# An Efficient Quantized Message Passing Receiver Design for SCMA Systems
## 1 Introduction  
The upcoming beyond fifth-generation and six-generation wireless networks [1, 2] are expected to support hundreds of billions of nodes in the Internet of Things (IoT) [3, 4, 5], such as the cognitive sensors as well as those found in remote driving [6] and virtual reality, to mention a few. To satisfy the demands of massive connectivity, high throughput and low latency in this IoT scenario, non-orthogonal multiple access (NOMA) [7, 8, 9, 10] has been identified as one of the key physical layer technology to provide higher spectral efficiency and support more connectivities, compared to traditional orthogonal multiple access schemes adopted in the existing 5G systems. The philosophy of NOMA is to allow the simultaneous data transmission for multiple nodes at the same time and frequency resources, and it can be roughly divided into two categories, that is, power domain NOMA (PD-NOMA) and code domain NOMA [11, 12, 13, 14]. In PD-NOMA, distinct transmit power levels are assigned to active users, followed by the superposition coding to multiplex, and the successive interference cancellation technology is applied to eliminate the interference from users with higher power levels in order to detect the transmit symbols of the intended user. Sparse code multiple access (SCMA) [15, 16, 17, 18], multiple user shared access, pattern division multiple access, and interleave division multiple access are several typical schemes of the code domain NOMA [19, 20]. In the past decade, significant attention has been directed toward the SCMA, which can be overloaded to enable massive connectivity and achieve high spectrum efficiency. The fundamental principle of SCMA involves mapping the information bits of each user to complex muti-dimensional sparse codewords from itspre-allocated unique codebook and decoding the transmit bits of different users by using the factor-graph-based message passing algorithm (MPA) detector [21]. In communication systems, it has been verified that SCMA can achieve a better sum rate [18] and bit error ratio (BER) [22] performance than PD-NOMA due to the shaping gain of its codewords at the cost of more computational complexity. In this way, various efforts have been made to explore low complexity MPA detectors for SCMA. The original MPA exchanges the message of resource nodes and variable nodes until the maximum number of iterations, which involves redundant calculations. To this end, the authors in [23] present a threshold-based scheme where the reliability of every codeword is computed in each iteration to judge whether the belief threshold is reached. Based on partial marginalization (PM), a fixed low complexity SCMA detector is proposed in [24], in which \(t\) symbols are fixed in the \(m\)-th iteration and the computations corresponding to these \(t\) symbols are not required in the rest iterative calculations. To further reduce its computational complexity, an improved PM-MPA detector [25] is proposed by updating the message more efficiently than the original PM-MPA [24] to obtain reliable codewords. To accelerate its convergence, a shuffled MPA has been proposed in [26] by immediately propagating the updated message between resource nodes and variable nodes in the current iteration. In addition, the authors in [27] also provide a residual-aided message exchanging procedure for scheduling messages in the asynchronous message passing algorithm detector by exploiting the message with the largest residual. The ascending order of the above serial scheduling strategy is not the best selection. In this way, an improved serial scheduling-based MPA method [28] is provided by taking advantage of the most reliable message updates in a timely manner. To address the computational cost challenge in the design of downlink multiple-input multiple-output SCMA systems, the parallel and serial schedules are considered to strike a balance between detector complexity and latency [29].