Codes for Graph Erasures

Motivated by systems where the information is represented by a graph, such as neural networks, associative memories, and distributed systems, we present in this work a new class of codes, called codes over graphs. Under this paradigm, the information is stored on the edges of an undirected graph, and a code over graphs is a set of graphs. A node failure is the event where all edges in the neighborhood of the failed node have been erased. We say that a code over graphs can tolerate $\rho$ node failures if it can correct the erased edges of any $\rho$ failed nodes in the graph. While the construction of such codes can be easily accomplished by MDS codes, their field size has to be at least $O(n^2)$, when $n$ is the number of nodes in the graph. In this work we present several constructions of codes over graphs with smaller field size. In particular, we present optimal codes over graphs correcting two node failures over the binary field, when the number of nodes in the graph is a prime number. We also present a construction of codes over graphs correcting $\rho$ node failures for all $\rho$ over a field of size at least $(n+1)/2-1$, and show how to improve this construction for optimal codes when $\rho=2,3$.Comment: To appear in IEEE International Symposium on Information Theor

Abelian Cayley digraphs with asymptotically large order for any given degree

Abelian Cayley digraphs can be constructed by using a generalization to Z(n) of the concept of congruence in Z. Here we use this approach to present a family of such digraphs, which, for every fixed value of the degree, have asymptotically large number of vertices as the diameter increases. Up to now, the best known large dense results were all non-constructive.Peer ReviewedPostprint (author's final draft

A Distributed and Privacy-Aware Speed Advisory System for Optimising Conventional and Electric Vehicles Networks

One of the key ideas to make Intelligent Transportation Systems (ITS) work effectively is to deploy advanced communication and cooperative control technologies among the vehicles and road infrastructures. In this spirit, we propose a consensus-based distributed speed advisory system that optimally determines a recommended common speed for a given area in order that the group emissions, or group battery consumptions, are minimised. Our algorithms achieve this in a privacy-aware manner; namely, individual vehicles do not reveal in-vehicle information to other vehicles or to infrastructure. A mobility simulator is used to illustrate the efficacy of the algorithm, and hardware-in-the-loop tests involving a real vehicle are given to illustrate user acceptability and ease of the deployment.Comment: This is a journal paper based on the conference paper "Highway speed limits, optimised consensus, and intelligent speed advisory systems" presented at the 3rd International Conference on Connected Vehicles and Expo (ICCVE 2014) in November 2014. This is the revised version of the paper recently submitted to the IEEE Transactions on Intelligent Transportation Systems for publicatio