On the inner and outer bounds for broadcast channels - II

We continue (from last year's talk) exploring for channels where the best known inner and outer bounds do not coincide. We concentrate on a 3-receiver broadcast channel with 2-degraded message sets setting, where the Korner-Marton inner bound is the best known. For a particular channel, we evaluate explicitly the inner bound (using a generalized Mrs. Gerber's Lemma) and also the outer bound (using FKG inequality) and demonstrate a gap between them. We then show that the inner bound is tight by suitably manipulating the general outer bound for this particular channel. We will also show that when evaluating the regions prescribed by the inner and outer bounds for various settings, some surprisingly simple optimal auxiliary channels emerge.