Linear codes for network information flow

Network information flow was recently introduced by Ahlswede et al. They studied the single-source problem. Their work revealed that it is in general not optimal to consider the information to be multicast in a network as a "fluid" which can simply be routed or replicated. Rather, by employing coding at the nodes, bandwidth can in general be saved. In this paper, we present a linear coding scheme for the single-source problem studied by Ahlswede et al. Such a coding scheme is specified by a linear-code multicast.