Optimal opportunistic routing and network coding for bidirectional wireless flows

There is growing interest in recent years in routing methods for wireless networks that leverage the broadcast nature of the wireless medium and the ability of nodes to overhear their neighbors' transmissions. Such methods include opportunistic routing (OR), which generally choose the next hop on a routing path only after the outcome of the previous transmission is known; and wireless network coding (NC), which linearly combines packets from different flows coexisting in the network. In this paper, we study the potential benefits of forwarding schemes that combine elements from both the OR and NC approaches, when traffic on a bidirectional unicast connection between two nodes is relayed by multiple common neighbors. We present a theoretically optimal scheme that provides a lower bound on the expected number of transmissions required to communicate a packet in both directions as a function of link error probabilities, and demonstrate that this bound can be up to 20% lower than with either OR or NC employed alone even in a small network. Using simulation, we further explore the control overhead in a direct implementation of the scheme with a simple coordination mechanism and show that the optimal bound can be closely approached for a wide range of link error rates.