Structural Routability of n-Pairs Information Networks

Information does not generally behave like a conservative fluid flow in communication networks with multiple sources and sinks. However, it is often conceptually and practically useful to be able to associate separate data streams with each source-sink pair, with only routing and no coding performed at the network nodes. This raises the question of whether there is a nontrivial class of network topologies for which achievability is always equivalent to routability, for any combination of source signals and positive channel capacities. This chapter considers possibly cyclic, directed, errorless networks with n source-sink pairs and mutually independent source signals. The concept of downward dominance is introduced and it is shown that, if the network topology is downward dominated, then the achievability of a given combination of source signals and channel capacities implies the existence of a feasible multicommodity flow.Comment: The final publication is available at link.springer.com http://link.springer.com/chapter/10.1007/978-3-319-02150-8_

Patterns in random walks and Brownian motion

We ask if it is possible to find some particular continuous paths of unit length in linear Brownian motion. Beginning with a discrete version of the problem, we derive the asymptotics of the expected waiting time for several interesting patterns. These suggest corresponding results on the existence/non-existence of continuous paths embedded in Brownian motion. With further effort we are able to prove some of these existence and non-existence results by various stochastic analysis arguments. A list of open problems is presented.Comment: 31 pages, 4 figures. This paper is published at http://link.springer.com/chapter/10.1007/978-3-319-18585-9_

A high-throughput overlay multicast infrastructure with network coding

Network coding has been recently proposed in information theory as a new dimension of the information multicast problem that helps achieve optimal transmission rate or cost. End hosts in overlay networks are natural candidates to perform network coding, due to its available computational capabilities. In this paper, we seek to bring theoretical advances in network coding to the practice of high-throughput multicast in overlay networks. We have completed the first real implementation of network coding in end hosts, as well as decentralized algorithms to construct the routing strategies and to perform random code assignment. Our experiences suggest that approaching maximum throughput with network coding is not only theoretically sound, but also practically promising. We also present a number of unique challenges in designing and realizing coded data dissemination, and corresponding solution techniques to address them

Homomorphic MACs: MAC-based integrity for network coding

Abstract. Network coding has been shown to improve the capacity and robustness in networks. However, since intermediate nodes modify packets en-route, integrity of data cannot be checked using traditional MACs and checksums. In addition, network coded systems are vulnerable to pollution attacks where a single malicious node can flood the network with bad packets and prevent the receiver from decoding the packets correctly. Signature schemes have been proposed to thwart such attacks, but they tend to be too slow for online per-packet integrity. They also force network coding coefficients to be picked from a large field which causes the size of the network coding header to be large. Here we propose a homomorphic MAC which allows checking the integrity of network coded data. Our homomorphic MAC is designed as a drop-in replacement for traditional MACs (such as HMAC) in systems using network coding.