A random coding theorem for "modulo-two adder" source network
  This paper has been withdrawn by the author, due a crucial error in the proof of the main Theorem (Sec. 3). In particular, in deriving the bound on the probability of error (Eq. 10) the contribution of those pairs (x', y') that are not equal to (x, y) has not been considered. By adding the contribution of these pairs, one can verify that a region of rates similar to the Slepian-Wolf region will emerge.   The author would like to acknowledge a critical review of the paper by Mr. Paul Cuff of Stanford University who first pointed out the error. 
Amin Zia