Efficient Reed-Solomon Iterative Decoder Using Galois Field Instruction Set

Iancu, Daniel; Moudgill, Mayan; Glossner, John; Takala, Jarmo

doi:10.1007/978-3-540-70550-5_14

Cited by 1 publication

(3 citation statements)

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“…(i) Correct codeword using Peterson-Gorenstein-Zieler (PGZ) [5] algorithm. (ii) If that fails to correct the errors, successively apply 2, 4, 6, 8 erasures, deriving an error locator polynomial, until an error locator polynomial of correct degree is derived [6,7]. (iii) If an error locator polynomial is identified, attempt to decode the word using the Forney-Messey-Berlekamp (FMB) method [8,9].…”

Section: Algorithmmentioning

confidence: 99%

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Galois Field Instructions in the Sandblaster 2.0 Architectrue

Moudgill

Iancu

2009

International Journal of Digital Multimedia Broadcasting

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This paper presents a novel approach to implementing multiplication of Galois Fields with . Elements of GF() 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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