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We define a class of multi-hop erasure networks that approximates a wireless multi-hop network. The network carries unicast flows for multiple users, and each information packet within a flow is required to be decoded at the flow destination within a specified delay deadline. The allocation of coding rates amongst flows/users is constrained by network capacity. We propose a proportional fair transmission scheme that maximises the sum utility of flow throughputs. This is achieved by jointly optimising the packet coding rates and the allocation of bits of coded packets across transmission slots.

Utility optimal coding for packet transmission over wireless networks — Part II: Networks of packet erasure channels