Capacity Theorems for Broadcast Channels with Two Channel State Components Known at the Receivers

We establish the capacity region of several classes of broadcast channels with random state in which the channel to each user is selected from two possible channel state components and the state is known only at the receivers. When the channel components are deterministic, we show that the capacity region is achieved via Marton coding. This channel model does not belong to any class of broadcast channels for which the capacity region was previously known and is useful in studying wireless communication channels when the fading state is known only at the receivers. We then establish the capacity region when the channel components are ordered, e.g., degraded. In particular we show that the capacity region for the broadcast channel with degraded Gaussian vector channel components is attained via Gaussian input distribution. Finally, we extend the results on ordered channels to two broadcast channel examples with more than two channel components, but show that these extensions do not hold in general.