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This paper studies the problem of blind source separation (BSS) from instantaneous mixtures with the assumption that the source signals are mutually correlated. We propose a novel approach to BSS by using precoders in transmitters. We show that if the precoders are properly designed, some cross-correlation coefficients of the coded signals can be forced to be zero at certain time lags. Then, the unique correlation properties of the coded signals can be exploited in receiver to achieve source separation. Based on the proposed precoders, a subspace-based algorithm is derived for the blind separation of mutually correlated sources. The effectiveness of the algorithm is illustrated by simulation examples.