  This paper focuses on the Layered Packet Erasure Broadcast Channel (LPE-BC)
with Channel Output Feedback (COF) available at the transmitter. The LPE-BC is
a high-SNR approximation of the fading Gaussian BC recently proposed by Tse and
Yates, who characterized the capacity region for any number of users and any
number of layers when there is no COF. This paper provides a comparative
overview of this channel model along the following lines: First, inner and
outer bounds to the capacity region (set of achievable rates with backlogged
arrivals) are presented: a) a new outer bound based on the idea of the
physically degraded broadcast channel, and b) an inner bound of the LPE-BC with
COF for the case of two users and any number of layers. Next, an inner bound on
the stability region (set of exogenous arrival rates for which packet arrival
queues are stable) for the same model is derived. The capacity region inner
bound generalizes past results for the two-user erasure BC, which is a special
case of the LPE-BC with COF with only one layer. The novelty lies in the use of
inter-user and inter-layer network coding retransmissions (for those packets
that have only been received by the unintended user), where each random linear
combination may involve packets intended for any user originally sent on any of
the layers. For the case of $K = 2$ users and $Q \geq 1$ layers, the inner
bounds to the capacity region and the stability region coincide; both
strategically employ the novel retransmission protocol. For the case of $Q = 2$
layers, sufficient conditions are derived by Fourier-Motzkin elimination for
the inner bound on the stability region to coincide with the capacity outer
bound, thus showing that in those cases the capacity and stability regions
coincide.
