  In this paper we describe a network coding scheme for the Broadcast Erasure
Channel with multiple unicast stochastic flows, in 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 involves a network of queues, along with special rules for
coding and moving packets among the queues, that ensure instantaneous
decodability. The system under consideration belongs to a class of networks
whose stability properties have been analyzed in earlier work, which is used to
provide a stabilizing policy employing the currently proposed coding scheme.
Finally, we show the optimality of the proposed policy for $N=4$ and i.i.d.
erasure events, in the sense that the policy's stability region matches a
derived outer bound (which coincides with the system's information-theoretic
capacity region), even when a restricted set of coding rules is used.
