Analyzing Random Network Coding With Differential Equations and Differential Inclusions
The authors develop a framework based on Differential Equations (DE) and Differential Inclusions (DI) for analyzing Random Network Coding (RNC) in an arbitrary wireless network. The DEDI framework serves as a powerful numerical and analytical tool to study RNC. For demonstration, they first build a system of DE's with this framework, under the fluid approximation, to model the means of the rank evolution processes. By converting this system to DI's and explicitly solving them, they show that the average multicast throughput is equal to the min-cut bound. They then turn to the precise system of DE's regarding the means and variances of the rank evolution processes.