Multicast capacity of multiple access erasure networks

We derive the capacity of multicast transmissions on a class of erasure networks. The network model incorporates interference in the form of a finite-field additive multiple-access channel for the receiver on each node, but there is no broadcast constraint (any node can transmit independent symbols on each of its outgoing edges). Assuming knowledge of erasure locations at destination nodes, we derive the capacity for a network with multiple sources transmitting independent messages, and each destination node decoding all messages from all source nodes. This capacity is achievable using linear codes at each node.