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The use of lattice reduction (LR) has been shown to be a very effective method for signal detection in multiple antenna systems. In this paper, the performance of the sub-optimal soft-output maximum a posteriori (MAP) detector with lattice reduction is studied. We propose a polynomial-time method to generate the desired size candidate list in the reduced lattice. This sub-optimal soft-output MAP detector provides a near-optimal performance in uncorrelated MIMO systems, but with significantly reduced computational complexity.