An improved SCMA codebook design based on uniquely decomposable constellation groups

In this paper, we propose an improved uniquely decomposable constellation group (I-UDCG) for codebook design of sparse code multiple access (SCMA) systems, which guarantees that the superimposed constellation of SCMA codebooks on each mapping resource satisfies the uniquely decomposable constraint. We optimize the bit error rate (BER) performance of the I-UDCG-based SCMA codebooks from two perspectives. One is to maximize the coding gain of the superimposed constellation of the I-UDCG, using the error probability bound (EPB) as the optimization criterion. The EPB is determined by a threshold distance rather than the minimum Euclidean distance (MED) among constellation points. The other approach focuses on maximizing the MED among the codebook's codewords to enlarge the coding gain of SCMA codebooks, thereby improving the BER performance of SCMA systems. Simulation results show that the two optimization methods can enhance the BER performance of SCMA. In particular, the first optimization method performs better in scenarios involving both small-size and large-size codebooks. Compared to other codebook design schemes, our proposal can exhibit strong anti-noise and antifading abilities for various codebook sizes.