Cutoff Rate of Sparse Code Multiple Access in Downlink Broadcast Channels

For the sake of supporting massive connectivity in the future 5G networks, non-orthogonal multiple access (NOMA) techniques are advocated. As a promising NOMA technique, in recent years sparse code multiple access (SCMA) has attracted substantial attention. However, there is a paucity of studies on the theoretical analysis of its error-freely achievable data rate, especially, in the downlink context. Hence, we derive the cutoff rate of SCMA in downlink broadcast channels, which indicates the lower-bound of a system's error-freely achievable rate. However, we will demonstrate that when considering the conventional categorization of pairwise error events, the accuracy of the cutoff rate rapidly degrades in the low-SNR region owing to the fact that multi-user SCMA systems typically encounter an extremely large constellation size. Alternatively, by invoking Bergmans' concept from 1973 in the categorization of pairwise error events, we obtain a more accurate cutoff rate both in the low- SNR regions and the high-SNR regions. Moreover, we provide insights into the cutoff rate derivation process, which reveals some general guidelines for designing a beneficial codebook, capable of improving SCMA with respect to its original low-density signature-based counterpart.