Optimality and approximate optimality of source-channel separation in networks

We consider the optimality of source-channel separation in networks, and show that such a separation approach is optimal or approximately optimal for a large class of scenarios. More precisely, for lossy coding of memoryless sources in a network, when the sources are mutually independent, and each source is needed only at one destination (or at multiple destinations at the same distortion level), the separation approach is optimal; for the same setting but each source is needed at multiple destinations under a restricted class of distortion measures, the separation approach is approximately optimal, in the sense that the loss from optimum can be upper-bounded. The communication channels in the network are general, including various multiuser channels with finite memory and feedback, the sources and channels can have different bandwidths, and the sources can be present at multiple nodes.