How Does Channel Coding Affect the Design of Uplink SCMA Multidimensional Constellations?

Sparse code multiple access (SCMA) is a potential non-orthogonal multiple access candidate for future wireless systems. The key performance indicators (KPIs) of uplink SCMA multidimensional constellations (MdCs) that should be considered in their design process have recently been identified in conjunction with the LTE turbo code for different channel scenarios. However, it is questionable whether the same KPIs are applicable to designing MdCs when a different error correcting code is employed. In this paper, we investigate the effect of the high-rate and low-rate 5G low density parity check (LDPC) codes on determining KPIs in designing MdCs for uplink SCMA systems under various channel scenarios. Through simulations, we show that similar results to the LTE turbo coded case occur in the presence of 5G LDPC code, with one notable exception over one specific scenario. The exception is in the performance of one MdC, which has a low number of distinct points; its performance is significantly worse than predicted by the KPIs when the low-rate 5G LDPC code is employed. This phenomenon happens due to the inherent structure of the 5G LDPC code, in which we propose a pseudorandom interleaver to rectify the problem.