  The two-receiver broadcast packet erasure channel with feedback and memory is
studied. Memory is modeled using a finite-state Markov chain representing a
channel state. The channel state is unknown at the transmitter, but
observations of this hidden Markov chain are available at the transmitter
through feedback. Matching outer and inner bounds are derived and the capacity
region is determined. The capacity region does not have a single-letter
characterization and is, in this sense, uncomputable. Approximations of the
capacity region are provided and two optimal coding algorithms are outlined.
The first algorithm is a probabilistic coding scheme that bases its decisions
on the past L feedback sequences. Its achievable rate-region approaches the
capacity region exponentially fast in L. The second algorithm is a
backpressure-like algorithm that performs optimally in the long run.
