Cost Advantage of Network Coding in Space for Irregular (5 + 1) Model

Network coding in space, a new direction also named space information flow, is verified to have potential advantages over routing in space if the geometric conditions are satisfied. Cost advantage is adopted to measure the performance for network coding in space. Present literatures proved that only in regular (5 + 1) model, network coding in space is strictly superior to routing in terms of single-source multicast, comparing with other regular (n + 1) models. Focusing on irregular (5 + 1) model, this paper uses geometry to quantitatively study the constructions of network coding and optimal routing when a sink node moves without limits in space. Furthermore, the upperbound of cost advantage is figured out as well as the region where network coding is strictly superior to routing. Some properties of network coding in space are also presented.