In this correspondence, the problem of distributed source coding (DSC) of binary sources with side information at the decoder is addressed. A scheme is proposed based on raptor codes which are a new class of rateless codes. The decoding scheme is adapted to this problem by implementing a message passing strategy between the constituent decoders of raptor codes at each decoding iteration. The case in which the sources are modeled as independent and identically distributed (i.i.d) processes as well as the more general case in which the sources are modeled as hidden Markov processes (HMPs) are considered. The proposed approach achieves better performance than those achieved by the solutions based on turbo codes, and by the solutions based on regular low density parity check (LDPC) codes when i.i.d. sources are considered. On the other hand, when modeling sources as HMPs, an additional module to exploit the underlying Markovian nature is necessary to achieve good performance.