In this paper, a low-complexity precoding scheme for minimizing the bit error rate (BER) subject to fixed power constraint for distributed antenna systems with non-Kronecker correlation over spatially correlated Rayleigh fading channels is presented. Based on an approximated BER bound and a newly defined compressed signal-to-noise ratio (CSNR) criterion, closed-form expressions of power allocation and beamforming matrix are derived for the developed precoding scheme. This scheme not only has the calculation of the power allocation less than and also obtain the BER performance close to that of the existing optimal precoding scheme. Simulation results show that the proposed scheme can provide BER lower than the equal power allocation and single mode beamforming scheme, has almost the same performance as the existing optimal scheme.