Stable XOR-Based Policies for the Broadcast Erasure Channel With Feedback

In this paper, we describe a network coding scheme for the Broadcast Erasure Channel with multiple unicast stochastic flows, for a single source transmitting packets to N users with per-slot ACK/NACK feedback. This scheme performs only binary (XOR) operations and involves a network of queues, along with special rules for coding and moving packets among the queues, that ensure instantaneous decodability. Additionally, for the scheme to work, one has to specify which packets to select for encoding at each time, based on the received feedback. Contrary to prior work where this packet selection was explicitly specified a priori, we employ a backpressure-type policy that makes the selection based only on queue backlogs. We next provide a stability region outer bound for arbitrary N and erasure patterns and show that this bound effectively coincides with a bound on the system's information-theoretic capacity region (accounting for idle slots). Finally, for N=4 and i.i.d. erasures, we provide a policy that achieves the stability outer bound and employs the proposed XOR scheme using a restricted set of coding rules.