Feedback-based Coding Algorithms for Braodcast Erasure Channels with Degraded Message Sets

We consider single-hop broadcast packet erasure channels (BPEC) with degraded message sets and instantaneous feedback regularly available from all receivers, and demonstrate that the main principles of the virtual-queue-based algorithms in [1], which were proposed for multiple unicast sessions, can still be applied to this setting and lead to capacity-achieving algorithms. Specifically, we propose a generic class of algorithms and intuitively describe its rationale and properties that result in its efficiency. We then apply this class of algorithms to three examples of BPEC channels (with different numbers of users and 2 or 3 degraded message sets) and show that the achievable throughput region matches a known capacity outer bound, assuming feedback availability through a separate public channel. If the feedback channel is not public, all users can still decode their messages, albeit at some overhead which results in an achievable throughput that differs from the outer bound by O(N/L), where L is the packet length. These algorithms do not require any prior knowledge of channel statistics for their operation.