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Recently low-density generator matrix (LDGM) codes along with various message-passing algorithms (e.g., survey propagation algorithm) have been used for lossy source coding. In contrast with most prior work which has focused exclusively on uniformly distributed sources, we address the problem of lossy coding for sources with arbitrary distributions. Built upon the idea of approximating the optimal output distribution indicated by the rate-distortion theory with a uniform distribution over a larger alphabet, two multilevel coding schemes are proposed: one uses multiple linear codes while the other requires a single linear code of extended length. The simulation results show that both schemes can significantly outperform the existing LDGM codes based methods.