# An Efficient Quantized Message Passing Receiver Design for SCMA Systems
## 1 Introduction
To enhance the bit error ratio (BER) performance of the SCMA, a scaling factor is introduced to compress likelihood messages [30] to solve the overestimation problem of the iterative multiuser SCMA receiver. By using the lookup table, two variances of the original MPA are provided [31], and these can balance a trade-off between computational complexity and BER performance. The idea of stochastic computing has been introduced into MPA [32] to design novel stochastic logic architectures by carrying out complex computations with very simple logics. In practical, it is essential to integrate SCMA with multi-carrier waveforms to investigate its effectiveness [33; 34]. To tackle the peak-to-average power ratio of SCMA combined with orthogonal frequency division multiplexing, a novel clipping noise aided MPA has been taken into consideration for decoding more accurately [33]. By means of the frequency domain implementation of the generalized frequency-division multiplexing (GFDM), a low complexity detection for SCMA-GFDM [34] has been established by applying the discrete Fourier transform operation. Apart from many solutions for reducing the computational complexity of the conventional MPA, there are several other approaches developed for SCMA detection. By utilizing the lattice structure of its codewords, a low-complexity list sphere decoding has been proposed by avoiding the exhaustive search for all possible hypotheses [35]. Inspired by the Tikhonov regularization, a reduced-complexity optimal modified sphere decoding scheme is provided in [36] by exploiting the sparse structure of the SCMA codebook. The authors in [37] put forward a novel low complexity solution for SCMA detection by adopting an appropriate parameter to narrow down the range of believable superposed constellation points. By sorting the channel matrix and computing a non-zero low bound before searching [38], the proposed modified single tree search-based SCMA detection scheme has lower computational complexity but achieves nearly the same BER performance as compared to the original MPA. However, the above mentioned sphere-decoding-baseddetectors can only be applied to SCMA with a certain structure of constellations. To address this issue, an improved sphere decoding scheme for SCMA has been provided, and this can serve any arbitrary regular or irregular constellations with the same BER performance as an optimal maximum likelihood detector [39]. Efforts to address the integration of SCMA with other physical techniques, such as multiple-input multiple-output, orthogonal time frequency space, and satellite communications, can be found in [40; 41; 42; 43; 44]. Despite many solutions for floating-point SCMA detectors, this paradigm has just emerged for a fixed-point SCMA system [45; 46; 47], which is more practical for hardware design and implementation. The pioneering work in [45] designs a unified quantization scheme independent of signal-to-noise ratios where the resource nodes' and variable nodes' message exchanging are processed synchronously to converge faster. A low complexity attempt has been reported in [46] in the sense that domain changing, probability approximation, early termination, adaptive decoding, and initial noise reduction are employed for SCMA detection, which generates the deterministic message passing algorithm. Moreover, a row-layered message passing algorithm has been provided in [47], which offers a good trade-off between the hardware implementation and BER performance. However, the above structures only consider the uniform quantization strategy, which suffers high complexity or BER degradation in implementations. In particular, the quantization precision is relatively high in order to achieve considerable BER performance; otherwise, the BER suffers a large degradation when using low quantization precision. To this end, we propose a new quasi-uniform quantizer for the SCMA system instead of the standard uniform one.