Performance study of MPA, Log-MPA and MAX-Log-MPA for an uplink SCMA scenario

Sparse code multiple access (SCMA) is a promising non-orthogonal multiple access scheme in order to fulfill the stringent 5G use cases requirements. SCMA can be seen as an improvement of low density signature orthogonal frequency division multiple access that takes advantage of codes sparsity to yield users overload. Generally, SCMA is implemented with message passing algorithm (MPA) at the decoder to benefit from the strong iterative decoding performance. On the other hand, it suffers from high complexity due to the large number of involved exponential operations to compute the log likelihood ratio (LLR). Hence, simplified sub-optimal versions of MPA known as MAX-Log-MPA and Log-MPA were proposed in order to ensure a trade-off between system complexity and performance. This paper presents a comprehensive comparison between those three algorithms in Gaussian and fading channels and precisely explains algorithms performance through a study of the extrinsic information behavior.