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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| Format: | Article |
| Language: | English |
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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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| _version_ | 1832555903610519552 |
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| author | Mayan Moudgill Andrei Iancu Daniel Iancu |
| author_facet | Mayan Moudgill Andrei Iancu Daniel Iancu |
| author_sort | Mayan Moudgill |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-0e810d48407f4e679df035749d0dd732 |
| institution | Kabale University |
| issn | 1687-7578 1687-7586 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Digital Multimedia Broadcasting |
| spelling | doaj-art-0e810d48407f4e679df035749d0dd7322025-02-03T05:46:52ZengWileyInternational Journal of Digital Multimedia Broadcasting1687-75781687-75862009-01-01200910.1155/2009/129698129698Galois Field Instructions in the Sandblaster 2.0 ArchitectrueMayan Moudgill0Andrei Iancu1Daniel Iancu2Sandbridge Technologies, Inc., White Plains, NY 10601, USASandbridge Technologies, Inc., White Plains, NY 10601, USASandbridge Technologies, Inc., White Plains, NY 10601, USAThis 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.http://dx.doi.org/10.1155/2009/129698 |
| spellingShingle | Mayan Moudgill Andrei Iancu Daniel Iancu Galois Field Instructions in the Sandblaster 2.0 Architectrue International Journal of Digital Multimedia Broadcasting |
| title | Galois Field Instructions in the Sandblaster 2.0 Architectrue |
| title_full | Galois Field Instructions in the Sandblaster 2.0 Architectrue |
| title_fullStr | Galois Field Instructions in the Sandblaster 2.0 Architectrue |
| title_full_unstemmed | Galois Field Instructions in the Sandblaster 2.0 Architectrue |
| title_short | Galois Field Instructions in the Sandblaster 2.0 Architectrue |
| title_sort | galois field instructions in the sandblaster 2 0 architectrue |
| url | http://dx.doi.org/10.1155/2009/129698 |
| work_keys_str_mv | AT mayanmoudgill galoisfieldinstructionsinthesandblaster20architectrue AT andreiiancu galoisfieldinstructionsinthesandblaster20architectrue AT danieliancu galoisfieldinstructionsinthesandblaster20architectrue |