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

网络编码被吹捧为可以构建与有线和无线网络的鲁棒操作相关的若干应用的基础。这种有前途的技术一直缺少一个简单的框架，可以解释其在任意无线网络中的演变。给定任意无线网络和网络编码策略，仍然需要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，如果通过PHY层、MAC层中的变化或由于诸如移动性或业务的其他因素而在底层无线网络中存在变化，则这如何影响在该任意网络上的网络编码的演进？这项研究涉及回答这些问题是至关重要的网络从业者。基于微分方程（DE）和微分包含（DI），提出了一个研究网络编码动力学的系统框架DEDI。使用解析方法和数值软件来求解微分方程和夹杂物，DEDI框架被用作网络编码的跨层设计和分析的工具。数值DE和DI求解器用于开发一个开源软件实用程序，该软件实用程序允许分析见解，而无需诉诸耗时的模拟，从而帮助设计实用的网络编码。使用的DE和DI连同相关的数值软件沿着还提供了一个教育机会，涉及研究生和本科生通过开发简单而说明性的模块，用于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.