Multi-source operator channels: Efficient capacity-achieving codes

The network communication scenario where one or more receivers request all the information transmitted by different sources is considered. We introduce the first polynomial-time (in network size) network codes that achieve any point inside the rate-region for the problem of multiple-source multicast in the presence of malicious errors, for any fixed number of sources. Our codes are fully distributed and different sources require no knowledge of the data transmitted by their peers. Our codes are "end-to-end", that is, all nodes apart from the sources and the receivers are oblivious to the adversaries present in the network and simply implement random linear network coding.