Capacity Regions of Two New Classes of Two-Receiver Broadcast Channels

Motivated by a simple broadcast channel, we generalize the notions of a less noisy receiver and a more capable receiver to an essentially less noisy receiver and an essentially more capable receiver, respectively. We establish the capacity regions of these classes by borrowing on existing techniques; however, these new classes contain additional interesting classes of broadcast channels, including the BSC/BEC broadcast channel. We also establish the relationships between the new classes and the existing classes.