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首页> 外文期刊>Information Theory, IEEE Transactions on >Analyzing Random Network Coding With Differential Equations and Differential Inclusions
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Analyzing Random Network Coding With Differential Equations and Differential Inclusions

机译：用微分方程和微分包含分析随机网络编码

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摘要

We develop a framework based on differential equations (DE) and differential inclusions (DI) for analyzing Random Network Coding (RNC) in an arbitrary wireless network. The DEDI framework serves as a powerful numerical and analytical tool to study RNC. For demonstration, we first build a system of DE's with this framework, under the fluid approximation, to model the means of the rank evolution processes. By converting this system to DI's and explicitly solving them, we show that the average multicast throughput is equal to the min-cut bound. We then turn to the precise system of DE's regarding the means and variances of the rank evolution processes. By analyzing this system, we show that the rank evolution processes asymptotically concentrate to the solution of the DI's obtained previously. From this result, it immediately follows that the min-cut bound can be achieved as the number of source packets becomes large. We demonstrate the numerical accuracy and flexibility in performance analysis enabled by the DEDI framework via illustrative examples of networks with multiple multicast sessions, complex topology and correlated reception. We also briefly discuss its application in MAC and PHY adaptation and the extension to Random Coupon Selection.
机译：我们开发了一个基于微分方程（DE）和微分包含物（DI）的框架，用于分析任意无线网络中的随机网络编码（RNC）。 DEDI框架是研究RNC的强大的数值和分析工具。为了进行演示，我们首先在流体近似下使用此框架构建DE的系统，以对秩演化过程的均值进行建模。通过将该系统转换为DI并明确解决它们，我们证明了平均多播吞吐量等于最小割限。然后，我们转向关于等级演化过程的均值和方差的DE的精确系统。通过分析该系统，我们表明等级演化过程渐近地集中于先前获得的DI的解。从该结果可以立即看出，随着源数据包数量的增加，可以实现最小割限。通过具有多个组播会话，复杂拓扑和相关接收的网络的示例，我们演示了DEDI框架支持的性能分析中的数值准确性和灵活性。我们还将简要讨论其在MAC和PHY自适应中的应用以及对随机优惠券选择的扩展。

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