The complexity of successive interference cancellation at the receiver's end is a challenging issue in conventional non-orthogonal multiple access assisted massive wireless networks. The computational complexity of decoding increases exponentially with the number of users. Further, under realistic channel conditions, a synchronous non-orthogonal multiple access scheme is impractical in the uplink deviceto-device communications. In this paper, an asynchronous non-orthogonal multiple access-based cyclic triangular successive interference cancellation scheme is proposed for a massive device-to-device network. The proposed scheme reduces the decoding complexity, energy consumption, and bit error rate of a superimposed signal received in an outband device-to-device network. More specifically, the scheme follows three consecutive stages; optimization, decoding, and re-transmission. In the optimization stage, a dual Lagrangian objective function is defined to maximize the number of data symbols decoded at the receiver by determining an optimal interference cancellation triangle, under the co-channel interference and data rate constraints. In the decoding stage, the data in the optimal interference cancellation triangle is decoded using a conventional triangular successive interference cancellation technique. Next, the remaining users' data are decoded in sequential iterations of the proposed scheme, using the retransmissions from such users. Utilizing the successive interference cancellation characteristics, the performance of the proposed deviceto-device network is defined in terms of energy efficiency, bit error rate, computational complexity, and decoding delay metrics. Moreover, the performance of the proposed decoding scheme is compared with the conventional triangular successive interference cancellation decoding scheme to demonstrate the superiority of the proposed scheme.