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 Csisz\'{a}r and K\"{o}rner in 1982 which fully characterized the reliability function of any discrete memoryless channel (DMC) with feedback for rates above capacity.

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