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Distributed coding is a new paradigm for compressing correlated distributed sources, based on Slepian-Wolf and Wyner-Ziv theorem. This scheme is appropriate for wireless sensor network and distributed video coding. In this paper, we address the problem of coding two Gaussian correlated non-binary sources with one of which is only available at the decoder using the non-binary low-density parity-check (LDPC) codes. The proposed approach is based on the extension of the channel coding concept of syndrome. The correlation between the sources is modeled as a virtual additive Gaussian backward channel. The use of non-binary LDPC codes in the proposed system makes coding without converting non-binary sources to binary bits feasible, and thus it overcomes the reduction in correlation caused by conversion. Experiments show that the proposed system achieves a good performance over GF(4) and GF(8), which enables us to reasonably conclude that the considered scheme is extremely suitable for distributed coding of correlated non-binary sources.