# Improving Polar-Coded SCMA System by Information Coupling and Parity Check
## 1 Introduction
However, for practical implementations, the iterative detection between the multiuser detector and the channel decoder can improve the performance of the SCMA system. In [16], a three-stage channel transform structure of the polar-coded NOMA system was proposed, and a joint successive cancellation (JSC) detection and decoding scheme was designed. Although the JSC algorithm improves the performance of the system, it increases the processing latency. In [17], based on the joint factor graph of SCMA and polar code, the authors have proposed a joint iterative detection and decoding (JIDD) receiver based on SCAN algorithm. The JIDD without inner iterations has best performance when compared with the general iterative detection and decoding (IDD) scheme. It improves the performance of the polar-coded sparse code multiple access (PC-SCMA) system significantly while also saving the complexity costs. However, since the performance of SCAN decoder is not good enough, this JIDD receiver is not ideal. In particular, the performance of the PC-SCMA system is worse than that of LDPC-coded SCMA (LDPC-SCMA) at low code rate. In order to improve the performance of PC-SCMA, the design of the code's structure and decoding algorithm are feasible. One approach that leads to better performance is to exploit the benefits of long code through spatial coupling. Theoretically, an infinite long codeword chain can be constructed by coupling an infinite number of finite length code blocks (CBs) in a certain structure. For long data sequence transmission, a class of partially information-coupled (PIC) Turbo code [18] and PIC LDPC code [19] have been proposed. In these schemes, a transport block (TB) is segmented into several finite-length CBs under the practical decoding complexity and decoding latency constraints. Every two consecutive codes blocks in a TB are coupled by sharing a few information bits. Thus, PIC code can also be regarded as a class of spatially coupled code. PIC polar code was also constructed by systematic polar code in [20], and a windowed decoder based on CA-SCL algorithm is used for decoding. The TB error rate (TBER) results show that the PIC polar code achieves approximately 0.3 dB coding gain over the uncoupled counterparts for variable code rates. Importantly, the PIC polar code also outperforms the PIC Turbo code at a high \(E_{\text{b}}/N_{0}\). Basis of this, in this paper, we consider improving the SCMA system by PIC polar code. Though the code construction of PIC polar code is straightforward, it is very challenging to obtain the promised coding gain over SCMA system compared to [17]. First, the coding gain of PIC polar code proposed in [20] is limited. To achieve more coding gain, one straightforward approach is to improve the code block error rate (CBER) of each CB. In the 3 GPP meetings, various \"assistant bits + basic polar\" schemes have been proposed. The idea of \"using assistant bits for polar decoding\" has been widely adopted, including CA-polar code [21], joint parity-check and CRC-aided (PCCA) polar code [22; 23], Hash-CRC polar code [24], and distributed CRC-aided (DCA)polar code [25; 26; 27]. The various solutions differ in terms of number of assistant bits, their usage (for error detection and/or correction), positions, and values. Especially, the PCCA-polar code uses the parity check bits for error correction in SCL decoder and gets better performance than other codes. Simultaneously, the Hash-CRC polar code and DCA-polar code have comparable performance to the CA-Polar code. By the way, the systematic polar code that was used in [20] is CA-polar code. To improve the performance of PIC polar code, PCCA-polar code can be considered as the base code. However, the design of the PCCA-polar code in the systematic form must be resolved. Second, besides the feed-back decoding mechanism based on coupling information bits, the reason why the PIC polar code can obtain excellent performance is that it uses the SCL algorithm for the basic decoder.