On the dynamics of random network coding: analyzing random network coding with differential equations

Abstract

OF THE DISSERTATION On the Dynamics of Random Network Coding Analyzing Random Network Coding with Differential Equations by Dan Zhang Dissertation Director: Prof. Narayan B. Mandayam As a network transport scheme, an important quantity for random network coding (RNC) is the non-redundant information a node or a set of nodes possess over time, which is called the rank. In general, the rank is a random process that is affected by a number of factors including the random coding operation, the channel and the randomness built in the MAC and PHY. Due to its complicated nature, previous approaches to random network coding chose to focus on the asymptotic behavior of the rank processes only. For the first time, we develop a dynamical system framework for analyzing RNC in a wireless network based on differential equations (DE). It turns out under the fluid approximation, ranks of different nodes and sets are intertwined in the form of a system of differential equations. The system of DEs allow us to focus on the transient behavior of RNC, rendering a more complete picture of RNC dynamics. The DE framework can be used to reveal the throughput of RNC, or numerically