A tighter Cut-Set bound for the multi-terminal erasure channel without side information

In this paper our recent results in the capacity of single relay erasure channels are used to derive a new and tighter cut-set bound. We initially present a simple and intuitive approach to derive the classical cut-set bound in general multi-terminal erasure channels. This derivation shows that attaining the bound supposes that a full level of collaboration exists between nodes in the channel. However under some scenarios the full collaboration is not possible. We thereafter use a bounding technique based on reducing every cut-set in a general multi-terminal erasure channel to a single relay super-channel consisting of super nodes. We show that if a rate setting is not achievable over the single relay super-channel it could not then achieved over the general multi-terminal erasure channel. This led us to a tighter cut-set type of bound for general multi-terminal erasure channel