Galois Field Instructions in the Sandblaster 2.0 Architectrue
This paper presents a novel approach to implementing multiplication of Galois Fields with 2N. Elements of GF(2N) 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 mu...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2009-01-01
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| Series: | International Journal of Digital Multimedia Broadcasting |
| Online Access: | http://dx.doi.org/10.1155/2009/129698 |
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| Summary: | This paper presents a novel approach to implementing multiplication of Galois Fields with 2N. Elements of GF(2N) 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. |
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| ISSN: | 1687-7578 1687-7586 |