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In this paper, we consider the massive non-orthogonal multiple access (NOMA) with hybrid automatic repeat request (HARQ) for short packet communications. To reduce the latency, each user can perform one re-transmission provided that the previous packet was not decoded successfully. The system performance is evaluated for both coordinated and uncoordinated transmissions. We first develop a Markov model (MM) to analyze the system dynamics and characterize the packet error rate (PER) and throughput of each user in the coordinated scenario. The power levels are then optimized for two scenarios, including the power constrained and reliability constrained scenarios. A simple yet efficient dynamic cell planning is also designed for the uncoordinated scenario. Numerical results show that both coordinated and uncoordinated NOMA-HARQ with a limited number of retransmissions can achieve the desired level of reliability with the guaranteed latency using a proper power control strategy. Results also show that NOMA-HARQ achieves a higher throughput compared to the orthogonal multiple access scheme with HARQ under the same average received power constraint at the base station.