Analyzing Random Network Coding with Differential Equations and Differential Inclusions

TL;DR

This paper introduces a differential equations and inclusions framework to analyze Random Network Coding and its nonlinear variant in wireless networks, providing theoretical insights and practical performance analysis tools.

Contribution

It develops a novel DEDI framework that enables both analytical and numerical study of RNC and RC in complex wireless network scenarios.

Findings

Proves theoretical results on multicast information flows using RNC and RC.

Demonstrates the framework's accuracy through examples with multiple multicast sessions.

Shows the framework's flexibility in analyzing networks with arbitrary topologies.

Abstract

We develop a framework based on differential equations (DE) and differential inclusions (DI) for analyzing Random Network Coding (RNC), as well as a nonlinear variant referred to as Random Coupon (RC), in a wireless network. The DEDI framework serves as a powerful numerical and analytical tool to study RNC. We demonstrate its versatility by proving theoretical results on multicast information flows in a wireless network using RNC or RC. We also demonstrate the accuracy and flexibility of the performance analysis enabled by this framework via illustrative examples of networks with multiple multicast sessions, user cooperation and arbitrary topologies.