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In this paper we propose a joint reduced-state sequence detector (JRSSD) for a multiple-input multiple-output (MIMO) system. The proposed JRSSD incorporates the set-partitioning principle to obtain a reduced-state trellis and is the space-time extension of the RSSD proposed in for a single-input single-output (SISO) equalization problem. We show that two elements are essential in achieving the desired complexity and performance tradeoff for the proposed JRSSD algorithm: 1) a proper multisymbol set-partition and 2) an efficient space-time structure that effectively decouples the spatial and temporal processing. We propose a simple multisymbol uniform set-partition (USP) that retains certain geometric symmetry in the partitioned subsets. We also develop two suboptimal algorithms, namely the decorrelating (DC) and ordered successive (OS) algorithms, to decouple the spatial multisymbol detection problem inherent in the processing of parallel transitions, into single-symbol detection problems. The symmetry in USP, together with the DC or OS algorithm, guarantees efficient processing of parallel transitions and leads to a low-complexity JRSSD. Furthermore, numerical simulations show that the performance of JRSSD is near that of the more complex delayed decision feedback sequence estimator (DDFSE).