The effect of zero-rate encoders in the multi-terminal source coding problem

This work focuses on the multi-terminal source coding problem and presents conditions when a rate point achievable with asymptotically zero-rate messages over a subset of network links, is also achievable with no communication over links in that subset. We show that when there exist block codes that are robust to small changes in the source distribution, zero-rate encoders can be ignored, i.e., their outgoing links can be assumed to be absent. Additionally, we show that when the decoder is given access to the strictly causal past realizations of the sources, zero-rate encoders can always be ignored.