The Cost Advantage of Network Coding in Uniform Combinatorial Networks

Coding advantage refers to the potential for network coding to improve end-to-end throughput or reduce routing cost. How large can the coding advantage be? We investigate this fundamental question in the classic undirected network model. So far, all known networks where such potential exists are based on a special class of topologies known as combinatorial networks. We try to prove a rather small upper-bound (close to 1) for the coding advantage for the class of combinatorial networks and its variations. Such a result, interestingly, will lead us to the following dilemma: either we are still missing the most appropriate network topologies for demonstrating the power of network coding, or we have been ignoring a very effective perspective for efficiently approximating the minimum Steiner tree problem, after a few decades of research in Steiner trees. We elaborate on the above arguments and present the early stage results of our research: the coding advantage (in terms of routing cost) is upper-bounded by 1.125 in the class of uniform combinatorial networks.