A random coding theorem for "modulo-two adder" source network

Suppose (X ,Y ) is a pair of sequence of independent and identically distributed samples from a binary symmetric source. Using linear random codes, Korner and Morton [1] showed that the modulotwo sum sequence Z = X ⊕Y can be described to a common decoder at rates Rx, Ry , and Rz bits iff Rx + Rz > H(Z) and Ry + Rz > H(Z) where H(Z) is the entropy of the random variable Z . Here we provide an alternative proof for the theorem based on a random coding scheme built upon Sanov’s theorem.