Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Complexity Analysis of Reed-Solomon Decoding over GF(2m) without Using Syndromes | Hindawi Publishing Corporation EURASIP Journal on Wireless Communications and Networking Volume 2008 Article ID 843634 11 pages doi 2008 843634 Research Article Complexity Analysis of Reed-Solomon Decoding over GF 2W without Using Syndromes Ning Chen and Zhiyuan Yan Department of Electrical and Computer Engineering Lehigh University Bethlehem PA 18015 USA Correspondence should be addressed to Zhiyuan Yan yan@ Received 15 November 2007 Revised 29 March 2008 Accepted 6 May 2008 Recommended by Jinhong Yuan 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. Copyright 2008 N. Chen and Z. Yan. 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. 1. INTRODUCTION Reed-Solomon RS codes are among the most widely used error control codes with .
