# Improving Polar-Coded SCMA System by Information Coupling and Parity Check
## 1 Introduction
In iterative receiver, in order to iteratively exchange their messages between the constituent MPA detector and polar decoder, they must be soft-input-soft-output (SISO). Therefore, the hard-output decoding algorithms such as SCL cannot be directly applied to the iterative receiver. The calculation of the extrinsic messages of the coupled polar decoder remains to be resolved. Third, with the coupled polar decoder, increasing the basic decoder's list size can improve the performance of the system, but it also increases the decoding complexity. On the premise of guaranteeing the performance, the complexity of the receiver should be reduced as far as possible. On the basis of above discussing, the main contributions of this paper can be summarized as follows:  
* The uplink information-coupled PC-SCMA system is proposed. At the transmitter, channel coding, SCMA mapping, and transmission are all performed based on CB. When the entire TB is received, the receiver performs iterative detection and decoding. * The PCCA-polar code in system form is designed. Then, every two consecutive systematic PCCA-polar code blocks are connected by information coupling technology to form a new type of PIC polar code. For windowed decoder, the list algorithm based on parity check can provide more accurate extrinsic messages for the coupling CBs. In addition, the windowed decoding algorithm is improved for the requirement of iterative system. * An extrinsic messages construction algorithm of coupled polar decoder is proposed. This algorithm enables the coupled polar decoder to exchange extrinsic messages with the MPA detector, and achieving iterative detection and decoding. * A joint iterative detection and SCL decoding algorithm (JIDS) based on variable list size is designed. During the iteration, those CBs who failed CRC verification improved the performance in the next iteration by increasing the list size, while others maintained a smaller list size. In addition, when all CBs are correctly decoded, the iteration is stopped immediately. * The extrinsic information transfer (EXIT) idea is used to optimize the weight factor of extrinsic messages construction algorithm and coupling ratio of PIC PCCA-polar code. The rest of this article is organized as follows. In Section 2, the system model of uplink information-coupled PC-SCMA is described. In Section 3, the characteristics of systematic PCCA-polar code are analyzed, and the corresponding encoding algorithm is introduced. Then, the construction method of PIC PCCA-polar code is proposed. In Section 4, a joint iterative detection and SCL decoding algorithm with variable list size is proposed to reduce the complexity. The extrinsic messages of coupled polar decoder are constructed and applied to the receiver. Based on EXIT idea, the transfer characteristics of various polar decoders are analyzed, and the PIC PCCA-polar code is optimized in Section 5. Section 6 shows the simulation results and the complexity comparison. Finally, conclusions are reached in Section 7. To read this article better, we summarize the abbreviations in Table 1.