Limits of Information Flow in Networks of Two-Way Channels

在当今的技术社会中，通信网络在信息传播中至关重要。几个学科对其运行的各个方面进行了研究，但一直缺乏一个完整的组网理论。网络优化理论的目标是最有效地利用网络资源，但最近在网络编码方面的工作表明，该理论中的流守恒的标准假设对通信网络的工作进行了人为的限制。网络信息论考虑了更一般的通信模型，并对多发送方和接收方的通信系统中的信息传输进行了一定的限制。本研究融合了网络优化理论和网络信息理论的各个方面，以发现和规定跨通信网络的信息传输的新的限制。研究人员使用信息论中的双向信道作为通信网络相邻处理器之间传输介质的通用模型，并解决与双向信道网络的分析和设计有关的基本优化问题。研究人员在多播环境中寻找最优路由算法，并对网络编码可以或不能在路由上改进的情况进行广泛分类。研究人员进一步致力于对由信息论论证得出的双向割集界限是紧的网络情景进行分类，并在双向割集界限不紧的情况下探索与基尔霍夫定律对应的网络信息。这项研究还涉及扩展最小成本浮动的概念，这是处理服务质量问题和设计满足信息传输要求的最低成本或容量的网络的初步方法。

Communication networks are critically important in thedissemination of information in today's technologicalsociety. Several academic disciplines have undertakenthe study of various aspects of their operation, butan integrated theory of networking has been elusive.The objective of network optimization theory is tomost effectively use network resources, but recentwork in network coding has demonstrated that a standardassumption of flow conservation from this theory hasimposed artificial restrictions on the workings ofcommunication networks. Network information theoryconsiders more general models of communication andoffers some bound on the limits of information transferin a communication system involving multiple sendersand receivers.This research fuses aspects of network optimizationtheory and network information theory in order to findand specify new limits of information transfer acrossa communication network. The investigators use thetwo-way channel from information theory as a generalmodel of the transmission medium between neighboringprocessors of a communication network and addressfundamental optimization problems pertaining to theanalysis and design of networks of two-way channels.The investigators seek optimal routing algorithms inmulticast settings and a broad classification ofsituations where network coding can or cannot improveupon routing. The investigators further aim tocategorize network scenarios in which a bidirectedcut set bound derived using information theoreticarguments is tight and to explore a network informationcounterpart to Kirchoff's law when the bidirectedcut set bound is not tight. The research alsoinvolves extending the notion of minimal cost flowas an initial approach to treating quality-of-serviceissues and devising networks with least cost orcapacity that meet requirements on information transfer.