Unicast Transmission Over Multiple Access Erasure Networks: Capacity and Duality

This paper determines the unicast capacity of a class of erasure networks which incorporate receiver interference. The networks under consideration are conglomerations of multiple-access channels: Each node has a single receiver, which obtains the finite-field sum of all the unerased inputs to that node. In this directed, acyclic graph model, nodes are allowed to transmit different symbols down each outgoing edge, in contrast to the broadcast constraint of the wireless erasure network of (Dana, 2006). This paper proves that a max-flow min-cut bound, which incorporates the interference properties of the model, is achievable using random coding arguments when knowledge of all erasure locations is provided to the destination node. In addition, the paper concludes by showing a duality relationship between multiple access erasure networks and wireless erasure networks.