Multi-terminal source coding: Zero-rate encoders cannot enlarge the rate region

This work proves that in the multi-terminal source coding problem, any achievable rate point achievable with asymptotically zero rate on a subset of links can also be achieved without any communication over the same subset of links, or equivalently, when the links in the subset are removed from the network. This work shows that asymptotically zero-rate communication over a subset of links cannot be crucial for the inclusion of a rate point in the rate region in spite of the absence of an explicit characterization of the rate region.