In this paper, a new Slepian-Wolf codec was constructed with spatially coupled Low-Density Parity-Check Convolutional (SP-LDPCC) codes. The approach is based on considering the correlation as a virtual binary erasure channel (BEC) and Binary-Input Additive White Gaussian Noise (BIAWGN)channel and applying the syndrome concept. The system is focusing on the compression of a equal-probable memory less binary source with side information at the decoder. Results obtained through both simulations and theoretical demonstrated that the proposed compression scheme performed better than the classical LDPC codes in asymmetric Slepian-Wolf framework.