  Resource allocation in wireless networks typically occurs at PHY/MAC layers,
while random network coding (RNC) is a network layer strategy. An interesting
question is how resource allocation mechanisms can be tuned to improve RNC
performance. By means of a differential equation framework which models RNC
throughput in terms of lower layer parameters, we propose a gradient based
approach that can dynamically allocate MAC and PHY layer resources with the
goal of maximizing the minimum network coding throughput among all the
destination nodes in a RNC multicast. We exemplify this general approach with
two resource allocation problems: (i) power control to improve network coding
throughput, and (ii) CSMA mean backoff delay control to improve network coding
throughput. We design both centralized algorithms and online algorithms for
power control and CSMA backoff control. Our evaluations, including numerically
solving the differential equations in the centralized algorithm and an
event-driven simulation for the online algorithm, show that such gradient based
dynamic resource allocation yields significant throughput improvement of the
destination nodes in RNC. Further, our numerical results reveal that network
coding aware power control can regain the broadcast advantage of wireless
transmissions to improve the throughput.
