I. Introduction
The rapidly growing need of high spectral efficiency and ubiquitous coverage for overloaded communication networks has stimulated interest in developing Multicarrier-Low Density Spreading Multiple Access (MC-LDSMA) [1]. The basic mechanism of MC-LDSMA is that the coded bits for each user are transmitted via multi-dimensional codewords and codewords from different users are spreading over a small subset of the subcarriers [2]–[6]. Therefore, each user suffers less interference from a small number of users on a given sub-carrier. And the receiver can employ the near optimal message passing algorithm (MPA) to recover the transmitted user information [2]. Thus, satisfactory performance could be achieved by optimizing the sparse spreading codebook when multiuser codewords are superimposed simultaneously [4].