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This paper investigates linear precoding scheme that maximizes mutual information for multiple-input multiple-output (MIMO) channels with finite-alphabet inputs. In contrast with recent studies, optimizing mutual information directly with extensive computational burden, this work proposes a low-complexity and high-performance design. It derives a lower bound that demands low computational effort and approximates, with a constant shift, the mutual information for various settings. Based on this bound, the precoding problem is solved efficiently. Numerical examples show the efficacy of this method for constant and fading MIMO channels. Compared to its conventional counterparts, the proposed method reduces the computational complexity without performance loss.