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A companding-based transformation method is introduced to quasi-maximum-likelihood (ML) detectors, such as the QR-decomposition-based M-algorithm (QRD-M) and list sphere decoding, for coded multiple-input-multiple-output (MIMO) systems in this paper. The key idea of the proposed companding technique is to compress (i.e., down-weight) the dubious observation of the accumulated branch metric by taking into account its statistical characteristics so that, after companding, the estimation error of the unreliable detected information bits due to insufficient candidate size and/or channel estimation error is significantly mitigated without disproportionate compromise of the reliable information bits. By employing the proposed companding method, the original leptokurtically distributed log-likelihood ratio of the detected information bits becomes more Gaussian distributed. As an illustrative example, the QRD-M detector is employed in this paper. Numerical results show that the QRD-M detector based on the proposed companding paradigm achieves significant performance gain over the conventional method and approaches the performance of the ML detector for a 16-ary quadrature-amplitude-modulated (16-QAM) 4×4 MIMO multiplexing system with lower-than-linear-detector computational complexity.