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A computationally efficient soft-output detector with lattice-reduction (LR) for the multiple-input multiple-output (MIMO) systems is proposed. In the proposed scheme, the sorted QR decomposition is applied on the lattice-reduced equivalent channel to obtain the tree structure. With the aid of the boundary control, the stack algorithm searches a small part of the whole search tree to generate a handful of candidate lists in the reduced lattice. The proposed soft-output algorithm achieves near-optimal performance in a coded MIMO system and the associated computational complexity is substantially lower than that of previously proposed methods.