Distributed design of network codes for wireless multiple unicasts

Previous results on network coding for low-power wireless transmissions of multiple unicasts rely on opportunistic coding or centralized optimization to reduce the power consumption. This paper proposes a distributed strategy for reducing the power consumption in a network coded wireless network with multiple unicasts. We apply a simple network coding strategy called ldquoreverse carpooling,rdquo which uses only XOR and forwarding operations. In this paper, we use the rectangular grid as a simple network model and attempt to increase network coding opportunities without the overhead required for centralized design or coordination. The proposed technique designates ldquoreverse carpooling linesrdquo analogous to a collection of bus routes in a crowded city. Each individual unicast then chooses a route from its source to its destination independently but in a manner that maximizes the fraction of its path spent on reverse carpooling lines. Intermediate nodes apply reverse carpooling opportunistically along these routes. Our network optimization attempts to choose the reverse carpooling lines in a manner that maximizes the expected power savings with respect to the random choice of sources and sinks.