Open Access

Complexity Analysis of Reed-Solomon Decoding over GF(2 m ) without Using Syndromes

EURASIP Journal on Wireless Communications and Networking20082008:843634

Received: 15 November 2007

Accepted: 6 May 2008

Published: 14 May 2008


There has been renewed interest in decoding Reed-Solomon (RS) codes without using syndromes recently. In this paper, we investigate the complexity of syndromeless decoding, and compare it to that of syndrome-based decoding. Aiming to provide guidelines to practical applications, our complexity analysis focuses on RS codes over characteristic-2 fields, for which some multiplicative FFT techniques are not applicable. Due to moderate block lengths of RS codes in practice, our analysis is complete, without big O notation. In addition to fast implementation using additive FFT techniques, we also consider direct implementation, which is still relevant for RS codes with moderate lengths. For high-rate RS codes, when compared to syndrome-based decoding algorithms, not only syndromeless decoding algorithms require more field operations regardless of implementation, but also decoder architectures based on their direct implementations have higher hardware costs and lower throughput. We also derive tighter bounds on the complexities of fast polynomial multiplications based on Cantor's approach and the fast extended Euclidean algorithm.


Complexity AnalysisBlock LengthDecode AlgorithmPolynomial MultiplicationField Operation

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Authors’ Affiliations

Department of Electrical and Computer Engineering, Lehigh University, Bethlehem, USA


© N. Chen and Z. Yan. 2008

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.