I. Introduction
Code domain non-orthogonal multiple access (NOMA) was considered as an important technique in future 5G [1]. Low density signature CDMA (LDS-CDMA), which is the first kind of code domain NOMA, was proposed in [2] and message passing algorithm (MPA) was introduced to realize low complexity detection. Subsequently, sparse code multiple access (SCMA) [3], [4] was proposed to combine low density spreading with multi-dimensional constellation optimization. Since its birth, SCMA has attracted much attention from both academia [5]–[10] and industry [11]. Recently, codebook optimization algorithms for maximizing mutual information between the discrete input and continuous output were proposed in [8] and [9]. In addition, codebook design was optimized according to superposed constellation distance in [10]. In the above existing works [8]–[10], joint codebook optimizations over multiple variables are performed, which always requires high computational complexity.