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Communication through dispersive direct-sequence code-division multiple-access channels suffers from intersymbol and multiple-access interference, which can significantly impair performance. Joint maximum a posteriori probability equalization and multiuser detection with error control decoding can be used to mitigate this interference and to achieve the optimal bit-error rate. Unfortunately, such optimal detection typically requires prohibitive computational complexity. This problem is addressed in this paper through the development of a reduced state trellis search detection algorithm, based on decision feedback from channel decoders. The performance of this algorithm is analyzed in the large-system limit. This analysis and simulations show that this reduced complexity algorithm can exhibit near-optimal performance under moderate signal-to-noise ratio and attains larger system load capacity than parallel interference cancellation.