Utility Optimal Coding for Packet Transmission over Wireless Networks - Part II: Networks of Packet Erasure Channels

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 {\em jointly optimising the packet coding rates and the allocation of bits of coded packets across transmission slots.}