Strong converse theorems for discrete memoryless networks with tight cut-set bound

This paper considers a multimessage network where each node may send a message to any other node in the network. Under the discrete memoryless model, we prove the strong converse theorem for any network with tight cut-set bound, i.e., whose cut-set bound is achievable. Our result implies that for any network with tight cut-set bound and any fixed rate vector that resides outside the capacity region, the average error probabilities of any sequence of length-n codes operated at the rate vector must tend to 1 as n grows. The proof is based on the method of types. The proof techniques are inspired by the work of Csiszar and Korner in 1982 which fully characterized the reliability function of any discrete memoryless channel (DMC) with feedback for rates above capacity.