Spatially-Coupled Protograph for NOMA Optimized by the Genetic Algorithm

In this paper we investigate the codebook design of the non-orthogonal multiple access through the spatially-coupled protograph. The optimization is realized by changing the edge connections in the protograph to maximize the sum rate and then permutating the identity matrices in the spatial coupling to improve the girth distribution. The edge connection in the protograph determines the interference at each resource element and the diversity for each user equipment, and the optimization finds the best tradeoff in between. The spatial coupling enlarges or removes the short girths in the protograph in favor of message-passing decoding, which makes the low-complexity detection applicable. The genetic algorithm is employed in the optimizations of both the protograph and the spatial coupling. Numerical results reveal the characteristics of the optimal superposition structures for different SNR regions and the improvement of girth distributions for different spatial coupling mechanisms. The optimized structures demonstrate better error performance than those proposed in the literature.