# Joint Iterative Decoding Design of Cooperative Downlink SCMA Systems
## 1 Introduction  
Non-orthogonal multiple access (NOMA) [1, 2, 3] has been considered as one of the key technologies of beyond fifth-generation and sixth-generation communication networks [4, 5] to provide high spectrum efficiency and massive connectivity, which are essential to Internet of Things (IoT) applications [6, 7, 8, 9]. The principle of NOMA allows multiple users to occupy the same time and frequency resources. There are two kinds of NOMA techniques, i.e., the power domain NOMA (PD-NOMA) and the code domain NOMA [10, 11, 12]. In PD-NOMA, all the users are allocated with different levels of power according to the strength of channel state information from the base station (BS), and successive interference cancellation is performed at the receive end to apply multiuser detection. In code domain NOMA, such as sparse code multiple access (SCMA) [13, 14, 15, 16], multiple user shared access, pattern division multiple access and interleave division multiple access [17, 18], the loading factor is high and thus can provide large connectivity and high spectrum efficiency in comparison to orthogonal multiple access. In SCMA, the most popular code domain NOMA scheme, each user is equipped with a unique codebook, where several carefully designed codewords are involved. At the transmitter, the information bits are mapped to the multi-dimensional sparse codewords and then spread to orthogonal resources. The sparsity of the codewords enables the widely used message passing algorithm (MPA) detector to recover transmitted bits. In recent years, most studies related to SCMA have focused on codebook design and low-complexity receivers. The authors in [19] propose a joint multiuser codebook design for uplink SCMA systems over Rayleigh fading channels based on the cutoff rate criterion of the equivalent multiple-input multiple-output system. By means of the golden angle modulation points, the authors in [20] provide two schemes for codebook design with a different number of optimization parameters, being independent of system configuration and simple to implement. An efficient SCMA codebook has been designed in [21] by introducing a one-dimensional searching algorithm to minimize the upper bound of pair-wise error probability. In [22], a novel codebook with large minimum Euclidean distance is provided by employing the star quadrature amplitude modulation signal constellations to meet the pair-wise error probability-based design criteria. The systematic construction procedure for the SCMA codebook design under various channel environments has been considered for small-scale application to achieve near-optimal performance, where the steps of rotation angle design, multi-dimensional codebook construction and labeling rule design are involved [23]. Unlike most existing codebook design structures, the authors in [24] present a novel class of an SCMA codebook design method, where power imbalance among different users is introduced instead of assuming uniform power allocation, by using the Star-QAM mother constellation and genetic algorithm in order to optimize the minimum Euclidean distance and the minimum product distance, respectively. Recent studies also focus on the SCMA codebook design with respect to specific channels. For the additive white Gaussian noise (AWGN) channel, a separable codebook scheme has been provided in [25] to simplify the maximization of the minimum Euclidean distance, where the multiple one-dimensional complex codebooks related to the resource element are maximized in terms of these criteria. By using the separable codebook structure to design heavily overloaded SCMA codebooks, the authors in [26] formulate a non-convex problem of minimizing codebook power under the distance constraints; then, the convex-concave procedure is adopted to solve it. By exploring the probability distribution of the Rician random variables and its indicators of multi-dimensional constellations, an enhanced codebook for various Rician scenarios has been generated in [27].