This paper addresses the problem of error correction in a multi-user trellis coded system in the presence of bit stuffing. In particular, one considers the situation in which automatic identification system (AIS) signals are received by a satellite. The proposed receiver uses a cyclic redundancy check (CRC) for error correction. A Viterbi algorithm based on a so-called extended trellis is developed. This trellis is defined by extended states composed of a trellis-code state and a CRC state. Moreover, special conditional transitions are defined in order to take into account the possible presence of bit stuffing. The proposed algorithm was first developed in a single-user context. It is generalized in this paper to a multi-user scenario by designing an interference mitigation method. This method allows one to derive a demodulation algorithm whose complexity is almost identical to that obtained in the single-user context. Some performance results are presented in the context of AIS and compared with results provided by existing techniques.