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Non-orthogonal multiple access (NOMA) is considered as one of the key technologies for the fifth generation (5G) wireless communications. The integration of NOMA and device-to-device (D2D) communications has recently attracted wide attention. In this paper, a relaying D2D communications as-sisted with cooperative relaying systems using NOMA (DRC-NOMA) is considered. We analyze the er-godic sum-rate for the proposed system and then de-rive the closed-form expressions. In addition, an opti-mal power allocation strategy maximizing the ergodic sum-rate is proposed based on these analysis results. Numerical results show the good agreement between the results of analysis and Monte Carlo method. The proposed DRC-NOMA has a great improvement of the ergodic sum-rate in the small regime of average chan-nel gain of D2D pair.