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

Capacity Regions of Two-User Broadcast Erasure Channels with Feedback and Hidden Memory