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International Journal of Digital Multimedia Broadcasting
Volume 2009, Article ID 129698, 5 pages
http://dx.doi.org/10.1155/2009/129698
Research Article

Galois Field Instructions in the Sandblaster 2.0 Architectrue

1Sandbridge Technologies, Inc., White Plains, NY 10601, USA
2Tampere University of Technology, Korkeakoulunkatu 1, 33720 Tampere, Finland

Received 20 November 2008; Revised 17 May 2009; Accepted 26 August 2009

Academic Editor: Mihai Sima

Copyright © 2009 Mayan Moudgill et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper presents a novel approach to implementing multiplication of Galois Fields with 2 N . Elements of GF( 2 N ) can be represented as polynomials of degree less than N over GF(2). Operations are performed modulo an irreducible polynomial of degree n over GF(2). Our approach splits a Galois Field multiply into two operations, polynomial-multiply and polynomial-remainder over GF(2). We show how these two operations can be implemented using the same hardware. Further, we show that in many cases several polynomial-multiply operations can be combined before needing to a polynomial-remainder. The Sandblaster 2.0 is a SIMD architecture. It has SIMD variants of the poly-multiply and poly-remainder instructions. We use a Reed-Solomon encoder and decoder to demonstrate the performance of our approach. Our new approach achieves speedup of 11.5x compared to the standard SIMD processor of 8x.