Compressed Sensing based Multi-User Detection (CS-MUD) is a novel MUD approach applied in sporadic Machine Type Communication (MTC) to identify actively transmitting sensors nodes at the same time as the transmitted data. In this context, different reconstruction algorithms from CS as well as detection concepts well established in communications have been adapted, but either are not exploiting finite alphabets or are highly complex. In this paper, we focus on an iterative soft interference cancellation scheme that efficiently exploits the sparsity of the signal, the finite alphabet of the transmit data and the usually employed channel coding to obtain a robust high performance detection scheme.