  This paper proves the separation between source-network coding and channel
coding in networks of noisy, discrete, memoryless channels. We show that the
set of achievable distortion matrices in delivering a family of dependent
sources across such a network equals the set of achievable distortion matrices
for delivering the same sources across a distinct network which is built by
replacing each channel by a noiseless, point-to-point bit-pipe of the
corresponding capacity. Thus a code that applies source-network coding across
links that are made almost lossless through the application of independent
channel coding across each link asymptotically achieves the optimal performance
across the network as a whole.
