  This letter proposes a novel hybrid automatic repeat request with chase
combining assisted sparse code multiple access (HARQ-CC-SCMA) scheme. Depending
on whether the same superimposed packet are retransmitted, synchronous and
asynchronous modes are considered for retransmissions. Moreover, factor graph
aggregation (FGA) and Log-likelihood ratio combination (LLRC) are proposed for
multi-user detection. Regarding FGA, a large-scale factor graph is constructed
by combining all the received superimposed signals and message passing
algorithm (MAP) is applied to calculate log-likelihood ratio (LLR). Whereas,
owing to the same unsuccessful messages required to be retransmitted, LLRC adds
up LLRs of erroneously received packets in previous HARQ rounds together with
currently received packets for channel decoding and saves the LLRs for failed
users. Finally, Monte Carlo simulations are preformed to show that FGA
surpasses LLRC and HARQ with incremental redundancy (HARQ-IR) in synchronous
mode. However, LLRC performs better than FGA at low signal-to-noise ratio (SNR)
in asynchronous mode. This is because failed messages after the maximum
allowable HARQ rounds in this mode can yield significant error propagation in
low SNR regime.
