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An approach of scaling and shifting constellation for MIMO lattice reduction(LR)-aided precoding is proposed. The proposed scheme is beneficial to improve the performance in terms of both BER and ergodic capacity. The feedback is a Gaussian integer matrix in which the entries are preserved in a region with respect to modulo operation. Then, the amount of feedback information is reduced significantly. Simulation results show that the LR-aided precoding scheme using the improved version of the constellation apparently improves system performance. [ABSTRACT FROM AUTHOR]