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Optimal multiuser detection of trellis coded signals has prohibitive complexity. A suboptimal concatenated scheme consisting of a maximum a posteriori (MAP) multiuser interference (MUI) detector followed by a deinterleaver and a soft trellis decoder has recently received considerable attention in the literature. We call this scheme concatenated multiuser detector and trellis decoder (CMDTD). An alternative to CMDTD is joint multiuser detection and group decoding (JMDGD). In JMDGD, reduced-state sequence estimation (RSSE) is used to jointly decode the coding information of a group of users and equalize the MUI. In this paper we show that JMDGD outperforms CMDTD in asynchronous trellis-coded DS-CDMA systems over high-interference AWGN channels. In these channels, the advantage of JMDGD is dramatic in near-far situations. Furthermore, the performance edge of JMDGD over CMDTD increases as the MUI increases. In fast fading channels, simulation results show that JMDGD performs close to CMDTD with significantly reduced complexity.