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This paper focus on the lossy compression of a binary symmetric source. We propose a new algorithm for binary quantization over low density generator matrix (LDGM) codes. The proposed algorithm is a modified version of the belief propagation (BP) algorithm used in the channel coding framework and has linear complexity in the code block length. We also provide a common framework under which the proposed algorithm and some previously proposed algorithms fit. Simulation results show that our scheme achieves close to state-of-the-art performance with reduced complexity.