An upper bound on relaying over capacity based on channel simulation

The upper bound on the capacity of a 3-node discrete memoryless relay channel is considered, where a sourceX wants to send information to destination Y with the help of a relay Z. Y and Z are independent given X , andthe link from Z to Y is lossless with rate R0. A new inequality is introduced to upper-bound the capacity whenthe encoding rate is beyond the capacities of both individual links XY and XZ. It is based on generalization ofthe blowing-up lemma, linking conditional entropy to decoding error, and channel simulation, to the case with sideinformation. The achieved upper-bound is strictly better than the well-known cut-set bound in several cases whenthe latter is CXY +R0, with CXY being the channel capacity between X and Y . One particular case is when thechannel is statistically degraded, i.e., either Y is a statistically degraded version of Z with respect to X , or Z is astatistically degraded version of Y with respect to X . Moreover in this case, the bound is shown to be explicitlycomputable. The binary erasure channel is analyzed in detail and evaluated numerically.