Piecewise Regular Arrays
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Piecewise Regular Arrays
Application-specific regular array processors have been widely used in signal and image processing, multimedia and communication systems, for example, in data compression and HDTV. One of the main problems of application-specific computing is how to map algorithms into hardware. The major achievement of the theory of regular arrays is that an algorithm, represented as a data dependence graph, is embedded into a Euclidean space, where the integer points are the elementary computations and the dependencies between computations are denoted by vectors between points. The process of mapping an algorithm into hardware is reduced to finding, for the given Euclidean space, a new coordinate system that can be associated with the physical properties of space and time - so called space-time. The power of the synthesis method is that it provides a bridge between "abstract" and "physical" representations of algorithms, thus providing a methodological basis for synthesizing computations in space and in time. This book will extend the existing synthesis theory by exploiting the associativity and commutativity of computations. The practical upshot being a controlled increase in the dimensionality of the Euclidean space representing an algorithm. This increase delivers more degrees of freedom in the choice of the space-time mapping and leads, subsequently, to more choice in the selection of cost-effective application-specific designs.
Parallel Processing on VLSI Arrays
Author: Josef A. Nossek
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
Guest Editor: JOSEF A. NOSSEK This is a special issue of the Journal of VLSI Signal Processing comprising eight contributions invited for publica tion on the basis of novel work presented in a special session on "Parallel Processing on VLSI Arrays" at the International Symposium on Circuits and Systems (ISCAS) held in New Orleans in May 1990. Massive parallelism to cope with high-speed requirements stemming from real-time applications and the restrictions in architectural and circuit design, such as regularity and local connectedness, brought about by the VLSI technology are the key questions addressed in these eight papers. They can be grouped into three subsections elaborating on: • Simulation of continuous physical systems, i. e. , numerically solving partial differential equations. • Neural architectures for image processing and pattern recognition. • Systolic architectures for implementing regular and irregular algorithms in VLSI technology. The paper by A. Fettweis and O. Nitsche advocates a signal processing approach for the numerical integration of partial differential equations (PD Es). It is based on the principles of multidimensional wave digital filters (MDWDFs) thereby preserving the passivity of energy dissipating physical systems. It is particularly suited for systems ofPDEs involving time and finite propagation speed. The basic ideas are explained using Maxwell's equa tions as a vehicle for the derivation of a multidimensional equivalent circuit representing the spatially infinitely extended arrangement with only very few circuit elements.
Algorithm Engineering for Integral and Dynamic Problems
Algorithm engineering allows computer engineers to produce a computational machine that will execute an algorithm as efficiently and cost-effectively as possible given a set of constraints, such as minimal performance or the availability of technology. Addressing algorithm engineering in a parallel setting, regular array syntheses offer powerful computation and embody best practice, but often face the criticism that they are applicable only to restricted classes of algorithms. Algorithm Engineering for Integral and Dynamic Problems reviews the basic principles of regular array synthesis and shows how to extend its use into classes of algorithms traditionally viewed to be beyond its domain of application. The author discusses the transformation of the initial algorithm specification into a specification with data dependencies of increased regularity in order to obtain corresponding regular arrays by direct application of the standard mapping techniques. The book includes a review of the basic principles of regular array synthesis followed by applications of these techniques to well-known algorithms, concluding with numerous case studies to illustrate the methods. Researchers and practitioners in algorithm engineering will find that this text significantly extends their understanding of the applications of regular array synthesis and regular array processors beyond the traditionally narrow field of relevance.