CIF: Small: DEDI: A New Framework for the Practice of Wireless Network Coding

Network coding is touted as the foundation on which several applications related to the robust operation of both wired and wireless networks can be built. This promising technique has been missing a simple framework that can allow explaining its evolution in an arbitrary wireless network. Given an arbitrary wireless network and a network coding strategy, a question that remains to be answered is how the rank or state of the nodes in the network evolves over time. Further, if there are changes in the underlying wireless network either through changes in the PHY layer, MAC layer or due to other factors such as mobility or traffic, how does this impact the evolution of network coding over this arbitrary network? This research involves answering such questions that are of paramount importance for network practitioners.

A systematic framework called DEDI, that is based on differential equations (DE) and differential inclusions (DI) which is a generalization of DEs with discontinuous right-hand sides, is developed to study the dynamics of network coding. Using both analytical methods and numerical software for solving differential equations and inclusions, the DEDI framework is used as a tool for the crosslayer design and analysis of network coding. Numerical DE and DI solvers are used to develop an open source software utility that allows analytical insights without having to resort to time consuming simulations, there by aiding the design of practical network coding. The use of DEs and DIs along with associated numerical software also offers an educational opportunity to involve both graduate students and undergraduate students by developing simple yet illustrative modules for studying the evolution of network coding.