Separation of source-network coding and channel coding in wireline networks

In this paper we prove the separation of source-network coding and channel coding in a wireline network, which is a network of memoryless point-to-point finite-alphabet channels used to transmit correlated sources. In deriving this result, we also prove that in a general memoryless network with correlated sources lossless and zero-distortion reconstruction are equivalent provided that the conditional entropy of each source given the other sources is non-zero. Furthermore, we extend the separation result to the case of well-behaved continuous-alaphabet point-to-point channels such as additive white Gaussian noise (AWGN) channels.