Decoding Algorithm for Quadruple-Error-Correcting Reed-Solomon Codes and Its Derived Architectures
| Autor: | Alfonso Sanchez-Macian, Mark F. Flanagan, Gary McGuire, Francisco Garcia-Herrero, Juan Antonio Maestro |
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| Rok vydání: | 2021 |
| Předmět: |
Polynomial
Degree (graph theory) 010308 nuclear & particles physics Computer science Latency (audio) Contrast (statistics) 02 engineering and technology 01 natural sciences 020202 computer hardware & architecture Properties of polynomial roots Reed–Solomon error correction 0103 physical sciences 0202 electrical engineering electronic engineering information engineering Electrical and Electronic Engineering Latency (engineering) Algorithm Decoding methods |
| Zdroj: | IEEE Transactions on Circuits and Systems II: Express Briefs. 68:1438-1442 |
| ISSN: | 1558-3791 1549-7747 |
| Popis: | This brief introduces a new method to compute in parallel the roots of a polynomial locator of degree four in a Reed-Solomon decoder. The novelty of this brief is the introduction of an algorithm that transforms the polynomial locator obtained with the Peterson-Gorenstein-Zierler’s algorithm into an equivalent one that allows a direct search for the four roots that indicate the location of the symbols in error. This new solution improves a previous approach proposed in the literature for a quadruple-error-correction decoder (QEC) that requires a cubic aid equation. This previous solution does not work in the cases in which the cubic aid does not have a solution. In contrast, the proposal of this brief works in 100% of cases (with $t\leq 4$ ) as it solves an equivalent polynomial. This new algorithm allows two different implementations: a fully parallel architecture which provides an extremely low latency at an extra area cost, and a fully serial architecture with less area, but a higher latency. |
| Databáze: | OpenAIRE |
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