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Lattice reduction (LR) techniques have been introduced to enhance the performance of linear equalizers by collecting diversity with low complexity for many transmission systems. Although LR-aided linear detectors may collect the same diversity as that collected by the maximum-likelihood (ML) detector, there still exists a performance gap between LR-aided and ML equalizers. One approach to fill this gap is to adopt soft-output detectors. Soft-output detectors enable iterative decoding when error-control codes are employed for a system. In this paper, we propose three LR-aided soft-output detectors with different methods to generate the candidate lists. We compare the performance and complexity of our algorithms with the existing alternatives and show that our methods achieve better performance with lower complexity. The performance-complexity tradeoffs of our proposed algorithms are also studied. Iterative decoders are performed based on these soft-output detectors in the simulations to validate the effectiveness of our algorithms.