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In this paper, we aim to design a power allocation strategy to minimize the average consumed power of a hybrid automatic repeat request with chase combining (HARQ-CC) enabled system under a strict outage constraint for each user. In particular, the non-orthogonal multiple access (NOMA) is incorporated to further improve the system spectrum efficiency and we assume the base station only knows the statistical channel state information of the users. To evaluate the performance of the HARQ-CC enabled NOMA system, we first analyze the outage probability of each user. Then, based on the derived outage probabilities, by optimizing the transmit power, an average power minimization problem is considered. However, the attained expressions of the outage probabilities are nonconvex and extremely complicated, and thus make the formulated problem difficult to deal with. To efficiently solve the original problem …