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In this paper, we propose a scheme for distributed source coding (DSC) that achieves any arbitrary rate on the Slepian-Wolf rate region using a single systematic LDPC code. This method is based on sending a fraction of the information bits along with a fraction of parity bits generated by the LDPC code. First, we study the problem of DSC of two correlated sources at the symmetric rate. We propose to use nonuniform LDPC codes for this application. Then, we generalize our approach to any arbitrary rate. The detailed construction of this scheme is investigated. We illustrate that the design procedure for the LDPC code simplifies to the design of rate-adaptive LDPC codes that need unequal error protection. It is shown that the performance of DSC at any arbitrary rate is almost the same as that of asymmetric rates. Because of the proposed decoding algorithm, each of the sources is decoded independently (only part of the information bits are being exchanged between the decoders). Therefore, this approach does not suffer from the problems of heavy damage or propagation of errors. This method can be easily applied to joint source-channel coding.