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Sparse Code Multiple Access (SCMA) is a disruptive code-domain non-orthogonal multiple access (NOMA) scheme to enable future massive machine-type communication networks. As an evolved variant of code division multiple access (CDMA), multiple users in SCMA are separated by assigning distinctive sparse codebooks (CBs). Efficient multiuser detection is carried out at the receiver by employing the message passing algorithm (MPA) that exploits the sparsity of CBs to achieve error performance approaching to that of the maximum likelihood receiver. In spite of numerous research efforts in recent years, a comprehensive one-stop tutorial of SCMA covering the background, the basic principles, and new advances, is still missing, to the best of our knowledge. To fill this gap and to stimulate more forthcoming research, we provide a holistic introduction to the principles of SCMA encoding, CB design, and MPA based decoding in a self-contained manner. As an ambitious paper aiming to push the limits of SCMA, we present a survey of advanced decoding techniques with brief algorithmic descriptions as well as several promising directions.

Sparse code multiple access (SCMA) and multiple input multiple output (MIMO) are considered as two efficient techniques to provide both massive connectivity and high spectrum efficiency for future machine-type wireless networks. However, the computational complexity of the conventional message passing algorithm (MPA) for the downlink MIMO-SCMA detection increases exponentially with the degree of variable nodes (VNs). To address this issue, two novel fixed low complexity MPA detectors are proposed by utilizing the sparse feature of codewords, which are based on the serial schedule strategy in order to accelerate their convergence. First, a maximum distance MPA (MDMPA) detector is introduced to reduce the number of VNs involved in the message updating procedure in the first $T_0$ iterations and fix $TJ_0$ codewords at the $L_0$ iteration, which subsequently drops the redundant codeword combinations in the remaining iterations. To further improve the bit error ratio (BER) performance, an improved MDMPA (IMDMPA) is proposed, in which, the VNs associated with the target user are always allowed to participate in the iterative propagation of message. An efficient linear squares (LS) channel estimation scheme is also derived based on block pilots by stacking all the received signals at the same subcarrier together. Simulation results illustrate that the proposed MDMPA and IMDMPA detectors significantly reduce the computational complexity of the original MPA, but with comparable decoding capabilities, and the proposed LS channel estimator can closely approach the corresponding lower bound over frequency selective channels. [ABSTRACT FROM AUTHOR]

A random access framework based on random interleaving multiplexing (RIM) is proposed to further improve throughput for internet of things in satellite networks, which resort to the state-of-art physical layer techniques that can resolve multiple packet collisions issue. The interleavers are randomly selected by active devices from a set of available interleavers, which are used to differentiate signals of different devices sharing a subframe that consists of multiple time slots. The message passing detector (MPD) is utilized to decode collided packets. By means of transmission diversity and interference cancellation, the proposed scheme can be linked with the irregular repetition slotted ALOHA (IRSA), the RIM-IRSA protocol is proposed. The analysis of packet loss ratio (PLR) of the RIM-IRSA is given by using the density evolution method, and the optimal degree distributions are given. Simulation results show that the RIM-IRSA outperforms traditional IRSA protocol.

Highmobility is an important scenario for the 5G wireless communications. However, the high mobility results in serious time-varying fading, bringing challenges to the reliabilities of wireless transmission. Diversity technique is an essential method to overcome the effect of fading. It is noted that an LDPC (low-density parity-check) code is a concatenation of single parity-check codes (SPC) and repetition codes (REP) by a random interleaver, and a REP can be viewed as a typical example for achieving time/frequency diversity. Thus, it is appealing to jointly consider LDPC codes and diversity techniques. This paper presents parity-check coding transmit diversity (PCTD) schemes based on half-rate invertible LDPC codes, which are capable of achieving both diversity and coding gains from the time-varying fading channels. Besides, we investigate two types of PCTD schemes, and take into consideration two transmission modes, which are single-carrier (SC) and orthogonal frequency division multiplexing (OFDM) transmission modes. A chase combining based message passing algorithm (CC-MPA) is proposed for the proposed schemes, which can take full advantages of signal processing and coding gains. Furthermore, the Shannon limits of time-varying fading channels with BPSK signaling are deduced. Simulation results show that the proposed PCTD with CC-MPA algorithm can provide better BER performances than the classical time-domain diversity scheme in time-varying fading channels, which is appealing for the high mobility communications. [ABSTRACT FROM AUTHOR]

Sparse code multiple access (SCMA) has exhibited superiority in spectrum efficiency, which is particularly essential in the Internet of Things (IoT) system where a steadily increasing number of device connections are accommodated. However, the computational complexity of the conventional message passing algorithm (MPA) for the multiuser SCMA detection increases exponentially with the degree of resource nodes (RNs). To address this issue, two low complexity MPA schemes are proposed by utilizing the sparse feature of codewords. First, a sorted MPA (SMPA) detector is introduced to reduce the message exchanging from RNs to variable nodes (VNs) by dropping the redundant superposed constellation points outside a belief interval. Next, in order to further speed up the sorting process of the Euclidean distances between the received signal and codeword combinations, a deep neural network aided MPA (DNNMPA) is proposed, in which, the DNN behaves as a function approximator to generate the belief interval and operates in parallel with the initialization procedure before iterative message passing. Simulation results illustrate that the proposed SMPA and DNNMPA detectors significantly reduce the computational complexity of the conventional MPA one, but with comparable decoding capabilities, for the uplink SCMA system. [ABSTRACT FROM AUTHOR]

Designing multidimensional constellations (MdCs) is an integral part of sparse code multiple access (SCMA). Since the optimal maximum a posteriori (MAP) receiver for SCMA is too complex in most applications, one highly popular technique is the near-optimal message passing algorithm (MPA), where its performance improves with increasing the signal-to-noise ratio (SNR) and the number of iterations. When the number of MPA iterations has to be limited (e.g., low-latency and/or low-complexity and/or energy-sensitive applications), the performance gap between MAP and MPA becomes significant, especially at low-to-medium SNRs. Inspired by the promising features of hypercubes when used along with bit-interleaved coded modulation, we construct novel MdCs which are based on a unitary rotation of a hypercube by a rotation angle that aims to achieve the minimum frame-error-rate (FER). By exploiting special properties of hypercubes, we fit a second-order rational polynomial to a few measured FER samples, and find a close-to-optimal rotation angle at each SNR and MPA iteration. Our proposed MdCs provide substantial performance gains (as much as 2 dB) in comparison to the best known SCMA MdCs in the literature, especially in low-to-medium SNR regions when the number of MPA iterations has to be low, and in the presence of 5G-compliant LDPC codes. [ABSTRACT FROM AUTHOR]

Multi-user spatial modulation (SM) assisted by sparse code multiple access (SCMA) has been recently proposed to provide uplink high spectral efficiency transmission. The message passing algorithm (MPA) is employed to detect the transmitted signals, which suffers from high complexity. This paper proposes three low-complexity algorithms for the first time to the SM-SCMA. The first algorithm is referred to as successive user detection (SUD), while the second algorithm is the modified version of SUD, namely modified SUD (MSUD). Then, for the first time, the tree-search of the SM-SCMA is constructed. Based on that tree-search, another variant of the sphere decoder (SD) is proposed for the SM-SCMA, referred to as fixed-complexity SD (FCSD). SUD provides a benchmark for decoding complexity at the expense of bit-error-rate (BER) performance. Further, MSUD slightly increases the complexity of SUD with a significant improvement in BER performance. Finally, FCSD provides a near-optimum BER with a considerable reduction of the complexity compared to the MPA decoder and also supports parallel hardware implementation. The proposed algorithms provide flexible design choices for practical implementation based on system design demands. The complexity analysis and Monte-Carlo simulations of the BER are provided for the proposed algorithms. [ABSTRACT FROM AUTHOR]

Similar to conventional orthogonal frequency division multiplexing (OFDM) signal, the signals of sparse code multiple access combine with orthogonal frequency division multiplexing (SCMA-OFDM) existing the problem that its peak-to-average power ratio (PAPR) is unbearable high. In this paper, the clipping method is adopted to reduce the PAPR of the SCMA-OFDM signal. However, the clipping process brings extra noise to the SCMA-OFDM signal while the clipping noise is not taken into account in the message passing algorithm (MPA), which makes the MPA detection inaccurate and leads to a phenomenon that the decoding performance declines sharply with the increasing of Eb/N0. Moreover, due to the distortion of SCMA-OFDM signals caused by clipping process, the system bit error rate (BER) performance degrades obviously. To tackle the issues above, we analyze the random characteristics of the clipping noise for the MPA detection scheme. Then, an iterative clipping noise elimination scheme is proposed to restore the BER performance of clipped SCMA-OFDM system. Simulation results show that our method can remove the phenomenon that the BER performance declines sharply at the high Eb/N0 region and the proposed iterative clipping noise elimination scheme restores the BER performance significantly.

Spatial modulation (SM) sparse code multiple access (SCMA) systems provide high spectral efficiency (SE) at the expense of using a high number of transmit antennas. To overcome this drawback, this paper proposes a novel SM-SCMA system operating in uplink transmission, referred to as rotational generalized SM-SCMA (RGSM-SCMA). For the proposed system, the following are introduced, first, transmitter design and its formulation, second, maximum likelihood and maximum a posteriori probability decoders, and finally, practical low-complexity message passing algorithm and its complexity analysis. Simulation results and complexity analysis show that the proposed RGSM-SCMA system delivers the same SE with significant savings in the number of transmit antennas, at the expense of close bit error rate and a negligible increase in the decoding complexity, when compared with SM-SCMA. [ABSTRACT FROM AUTHOR]

Sparse code multiple access (SCMA) is one type of non-orthogonal multiple access techniques for the fifth-generation wireless communication networks. Existing multiuser detection algorithms for SCMA uplink systems are based on the assumption that signals are in synchronization. However, asynchrony cannot be neglected due to the propagation delays in practical environments. In this paper, we present three detection algorithms for uplink asynchronous SCMA systems, namely belief propagation message passing algorithm, belief propagation with equal gain combining message passing algorithm, and partial phase-coherent algorithms. Simulation results show that our proposed asynchronous detection algorithms are able to offer descent bit error rate performances, with only a small performances loss compared to the synchronous case. Moreover, our proposed algorithms converge well in the uplink asynchronous SCMA systems. [ABSTRACT FROM AUTHOR]

Due to limited radio resources, non-orthogonal multiple access (NOMA) is a promising technology to enable massive connectivity in future 5G and beyond wireless networks. However, it suffers from the multiple access interference, which usually requires a high detection complexity to mitigate. In this paper, we consider NOMA with sparse multiple-access sequences, so as to leverage the message passing algorithm (MPA) for low-complexity and high-reliability multiuser detection. The optimal sparsity of spreading sequences is analyzed by minimizing the average bit error rate in the asymptotic largesystem limit. Based on the analysis, the optimal sparse sequences that optimize the performance of MPA detector are designed in a systematically hierarchical way. The sparse structure is constructed given the target girth. Then, the values of nonzero entries are determined to maximize the minimum distance. The detection performance of the designed sparse sequences is presented for both additive white Gaussian noise and Rayleigh fading channels. Simulation results show the superiority of the proposed design in comparison with existing schemes.

This paper proposes a prototype single light-emitting diode (LED) multiple-channel transmission system with visible light communication (VLC) for electromagnetic wave-free indoor healthcare monitoring. Sparse code multiple access (SCMA) is employed for the transfer of multiple medical data with higher bandwidth efficiency in real time. Multiuser data spread to time domain chips with non-orthogonal codebook are simultaneously transmitted using a single LED, where each chip signal is transmitted as a difference voltage level, and LED illumination is detected by a single photodiode (PD). The received signal, which includes multiuser data, is separated by the message passing algorithm with high reliability, and is simultaneously rearranged for transmission to a user interface (PC or mobile). The collected multiple data are then monitored in real time and analyzed for the appropriate medical care service. With SCMA, VLC can achieve higher bandwidth efficiency (50%–200%). Furthermore, the proposed system is designed with a simple structure (single LED to single PD) for practical deployment, and multiple medical signals can be monitored via a designed user interface in real time. [ABSTRACT FROM AUTHOR]

Sparse code multiple access combined with orthogonal frequency division multiplexing (SCMA-OFDM) is a promising wireless air-interface technology for fifth generation (5G) networks to support massive connections. The existing problem for SCMA-OFDM system is that the peak-to-average power ratio (PAPR) is unbearable high. The clipping method is often adopted to reduce the PAPR. However, the clipping brings extra noise to the SCMA-OFDM system. Due to the conventional message passing algorithm (C-MPA) didn’t consider the clipping noise, it will cause the C-MPA decoding to be inaccurate and degrade the bit error rate performance. To tackle this issue, a novel clipping noise-aided MPA scheme, named CNA-MPA, which take both the additive white Gaussian noise (AWGN) and the clipping noise into consideration for decoding accurately is proposed. Simulation results show that the analysis of the clipping noise is accurate and the proposed CNA-MPA scheme leveraging both the AWGN and clipping noise can handle the phenomenon of the performance deterioration occurred in the C-MPA scheme at high Eb/N0 regime. [ABSTRACT FROM AUTHOR]

Sparse code multiple access (SCMA) has been proposed to support massive connections, and becomes a promising non-orthogonal multiple access in future fifth generation wireless communication systems. In SCMA, message passing algorithm (MPA) is utilized to achieve nearly optimal multiuser detection, but the high complexity of MPA detector still makes it hard to implement in practice. To tackle this issue, we present a low complexity MPA detector based on the dynamic factor graph, named DFG-MPA, in which the branches with large belief values in the factor graph model do not participate in the message propagation in current and later iterations. Moreover, choosing the number of partial branches with large belief values for each iteration adaptively depends on practical application scenarios. Numerical results show that the proposed detection scheme provides a commendable tradeoff between bit-error-rate (BER) performance and computational complexity compared with some existing MPA schemes. [ABSTRACT FROM PUBLISHER]

Sparse code multiple access (SCMA) has been proposed to obtain high capacity and support massive connections. Due to the sparse feature of codewords, SCMA achieves low complexity multiuser detection by utilizing message passing algorithm (MPA). However, the complexity reduction of MPA is still a significant issue. In this letter, a novel MPA based on sphere decoding, called SD-MPA, is proposed, which narrows down the range of believable superposed constellation points. Furthermore, simulation results show that SD-MPA detector can reach low complexity detection and maintain negligible bit error ratio performance decline compared with conventional MPA. [ABSTRACT FROM PUBLISHER]

One of the challenges in the design of sparse code multiple access systems is developing low-complexity detectors. To achieve this goal, we propose a novel low-complexity detector based on an edge selection approach, which remarkably reduces the computational complexity. First, the proposed detector applies adaptive Gaussian approximation to the unselected edges that have smaller modulus of the channel coefficients, on the basis of the different channel qualities. As a result, the original factor graph can be simplified. In addition, a mean and variance feedback mechanism is employed to further compensate the information loss brought by unselected edges. Simulations show that, compared with the original message passing algorithm-based detector, the computational complexity is reduced substantially with negligible bit error rate performance degradation. [ABSTRACT FROM PUBLISHER]

The existing multiuser detection schemes for uplink (UP) sparse code multiple access (SCMA) systems are based on a parallel message update for message passing algorithm (MPA). In this letter, a shuffled MPA (S-MPA) scheme for UP SCMA systems is proposed, based on a serial message update strategy. Since the updated messages can join the message propagation immediately in current iteration, the convergence rate is accelerated, so that the complexity of the proposed S-MPA scheme can be substantially reduced with negligible bit error rate (BER) degradation. Simulations show that the proposed S-MPA scheme with two iterations provides similar BER performance to the original MPA scheme with six iterations. Furthermore, a parallel form of the proposed S-MPA scheme, termed group S-MPA, is developed to decrease the detection delay of the proposed S-MPA scheme, which offers a good BER-latency tradeoff. [ABSTRACT FROM PUBLISHER]