This project investigates aspects of reliable communications for very different types of network variability. The first part of the project is concerned with capacity and robustness of networks to permanent failures such as removal of a link or node. The approach in this project moves away from a pure graph-theoretic approach, based purely on routing, to consider network capacity using an algebraic framework. Capacity is considered as the characterization of the set of connections that can be supported by a network in which the nodes are not only capable of traditional routing functions, but can also perform processing of the data that arrives to them. Such processing is considered as a code over the network. Coding is also applied to recovery to maintain certain connections in a network even after failure of a portion of the network, for instance after the disappearance of a link in the network. The second part of the project considers robustness in channels where fading varies over both time and frequency, especially over ultra wide frequency bands. The goal of this part of the project is to establish theoretical results that relate capacity, peak power, energy, bandwith and probability of error in such a way as to characterize the practical achievable performance in wide band wireless systems.
The first part of this project investigates the reliability of networks under normal and failure conditions when coding is used to ensure continuity of connections. This project shows that traditional methods of recovery in networks, such as rerouting, are subsets of network coding and establishes coding methods to increase the realibility of networks under failure conditions. Moreover, the projects investigates the issue of network management, where network management represents the information needed to modify the behavior of the network, defined as the code of the network, in response to failures. The algebraic approach taken in this project allows some characterization of the fundamental limits of the number of bits required to effect changes on the network code and of the portions of the network that require knowledge of failures. The second part of the project considers capacity of very wide band channels and the applicability of different types of signals and codes to achieve performance at or near the theoretical maximum. In particular, it explores to what extent very high peak power symbols, which are known to achieve capacity in the limit of very large bandwidths, are necessary to achieve capacity. The project also explores the ranges of bandwidth in which ultra-wideband results are achievable. This work bridges the theoretical limits of the channel (capacity) with the applicability of the techniques that achieve capacity by providing an explicit bound to the probability of error in terms of rate, bandwidth and peak power of the signal. Finally, the project consider the applicability, in the range of moderate to large bandwidths, of traditional spread spectrum approaches, such as direct-sequence code-division multiple access, that perform poorly in the limit of very large bandwidths.