Strong Converse for Discrete Memoryless Networks with Tight Cut-Set Bounds

This paper proves the strong converse for any discrete memoryless network (DMN) with tight cut-set bound, i.e., whose cut-set bound is achievable. Our result implies that for any DMN with tight cut-set bound and any fixed rate tuple that resides outside the capacity region, the average error probabilities of any sequence of length-n codes operated at the rate tuple 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 Csiszár and Körner in 1982 which fully characterized the reliability function of any discrete memoryless channel (DMC) with feedback for rates above capacity.