In the user identification (UI) scheme for a multiple-access fading channel based on a randomly generated (0, 1, -1)-signature code, previous studies used the signature code over a noisy multiple-access adder channel, and only the user state information (USI) was decoded by the signature decoder. However, by considering the communication model as a compressed sensing process, it is possible to estimate the channel coefficients while identifying users. In this study, to improve the efficiency of the decoding process, we propose an iterative deep neural network (DNN)-based decoder. Simulation results show that for the randomly generated (0, 1, -1)-signature code, the proposed DNN-based decoder requires less computing time than the classical signal recovery algorithm used in compressed sensing while achieving higher UI and channel estimation (CE) accuracies.