hich results in interference diversity by avoid- ing strong interferers to destroy the signal of a user on all the subcarriers. Belief propaga- tion based multi-user detection can be implemented with linear complexity in the number of subcarriers [50-52]. The LDS and SCMA share the same concept which is to use a low-density or sparse non- zero element sequence to reduce the complexity of MPA processing at the receiver. However, in SCMA, bit streams are directly mapped to different sparse codewords. An exam- ple is illustrated in Fig. 3.34, where each user has a codebook and there are six users. All codewords in the same codebook contain zeros in the same two dimensions, and the positions New Radio Access Physical Layer Aspects (Part 1) 361 B11b12... SCMA modulation FEC encoder 1 codebook mapping SCMA codeword 1 SCMA block 1 SCMA modulation FEC encoder 2 codebook mapping B31b32--- SCMA modulation FEC encoder 3 codebook mapping B41b42.. SCMA modulation FEC encoder 4 codebook mapping B51b52.. SCMA modulation FEC encoder 5 codebook mapping Frequency B61b62... SCMA codeword 6 SCMA modulation FEC encoder 6 codebook mapping Figure 3.34 Illustration of SCMA concept [52]. of the zeros in the different codebooks are distinct to facilitate the collision avoidance of any two users. For each user, two bits are mapped to a complex codeword. Codewords for all users are multiplexed over four shared orthogonal resources. The key difference between LDS and SCMA is that a multi-dimensional constellation for SCMA is designed to generate codebooks, which provides a shaping gain that is not possible with LDS. In order to simplify the design of the multi-dimensional constellation, a baseline constellation can be generated by minimizing the average alphabet energy for a given minimum Euclidian distance between constellation points, and also taking into account the codebook-specific operations such as phase rotation, complex conjugate, and dimensional permutation [50-52]. We use the uplink multiple-access system shown in Fig. 3.35 to exp