A multi-dimensional set-partitioning scheme is proposed for joint reduced-state sequence detection (JRSSD) of vector sequences corrupted by intersymbol interference (ISI) and additive white Gaussian noise (AWGN). The existing multi-dimensional set-partitioning schemes result in complexity exponential in the dimensionality of the vectors in the vector sequence. The proposed set-partitioning scheme allows the construction of reduced-state trellises with very few states even when the vectors are of high dimensionality. One of the key requirements of the JRSSD algorithm is an efficient algorithm for spatial multi-symbol detection, for which we propose the reduced-state tree (RST) detection algorithm. In addition to performance improvement, the inclusion of RST algorithm for spatial multi-symbol detection provides a common framework for designing receivers for both flat-fading and frequency-selective fading MIMO channels. © 2014 IEEE.