Fading broadcast channels with state information at the receivers

Despite considerable progress on the information-theoretic broadcast channel, the capacity regions of fading broadcast channels with channel state known at the receivers but unknown at the transmitter remain unresolved. We address this subject by introducing a layered erasure broadcast channel model in which each component channel has a state that specifies the received signal levels in an instance of a deterministic binary expansion channel. We find the capacity region of this class of broadcast channels. The inner bound assigns each signal level to the user that derives the maximum expected rate from that level. The outer bound is based on a channel enhancement that creates a degraded broadcast channel for which the capacity region is known. This same approach is then used to find outer bounds to the capacity region of fading Gaussian broadcast channels.