Multiple Access Network Information-flow And Correction codes

The network communication scenario where one or more receivers request all the information transmitted by different sources is considered. We introduce distributed polynomial-time network codes in the presence of malicious nodes. Our codes can achieve any point inside the rate region of multiple-source multicast transmission scenarios both in the cases of coherent and non-coherent network coding. For both cases the encoding and decoding algorithm runs in poly(|E|)exp(s) time, where poly(|E|) is a polynomial function of the number of edges |E| in the network and exp(s) is an exponential function of the number of sources s. 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.