Accelerated Processing for Maximum Distance Separable Codes Using Composite Extension Fields

TY - GEN

T1 - Accelerated Processing for Maximum Distance Separable Codes Using Composite Extension Fields

AU - Ruano, Diego

AU - Lucani Rötter, Daniel Enrique

AU - Geil, Olav

PY - 2019

Y1 - 2019

N2 - This paper describes a new design of Reed-Solomon (RS) codes when using composite extension fields. Our ultimate goal is to provide codes that remain Maximum Distance Separable (MDS), but that can be processed at higher speeds in the encoder and decoder. This is possible by using coefficients in the generator matrix that belong to smaller (and faster) finite fields of the composite extension and limiting the use of the larger (and slower) finite fields to a minimum. We provide formulae and an algorithm to generate such constructions starting from a Vandermonde RS generator matrix and show that even the simplest constructions, e.g., using only processing in two finite fields, can speed up processing by as much as two-fold compared to a Vandermonde RS and Cauchy RS while using the same decoding algorithm, and more than two-fold compared to other RS Cauchy and FFT-based RS.

AB - This paper describes a new design of Reed-Solomon (RS) codes when using composite extension fields. Our ultimate goal is to provide codes that remain Maximum Distance Separable (MDS), but that can be processed at higher speeds in the encoder and decoder. This is possible by using coefficients in the generator matrix that belong to smaller (and faster) finite fields of the composite extension and limiting the use of the larger (and slower) finite fields to a minimum. We provide formulae and an algorithm to generate such constructions starting from a Vandermonde RS generator matrix and show that even the simplest constructions, e.g., using only processing in two finite fields, can speed up processing by as much as two-fold compared to a Vandermonde RS and Cauchy RS while using the same decoding algorithm, and more than two-fold compared to other RS Cauchy and FFT-based RS.

M3 - Article in proceedings

SN - 978-3-8007-4948-5

SP - 14

EP - 18

BT - European Wireless 2019 Conference, EW 2019

PB - VDE Verlag GmbH

T2 - European Wireless 2019 - 25th European Wireless Conference

Y2 - 2 May 2019 through 5 May 2019

ER -