A Deterministic Polynomial--Time Algorithm for Constructing a Multicast Coding Scheme for Linear Deterministic Relay Networks

We propose a new way to construct a multicast coding scheme for linear deterministic relay networks. Our construction can be regarded as a generalization of the well-known multicast network coding scheme of Jaggi et al. to linear deterministic relay networks and is based on the notion of flow for a unicast session that was introduced by the authors in earlier work. We present randomized and deterministic polynomial–time versions of our algorithm and show that for a network with $g$ destinations, our deterministic algorithm can achieve the capacity in $\lceil \log (g+1)\rceil$ uses of the network.