On Marton's Inner Bound for the General Broadcast Channel

We establish several new results on Marton’s inner bound on the capacity region of the general broadcastchannel. Inspired by the fact that Marton’s coding scheme without superposition coding is optimal in the Gaussiancase, we consider the class of binary input degraded broadcast channels with no common message that have thesame property. We characterize this class. We also establish new properties of Marton’s inner bound that help restrictthe search space for computing the Marton sum-rate. In particular we establish an extension of the XOR case ofthe binary inequality of Nair, Wang, and Geng.