  We consider the source-channel separation architecture for lossy source
coding in communication networks. It is shown that the separation approach is
optimal in two general scenarios, and is approximately optimal in a third
scenario. The two scenarios for which separation is optimal complement each
other: the first is when the memoryless sources at source nodes are arbitrarily
correlated, each of which is to be reconstructed at possibly multiple
destinations within certain distortions, but the channels in this network are
synchronized, orthogonal and memoryless point-to-point channels; the second is
when the memoryless sources are mutually independent, each of which is to be
reconstructed only at one destination within a certain distortion, but the
channels are general, including multi-user channels such as multiple access,
broadcast, interference and relay channels, possibly with feedback. The third
scenario, for which we demonstrate approximate optimality of source-channel
separation, generalizes the second scenario by allowing each source to be
reconstructed at multiple destinations with different distortions. For this
case, the loss from optimality by using the separation approach can be
upper-bounded when a "difference" distortion measure is taken, and in the
special case of quadratic distortion measure, this leads to universal constant
bounds.
