Simplified procedure for decoding nonsystematic reed-Solomon codes over GF(2m) using Euclid's algorithm and the fast Fourier transform

Authors:
Tsung-Ching Lin;Pe-Din Chen;Trieu-Kien Truong
Affiliations:
Department of Information Engineering, I-Shou University, Kaohsiung Country, Taiwan, R.O.C.;Department of Information Engineering, I-Shou University, Kaohsiung Country, Taiwan, R.O.C.;Department of Information Engineering, I-Shou University, Kaohsiung Country, Taiwan, R.O.C.
Venue:
IEEE Transactions on Communications
Year:
2009

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Abstract

Gao's algorithm similar to Shiozaki's algorithm for decoding nonsystematic Reed-Solomon (RS) codes which is a subclass of the redundant residue polynomial codes is considered here. This algorithm computes the message polynomial directly without explicitly finding the error-locator polynomial and error-evaluator polynomial. In this letter, a simplified decoding algorithm to correct both errors and erasures is used in conjunction with Gao's algorithm for efficiently decoding RS codes. In addition, we show that the extended Gao algorithm similar to the Shiozaki-Truong-Cheung-Reed algorithm significantly reduces the decoding complexity.