A new upper-bounding technique for a primitive relay channel based on channel simulation

We consider the following primitive relay channel. A source X wants to send information to a destination Y with the help of a relay Z. The link from Z to Y is assumed to be lossless with rate R₀. It is shown that destination Y´s capability in simulating relay Z´s observations, a function of the channel, is fundamentally linked to Z´s capability in utilizing the full rate of the ZY link. A general upper bound based on combining channel simulation and the blowing-up lemma is presented. In several cases, e.g. stochastistically degraded, we show that the rate C_XY + R₀ is not achievable, where C_XY is the capacity of the XY link. This method reveals an interesting relationship between channel simulation theory and characterizing the relay channel´s capacity.