A Generalized Rational Interpolation Problem and the Solution of theWelch–Berlekamp Key Equation
Designs, Codes and Cryptography
Towards a VLSI Architecture for Interpolation-Based Soft-Decision Reed-Solomon Decoders
Journal of VLSI Signal Processing Systems
StoreGPU: exploiting graphics processing units to accelerate distributed storage systems
HPDC '08 Proceedings of the 17th international symposium on High performance distributed computing
On GPU's viability as a middleware accelerator
Cluster Computing
On Cauchy matrices for remainder decoding of Reed-Solomon codes
IEEE Communications Letters
A GPU accelerated storage system
Proceedings of the 19th ACM International Symposium on High Performance Distributed Computing
Applications of Reed-Solomon codes in mobile digital video communications systems
International Journal of Mobile Network Design and Innovation
| Hi-index | 754.84 |
The problem of decoding cyclic error correcting codes is one of solving a constrained polynomial congruence, often achieved using the Berlekamp-Massey or the extended Euclidean algorithm on a key equation involving the syndrome polynomial. A module-theoretic approach to the solution of polynomial congruences is developed here using the notion of exact sequences. This technique is applied to the Welch-Berlekamp (1986) key equation for decoding Reed-Solomon codes for which the computation of syndromes is not required. It leads directly to new and efficient parallel decoding algorithms that can be realized with a systolic array. The architectural issues for one of these parallel decoding algorithms are examined in some detail