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The authors consider multi-hop networks comprising Binary Symmetric Channels (BSCs). The network carries unicast flows for multiple users. The utility of the network is the sum of the utilities of the flows, where the utility of each flow is a concave function of its throughput. Given that the network capacity is shared by the flows, there is a contention for network resources like coding rate (at the physical layer), scheduling time (at the MAC layer), etc., among the flows. They propose a proportional fair transmission scheme that maximises the sum utility of flow throughputs subject to the rate and the scheduling constraints. This is achieved by jointly optimising the packet coding rates of all the flows through the network.
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