CAREER

CCR-0093349 ABSTRACT本项目研究各种不同类型网络的可靠通信。本项目的第一部分涉及网络对永久性故障的容量和稳健性，例如链路或节点的移除。本项目中的方法不再是纯粹基于路由的纯图论方法，而是使用代数框架来考虑网络容量。容量被认为是网络所能支持的一组连接的特征，在该网络中，节点不仅能够执行传统的路由功能，而且还能够处理到达它们的数据。这样的处理被认为是网络上的代码。编码还被应用于恢复，以便即使在网络的一部分发生故障之后，例如在网络中的链路消失之后，也能维持网络中的某些连接。该项目的第二部分考虑在衰落随时间和频率变化的信道中的稳健性，特别是在超宽带上。这部分项目的目标是建立理论结果，将容量、峰值功率、能量、带宽和差错概率联系起来，以表征宽带无线系统中的实际可实现性能。本项目的第一部分研究了使用编码来确保连接的连续性时，在正常和故障条件下网络的可靠性。这个项目表明，传统的网络恢复方法，如重路由，是网络编码的子集，并建立了编码方法，以增加网络在故障条件下的可靠性。此外，这些项目还调查了网络管理问题，其中网络管理代表了修改网络行为所需的信息，该网络行为被定义为网络代码，以响应故障。在本项目中采用的代数方法允许对对网络代码进行更改所需的比特数的基本限制以及需要故障知识的网络部分进行一些表征。该项目的第二部分考虑了甚宽频带信道的容量以及不同类型的信号和编码的适用性，以实现达到或接近理论最大值的性能。特别是，它探讨了在非常大的带宽限制下实现容量所需的非常高的峰值功率符号在多大程度上是必要的。该项目还探索了可实现超宽带结果的带宽范围。这项工作将信道(容量)的理论极限与通过提供关于信号的速率、带宽和峰值功率方面的差错概率的显式界限来实现容量的技术的适用性联系起来。最后，该项目考虑了传统扩频方法在中到大带宽范围内的适用性，例如直接序列码分多址，这些方法在非常大的带宽限制下表现得很差。

CCR-0093349ABSTRACTThis project investigates aspects of reliable communications for verydifferent types of network variability.The first part of the project is concerned with capacity and robustness ofnetworks to permanent failures such as removal of a link or node. Theapproach in this project moves away from a pure graph-theoretic approach,based purely on routing, to consider network capacity using an algebraicframework. Capacity is considered as the characterization of the set ofconnections that can be supported by a network in which the nodes are notonly capable of traditional routing functions, but can also performprocessing of the data that arrives to them. Such processing is consideredas a code over the network. Coding is also applied to recovery to maintaincertain connections in a network even after failure of a portion of thenetwork, for instance after the disappearance of a link in the network. Thesecond part of the project considers robustness in channels where fadingvaries over both time and frequency, especially over ultra wide frequencybands. The goal of this part of the project is to establish theoreticalresults that relate capacity, peak power, energy, bandwith and probabilityof error in such a way as to characterize the practical achievableperformance in wide band wireless systems.The first part of this project investigates the reliability of networksunder normal and failure conditions when coding is used to ensurecontinuity of connections. This project shows that traditional methods ofrecovery in networks, such as rerouting, are subsets of network coding andestablishes coding methods to increase the realibility of networks underfailure conditions. Moreover, the projects investigates the issue of networkmanagement, where network management represents the information needed tomodify the behavior of the network, defined as the code of the network, inresponse to failures. The algebraic approach taken in this project allowssome characterization of the fundamental limits of the number of bitsrequired to effect changes on the network code and of the portions of thenetwork that require knowledge of failures. The second part of the projectconsiders capacity of very wide band channels and the applicability ofdifferent types of signals and codes to achieve performance at or near thetheoretical maximum. In particular, it explores to what extent very highpeak power symbols, which are known to achieve capacity in the limit of verylarge bandwidths, are necessary to achieve capacity. The project alsoexplores the ranges of bandwidth in which ultra-wideband results areachievable. This work bridges the theoretical limits of the channel(capacity) with the applicability of the techniques that achieve capacity byproviding an explicit bound to the probability of error in terms of rate,bandwidth and peak power of the signal. Finally, the project consider theapplicability, in the range of moderate to large bandwidths, of traditionalspread spectrum approaches, such as direct-sequence code-division multipleaccess, that perform poorly in the limit of very large bandwidths.