# Joint Iterative Decoding Design of Cooperative Downlink SCMA Systems
## 1 Introduction
Based on the cross-entropy method, novel multiple-input multiple-output SCMA codebooks have been developed for both uplink and downlink Rayleigh fading channels [28]. In general, low-complexity decoders for SCMA can be classified into two categories: reducing the computation cost of the original MPA detector and exploring more efficient ones. The authors in [29] put forward a threshold-based MPA by setting a belief threshold to build an early stop criterion of the iteration process. The partial marginalization [30] MPA aims to reduce the computation complexity of the original one at the cost of negligible bit-error rate (BER) degradation by propagating messages the same as the original MPA role and determining part codewords at the \(m\)-th iteration. To accelerate its convergence, the authors in [31] provide the asynchronous MPA detector by allowing all the likelihood probabilities to update in a parallel manner. However, the ascending order of this strategy is not always the best choice; in this way, an improved serial scheduling-based MPA has been proposed in [32] to further accelerate its convergence, where the edges are selected according to the maximum value of the messages. The authors in [33] optimize the original MPA in two aspects: a lookup table is adopted to reduce the computational cost of the message exchanging instead of the extensive Jacobian approximation; thus, the stable convergence of the MPA can be guaranteed. The convergence of the original MPA is sped up by using a series of novel scheduling schemes. By extending stochastic computing to MPA [34], a low-complexity stochastic detector has been proposed by designing three novel stochastic logic architectures with low hardware cost bit-stream generation and resource node updating architecture, as well as the fast converging stochastic variable node updatingrule. By using its lattice structure, a low-complexity decoding algorithm based on list sphere decoding [35], where the exhaustive search for all possible hypotheses, can be avoided. By narrowing down the range of believable superposed constellation points, a novel sphere decoding-based MPA structure is proposed in [36]. A low-complexity attempt for joint SCMA and generalized frequency-division multiplexing detection has been reported in [37] by virtue of the frequency-domain implementation, where the closed form average BER bound is also investigated. A novel joint iteration detection and decoding of multiple-input multiple-output and SCMA scheme has been investigated in [38] by designing the corresponding virtual sparse factor graph. An improved approximate message passing SCMA detection scheme has been provided in [39] for the imperfect channels in low-Earth-orbit satellite communications. The authors in [40] propose a linear minimum mean square error-based detection structure to construct an efficient transceiver design for affine frequency-division multiplexing-aided sparse code multiple access system. To address the inflexibility of user grouping and the diverse data rate support in SCMA, a variable modulation scheme has been proposed in [41] to allow different users to employ codebooks with diverse modulation orders. Recently, the artificial intelligence-based techniques in SCMA design and optimization have gained much attention in the literature. For example, to enable near-optimal codebook and low-complexity decoder design, an auto-encoder-based encoding-decoding structure for SCMA has been proposed in [42]. The cooperative transmission decode-and-forward strategy is able to enhance the performance of communication systems, especially for cell edge nodes, by using dedicated relays or allowing users to act as the relay in order to provide spatial diversity. This cooperative strategy has attracted much attention in PD-NOMA systems [43]. The cooperative NOMA scheme is first proposed in [43] by fully exploiting the prior knowledge. The authors in [43] also analyze the achieved outage probability and diversity order.