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The fifth generation wireless networks focus on the design of low latency,high data rate, high reliability, and massive connectivity communications.Non-orthogonal multiple access (NOMA) is an essential enabling technology toaccommodate the wide range of communication requirements. By coordinating themassive devices within the same resource block on power domain, frequencydomain or code domain, NOMA is superior to conventional orthogonal multipleaccess in terms of the network connectivity, the throughputs of system and etc.Sparse code multiple access (SCMA) is a kind of multi-carrier code domain NOMAand has been studied extensively. The challenges for designing a high qualitySCMA system is to seek the feasible encoding and decoding schemes to meet thedesired requirements. In this article, we present some recent progressestowards the design of multi-dimensional codebooks, the practical low complexitydecoder, as well as the Grant-Free multiple access for SCMA system. Inparticular, we show how the SCMA codebooks construction are motived by thecombined design of multi-dimensional constellation and factor graphs. Inaddition, various low complexity SCMA decoders are also reviewed with a specialfocus on sphere decoding. Moreover, based on the framework of beliefpropagation, the SCMA Grant-Free transmission is introduced and the problem ofcollision resolution is also discussed.

Towrad 5G Air Interface Technology: Sparse Code Muliple Access