Abstract

Abstract- We present a low complexity algorithm for designing algebraic codes that achieve the infor-mation theoretic capacity for the multicast problem on directed acyclic networks. These codes operate over field sizes which are significantly smaller than those previously known, leading to significantly lower design and implementation complexity, and network link usage. These codes can be extended for networks with cycles and delays, and for robustness properties. A network is represented by a directed graph Ei = ( V, E) with a vertex set V and edge set E. Multiple edges are allowed between vertices, and 6 is acyclic. A source node s E V gen-erating information at rate R, and a set of N receiver nodes R = { T I, r2,..., T N} C V, axe specified. Nodes are allowed to transmit on outgoing edges any causal function of information