Forwarding and optical indices of 4-regular circulant networks

An all-to-all routing in a graph $G$ is a set of oriented paths of $G$, with exactly one path for each ordered pair of vertices. The load of an edge under an all-to-all routing $R$ is the number of times it is used (in either direction) by paths of $R$, and the maximum load of an edge is denoted by $\pi(G,R)$. The edge-forwarding index $\pi(G)$ is the minimum of $\pi(G,R)$ over all possible all-to-all routings $R$, and the arc-forwarding index $\overrightarrow{\pi}(G)$ is defined similarly by taking direction into consideration, where an arc is an ordered pair of adjacent vertices. Denote by $w(G,R)$ the minimum number of colours required to colour the paths of $R$ such that any two paths having an edge in common receive distinct colours. The optical index $w(G)$ is defined to be the minimum of $w(G,R)$ over all possible $R$, and the directed optical index $\overrightarrow{w}(G)$ is defined similarly by requiring that any two paths having an arc in common receive distinct colours. In this paper we obtain lower and upper bounds on these four invariants for $4$-regular circulant graphs with connection set $\{\pm 1,\pm s\}$, $1<s<n/2$. We give approximation algorithms with performance ratio a small constant for the corresponding forwarding index and routing and wavelength assignment problems for some families of $4$-regular circulant graphs.Comment: 19 pages, no figure in Journal of Discrete Algorithms 201

Methods and problems of wavelength-routing in all-optical networks

We give a survey of recent theoretical results obtained for wavelength-routing in all-optical networks. The survey is based on the previous survey in [Beauquier, B., Bermond, J-C., Gargano, L., Hell, P., Perennes, S., Vaccaro, U.: Graph problems arising from wavelength-routing in all-optical networks. In: Proc. of the 2nd Workshop on Optics and Computer Science, part of IPPS'97, 1997]. We focus our survey on the current research directions and on the used methods. We also state several open problems connected with this line of research, and give an overview of several related research directions

Recursive cubes of rings as models for interconnection networks

We study recursive cubes of rings as models for interconnection networks. We first redefine each of them as a Cayley graph on the semidirect product of an elementary abelian group by a cyclic group in order to facilitate the study of them by using algebraic tools. We give an algorithm for computing shortest paths and the distance between any two vertices in recursive cubes of rings, and obtain the exact value of their diameters. We obtain sharp bounds on the Wiener index, vertex-forwarding index, edge-forwarding index and bisection width of recursive cubes of rings. The cube-connected cycles and cube-of-rings are special recursive cubes of rings, and hence all results obtained in the paper apply to these well-known networks

FPGE implementation of LDPC codes

Low density parity check LDPC Code is a type of Block Error Correction code discovered and performance very close to Shanon’s limit .Good error correcting performance enables reliable communication. Since its discovery by Gallagar there is more research going on for its efficient construction and implementation. Though there is no unique method for constructing LDPC codes. Implementation of LDPC Code is done by taking different factors in to consideration such as error rate, parallelism of decoder, ease in implementation etc. This thesis is about FPGA implementation of LDPC codes and their performance evaluation. Protograph codes were introduced and analyzed by NASA's Jet Propulsion Laboratory in the early years of this century. Part of this thesis continues that work, investigating the decoding of specific protograph codes and extending existing tools for analyzing codes to protograph codes In this thesis I have taken the performance of LDPC coded BPSK modulated signal which is transmitted through AWGN channel and the performance is tested using MATLAB Simulation

Towards Massive Connectivity Support for Scalable mMTC Communications in 5G networks

The fifth generation of cellular communication systems is foreseen to enable a multitude of new applications and use cases with very different requirements. A new 5G multiservice air interface needs to enhance broadband performance as well as provide new levels of reliability, latency and supported number of users. In this paper we focus on the massive Machine Type Communications (mMTC) service within a multi-service air interface. Specifically, we present an overview of different physical and medium access techniques to address the problem of a massive number of access attempts in mMTC and discuss the protocol performance of these solutions in a common evaluation framework

A graph theoretic approach to transputer network design for computer vision

The work in this thesis is concerned with parallel architectures based on the Inmos transputer-type processors and parallelisation of some computer vision tasks chosen from low to high level. The transputer is a microprocessor with a micro-programmed scheduler and four serial communication links. It directly supports parallel processing since several transputers can be connected through their links to co-operate on solving a problem. Also several processes can be run on the same transputer. A major issue in parallel processing is the communication overhead introduced by parallelising a given task. This overhead is not present in sequential processing and must be curbed if the implementation of a task on a parallel machine is to be successful. The interconnection network underlying the architecture of a parallel computer is therefore of the utmost importance. Computer Vision consists of a hierarchy of tasks ranging from low-level operations dealing with large amounts of relatively simple data to high level operations handling increasingly complex structures. In this work a novel edge detector based on adaptive filtering and an edge detector operating on colour images are presented and implemented on a number of transputers. These parallel implementations together with implementations of vector quantisation, Fourier descriptors for shape discrimination, the Hough transform and the Maximum clique algorithm, offer a notable performance increase when compared with sequential implementations. However, every algorithm required the design of a specific network of transputers to take advantage of the parallelism and data dependencies inherent in each. Consequently, attention is focused on the topology of interconnection networks. In particular, the communication requirements of computer vision algorithms as identified by the various computer vision tasks are analysed. These requirements together with graph theoretical considerations are then used to suggest a topology for large transputer networks. The latter is based on sub-graphs, with proven performance when used to implement interconnection networks, combined to form an architecture with improved performance. This architecture consists of a fixed structure supplemented with a dynamically reconfigured network. After describing this topology, a routing algorithm that conveys messages along shortest paths in the network is given and implemented. And finally, some practical issues in the use of transputers are considered and solutions proposed