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 broadcast channel. Inspired by the fact that Marton´s coding scheme without superposition coding is optimal in the Gaussian case, we consider the class of binary input degraded broadcast channels with no common message that have the same property. We characterize this class. We also establish new properties of Marton´s inner bound that help restrict the search space for computing the Marton sum rate. In particular, we establish an extension of the XOR case of the binary inequality of Nair, Wang, and Geng.