receiver would not achieve ideal error performance and the computational complexity is relatively high. However, attributed to performing external iteration and minimizing the loss of intermediate messages, the system performance can be effectively improved by the joint detection and decoding method. Further, since the \"hard\" feedback will lose information during the decoding process, which limits the performance of the system at the same time the joint detection and decoding cannot be performed, the PC-SCMA receiver must be SISO. In [16], the intermediate messages can be fully utilized to improve the system performance by the joint algorithm which combines MPA with BP decoding, and soft messages can be propagated in parallel for higher data throughput. However, the BP scheme suffers high computational complexity in the process of internal iteration, which also leads to a large decoding delay. In addition, it takes dozens or even hundreds of iterations for the BP algorithm to converge.