Fast Transform for Decoding Both Errors and Erasures of Reed-Solomon Codes Over GF(2%5Em)for8le mle 10

In this letter, it is shown that a fast, prime-factor discrete Fourier transform (DFT) algorithm can be modified to compute Fourier-like transforms of long sequences of2m-1points over GF(2m), where8le mle 10. Using these transforms, together with the Berlekamp-Massey algorithm, the complexity of the...

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Published inIEEE transactions on communications Vol. 54; no. 2; pp. 181 - 186
Main Authors Truong, T K, Chen, P D, Wang, L J, Cheng, T C
Format Journal Article
LanguageEnglish
Published 01.02.2006
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Abstract In this letter, it is shown that a fast, prime-factor discrete Fourier transform (DFT) algorithm can be modified to compute Fourier-like transforms of long sequences of2m-1points over GF(2m), where8le mle 10. Using these transforms, together with the Berlekamp-Massey algorithm, the complexity of the transform-domain decoder for correcting both errors and erasures of the Reed-Solomon codes of block length2m-1over GF(2m)for8le mle 10is reduced substantially from the previous time-domain decoder. A computer simulation verifies these new results.
AbstractList In this letter, it is shown that a fast, prime-factor discrete Fourier transform (DFT) algorithm can be modified to compute Fourier-like transforms of long sequences of2m-1points over GF(2m), where8le mle 10. Using these transforms, together with the Berlekamp-Massey algorithm, the complexity of the transform-domain decoder for correcting both errors and erasures of the Reed-Solomon codes of block length2m-1over GF(2m)for8le mle 10is reduced substantially from the previous time-domain decoder. A computer simulation verifies these new results.
Author Cheng, T C
Chen, P D
Truong, T K
Wang, L J
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