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Precoder optimization with full channel state information for finite alphabet signals over multiple-input multiple-output random channels is investigated in this paper. The precoder is represented by a product of power allocation matrix and constellation-forming matrix. There was an optimal algorithm introduced in the literature to globally maximize the channel mutual information by iteratively optimizing these two matrices. However, the computational complexity of the optimal algorithm is painfully high, especially when it is used with the high-order modulation and the high-data stream number. In this paper, we propose a novel sub-optimal low-complexity precoding algorithm and compare it with the optimal one. The new algorithm proceeds in two steps. First, the constellation-forming matrix is fixed in order to maximize the minimum Euclidean distance between the received symbols, which ensures high channel mutual information. Then, given the constellation-forming matrix, an iterative algorithm searches for the power allocation matrix that maximizes the channel mutual information. Since optimizing only one matrix instead of two, the new algorithm not only achieves a lower computational complexity but also avoids the use of initial values, which must be carefully selected for each channel and signal-to-noise ratio for fast convergence. Another advantage of the new algorithm is that the resulting precoder has a fixed form of received constellation thanks to the fixed constellation-forming matrix. This allows us to optimize the symbol mapping on the received constellation. Simulation results show that the proposed low-complexity precoder achieves error-rate performance that is close to performance of the optimal one when the conventional mapping is used. In addition, the new precoder used with optimized mapping at received constellation shows significant error-rate performance improvement. [ABSTRACT FROM AUTHOR]