# Improving Polar-Coded SCMA System by Information Coupling and Parity Check
## 1 Introduction  
With the rapid increasing demand of the future mobile wireless network, new requirements are put forward for the communication technologies and the applications. The typical application scenarios of the fifth generation (5G) wireless networks consist of enhanced Mobile BroadBand (eMBB), massive Machine Type Communications (mMTC) and Ultra-Reliable and Low Latency Communications (URLLC). For 5G scenarios, the non-orthogonal multiple access (NOMA) has been proposed to increase the system throughput and accommodate massive communication connectivity. Moreover, as opposed to orthogonal multiple access (OMA), the NOMA has low transmission latency and signaling cost. Recently, many NOMA schemes were proposed for 5G, such as the sparse code multiple access (SCMA) [1], pattern division multiple access (PDMA) [2], multi-user shared access (MUSA) [3], low-density signatures (LDS) multiple access [4], and so on. Among the available NOMA schemes, SCMA is a coding-based multiplexing scheme, which can achieve an obvious increase in spectral efficiency compared to OMA. Its codes are mapped to multi-dimensional sparse codebooks for transmission. Due to the sparsity of the codebook, the message passing algorithm (MPA) [5] with moderate complexity can be used for multi-user detection (MUD). Actually, the quality of service (QoS) of NOMA system can be realized by using effective channel coding. Turbo code and low-density parity-check (LDPC) code are studied in many existing NOMA systems for the error correction [6,7]. Furthermore, according to the results in [7], the new radio (NR) LDPC-coded NOMA schemes have almost the same block error rate (BLER) performance as the corresponding Turbo-coded NOMA schemes. Polar code proposed by [PERSON] [8] is the first constructive code that provably achieves the symmetric capacity of binary-input memoryless channels (BMCs). In [8], [PERSON] proposed a hard-output successive cancellation (SC) decoder that achieved capacity in the limit of large block length; its performance with finite-length codes was less promising. [PERSON] and [PERSON] proposed the successive cancellation list (SCL) algorithm whose performance is very close to that of a maximum likelihood decoder [9]. SCL decoding not only improves the block-error probability of polar code, but also enables one to use modified polar code constructed by concatenating a polar code with a cyclic redundancy check (CRC) code as an outer code [10; 11]. The simulation results demonstrate that the short-block-size polar code with CRC-aided (CA) SCL has performance advantage over the corresponding LDPC code. Although all of these decoders offer better performance than the SC decoder, none provides the soft outputs essential for turbo-based receivers. Improving the performance of the SC decoder has been at the key of the related research while the generation of soft information. In [12], the belief propagation (BP) decoder is proposed to decode polar code. It has the advantages of having better performance than the SC decoder and providing soft outputs, but has very high storage and processing complexity. In [13], the authors developed a low-complexity soft-output version of the SC decoder called the soft cancellation (SCAN) decoder that produces reliability information for both the coded and message bits. The SCAN decoder achieves comparable performance with far less complexity and storage than the BP decoder. However, it cannot achieve the performance of SCL decoder with large list size. According to 3 GPP TS 38.212 [14], polar code is elected as the standard coding technique for the control channel in support of the eMBB service, since it has an excellent error-correction capability based on SCL decoding, especially for short-length packet transmissions. With the abundant research results of polar code, the application of polar code in NOMA system has also made progress. In [15], a polar-coded SCMA (PC-SCMA) was proposed, but there is no iteration between the MPA detector and the polar decoder.