Flow-based XOR network coding for lossy wireless networks

A practical way for maximizing the throughput of a wireless network is to decompose the network into a superposition of small two-hop networks such that network coding can be performed inside these small networks to resolve bottlenecks. We call these networks 2-hop relay networks. Therefore, studying the capacity of 2-hop relay networks is very important. Most practical network coding protocols that perform the superposition ignore the diversity among the links by turning off coding when the channels are lossy. Other protocols deal with the packets separately not as members of flows which makes the network coding problem with lossy links intractable. In this paper, we use a different approach by looking at flows or batches instead of individual packets. We characterize the capacity region of the 2-hop relay network with packet erasure channels when the coding operations are limited to XOR. We derive our results by constructing an upper bound on the capacity region and then providing a coding scheme that can achieve the upper bound. The capacity characterization is in terms of linear equations. We also extend our 2-hop relay networks results to multihop wireless networks by providing a linear program that can perform the superposition optimally. We perform extensive simulations for both the 2-hop relay and large wireless networks and show the superiority of our protocols over the network coding protocols that deal with the packets separately.