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Sparse code multiple access (SCMA) is a promising candidate air interface of the next generation mobile networks. However, the decoding complexity of current message passing algorithm for SCMA is very high. In this study, the authors map SCMA constellation to q-order Galois field (GF(q)) and introduce a trellis representation to SCMA. Based on the trellis representation, they propose low-complexity decoding algorithms for SCMA by using truncated messages, which is referred as extended max-log (EML) algorithm. As the truncated length of EML is unitary for each user, they further propose a channel-adaptive EMLalgorithm to truncate the messages with a rule that can be adaptive to the channel state. Simulation results show that the proposed schemes obtain a low computational complexity with only a slight performance degradation when the truncated length is selected appropriately. [ABSTRACT FROM AUTHOR]