Strong Converse Theorems for Classes of Multimessage Multicast Networks: A Rényi Divergence Approach

This paper establishes that the strong converse holds for some classes of discrete memoryless multimessage multicast networks (DM-MMNs) whose corresponding cut-set bounds are tight, i.e., coincide with the corresponding sets of achievable rate tuples. Our strong converse result implies that for any DM-MMN of these classes, the average error probabilities of any sequence of codes operated at a rate tuple belonging to the exterior of the cut-set bound must tend to one (and are not simply bounded away from zero) as the block length grows. Examples in the classes of DM-MMNs include wireless erasure networks, DM-MMNs consisting of independent discrete memoryless channels (DMCs) as well as single-destination DM-MMNs consisting of independent DMCs with destination feedback. Our elementary proof technique leverages properties of the Rényi divergence.