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

网络编码被吹捧为与有线和无线网络健壮运行相关的几个应用程序可以建立的基础。这种有前途的技术一直缺少一个简单的框架来解释它在任意无线网络中的演变。给定一个任意的无线网络和网络编码策略，一个有待回答的问题是网络中节点的秩或状态如何随时间演变。此外，如果底层无线网络由于PHY层、MAC层的变化或由于移动性或流量等其他因素而发生变化，这将如何影响该任意网络上网络编码的演变？这项研究包括回答这些对网络从业者至关重要的问题。为了研究网络编码的动力学特性，提出了一个基于微分方程（DE）和微分包含（DI）的系统框架。微分包含是微分方程中右手边不连续的一种推广。使用解析方法和数值软件来求解微分方程和包含，DEDI框架被用作网络编码跨层设计和分析的工具。数值DE和DI求解器用于开发开源软件实用程序，该实用程序允许分析见解，而不必求助于耗时的模拟，从而帮助设计实用的网络编码。使用DEs和DIs以及相关的数值软件也为研究生和本科生提供了一个教育机会，通过开发简单但说明性的模块来研究网络编码的演变。

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.