Optimal scheduling of pairwise XORs under statistical overhearing and feedback

We study the problem of scheduling transmissions of packets belonging to several flows traversing a given node while making local encoding decisions. Practical wireless network coding solutions rely on knowledge of key knowledge which is obtained at the transmitter/scheduler either by acknowledgments or statistically. In the latter case, the knowledge of overhearing events for each packet improves progressively with feedback from the transmissions. We propose a virtual network mechanism in order to characterize the throughput region of such a system for the case where we allow only pairwise XORing. We also provide the policy which achieves the throughput region.