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This paper addresses the problem of distributed source coding (DSC) of binary sources with unknown varying correlation statistics over erasure channels. We propose an adaptive asymmetric Slepian-Wolf (SW) decoding scheme using particle-based belief propagation (BP) based on Raptor codes. We show through the experiments that the proposed algorithm can simultaneously reconstruct the compressed sources and estimate the correlation between source and side information. Moreover, compared to the conventional Raptor decoder, the proposed approach can achieve a higher compression ratio and provide stronger erasure protection under unknown varying correlation statistics. The ability to estimate the statistical correlation in the code structure makes our approach very useful for real applications.