An Outer Bound to the Admissible Source Region of Broadcast Channels with Arbitrarily Correlated Sources and Channel Variations

In this paper we apply the "potential function method" introduced by the authors in [5] and [6] to prove an outer bound on the admissible source region of an arbitrarily varying general broadcast channel with arbitrarily correlated sources. We are not aware of any previous work discussing any interesting outer bounds on the admissible source region of the general broadcast channel either when the sources are allowed to be arbitrarily correlated, the channel is allowed to vary arbitrarily, or both. Specializing by removing the variability of the channel and assuming independent sources, our outer bound reduces to one that is included inside the region defined by Liang, Kramer and Shamai, a recent outer bound on the capacity region of the traditional broadcast channel [12]. We don't know if the inclusion is strict. The arbitrarily varying channel aspect of our bound is rather superficial; the main interest is in the arbitrarily correlated source part.