On benefits of network coding in bidirected networks and hyper-networks

Network coding is a technique that allows information flows to be encoded while routed across a data network. It was shown that network coding helps increase the throughput and reduce the cost of data transmission, especially for one-to-many multicast applications. An important direction in network coding research is to understand and quantify the coding advantage and cost advantage, i.e., the potential benefits of network coding, as compared to routing, in terms of increasing throughput and reducing transmission cost, respectively. Two classic network models were considered in previous studies of coding advantage: directed networks and undirected networks. The study of coding advantage in this work further focuses on two types of parameterized networks, including bidirected networks and hyper-networks, which generalizes the directed and the undirected network models, respectively. With proper parameter setting, more realistic modeling of networks in practice can be achieved. We prove upper-bounds and lower-bounds on the coding advantage for multicast in these models. Some of our bounds are new and unknown before, some improve upon previously proven bounds, and some answer open questions in the literature.