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Iterative detection and decoding (IDD) method based on soft interference cancellation and minimum-mean squared-error filtering (SIC-MMSE) has received considerable attention in recent years due to its good performance-complexity tradeoff for coded multiple-input multiple-output (MIMO) systems. The Gaussianity of the a priori and a posteriori log-likelihood ratios (LLRs) computed at the constitute stages of the SIC-MMSE iterative receiver is a presumption for IDD to work. In this letter, the Gaussianity assumption is first shown to be not tight for high rate coded MIMO systems and thus leads to poor performance (for high rate coded MIMO systems). Then a non-linear companding based transformation method is incorporated into the SIC-MMSE iterative receiver to alleviate the non-Gaussianity of the a priori and a posteriori LLRs due to the imperfection of the (high-rate) code and per-stream approximation. Analytical and numerical results show that the proposed transformed SIC-MMSE iterative receiver achieves significant performances gains over the conventional one for coded MIMO systems, in particular, high rate coded ones with even lower computational complexity.