An upper bound on relaying over capacity

The upper bound on the capacity of a 3-node discrete memoryless relay channel is considered, where a source X wants to send information to destination Y with the help of a relay Z. Y and Z are independent given X, and the channel is statistically degraded in the sense that XY Z or XZY can be re-described statistically as a Markov chain. The link from Z to Y is lossless with rate R₀. A new method is introduced to bound the capacity when the encoding rate is beyond both individual links XY and XZ. It generalizes the well-known blowing-up lemma and links it with conditional entropy. The new bound is explicitly computable and strictly better than the well-known cut-set bound when the latter is C_XY + R₀. The binary erasure channel is analyzed in detail as an example, and generalization to more cases is also discussed.