Despite considerable progress on the information-theoretic broadcast
channel, the capacity region of fading broadcast channels with
channel state known at the receivers but unknown at the transmitter
remains 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 inner and
outer bounds to the capacity region of fading Gaussian broadcast
channels.  We show that the achievable rate region is within 6.386
bits/s/Hz of the capacity region for all fading AWGN broadcast
channels.