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In this paper, a deep neural network (DNN)-based detector for an uplink single-carrier index modulation nonorthogonal multiple access (SC-IM-NOMA) system is proposed, where SC-IM-NOMA allows users to use the same set of subcarriers for transmitting their data modulated by the sub-carrier index modulation technique. More particularly, users of SC-IMNOMA simultaneously transmit their SC-IM data at different power levels which are then exploited by their receivers to perform successive interference cancellation (SIC) multi-user detection. The existing detectors designed for SC-IM-NOMA, such as the joint maximum-likelihood (JML) detector and the maximum likelihood SIC-based (ML-SIC) detector, suffer from high computational complexity. To address this issue, we propose a DNN-based detector whose structure relies on the model-based SIC for jointly detecting both M-ary symbols and index bits of all users after trained with sufficient simulated data. The simulation results demonstrate that the proposed DNN-based detector attains near-optimal error performance and significantly reduced runtime complexity in comparison with the existing hand-crafted detectors.