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This paper considers the cooperative device-to-device (D2D) systems with non-orthogonal multiple access (NOMA). We assume that the base station (BS) can communicate simultaneously with all users to satisfy the full information transmission. In order to characterize the impact of the weak channel and different decoding schemes, two kinds of decoding strategies are proposed: \emph{single signal decoding scheme} and \emph{MRC decoding scheme}, respectively. For the \emph{single signal decoding scheme}, the users immediately decode the received signals after receptions from the BS. Meanwhile, for the \emph{MRC decoding scheme}, instead of decoding, the users will keep the receptions in reserve until the corresponding phase comes and the users jointly decode the received signals by employing maximum ratio combining (MRC). Considering Rayleigh fading channels, the ergodic sum-rate (SR), outage probability and outage capacity of the proposed D2D-NOMA system are analyzed. Moreover, approximate expressions for the ergodic SR are also provided with a negligible performance loss. Numerical results demonstrate that the ergodic SR and outage probability of the proposed D2D-NOMA scheme overwhelm that of the conventional NOMA schemes. Furthermore, it is also revealed that the system performance including the ergodic SR and outage probability are limited by the poor channel condition for both the \emph{single signal decoding scheme} and conventional NOMA schemes., Comment: 24pages, 8figures