Stable and capacity achieving 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 the case of a single source transmitting packets to N users, where per-slot feedback is fed back to the transmitter in the form of ACK/NACK messages. This scheme performs only binary (XOR) operations and includes special rules for coding packets that ensure instantaneous decodability. Drawing on the results of network stability under statistical overhearing, we provide a stabilizing policy using this coding scheme. Furthermore, we show that, for N = 4 and i.i.d. erasure events, the stability region of such a system effectively coincides with its information-theoretic capacity region, and provide a stabilizing policy that employs this XOR-based scheme.