A fast algorithm for polynomial evaluation in Reed-Solomon codec

Chen, Yan-Haw; Chen, Chien-Wen; Chang, Jack S. K.; Truong, Trieu‐Kien; Liaw, Guan-Hsiung

doi:10.1080/02533839.2015.1027743

Cited by 1 publication

(3 citation statements)

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“…The latter operation is executed recursively or we can apply short cyclic convolutions from [6,Fig. 11 11.1], [4], [12], [40], [41]. [7], [21].…”

Section: The Truncated Normalized Cyclic Convolution a Normalizementioning

confidence: 99%

“…where P 8 is the binary matrix of postadditions for the calculation of the normalized cyclic convolution of length m = 8, we compute the column vector r 5 of length 8 as the truncated normalized cyclic convolution (12) which is based on the cyclotomic coset C 9 .…”

Section: Examplementioning

confidence: 99%

“…These methods can be used to construct the cyclotomic DFT algorithm. Reducing the complexity of decoding the Reed-Solomon codes by speeding up the calculation of the DFT, Chien search or syndrome calculation is described in [9], [30], [12], [37], [42]. 4) Several algorithms for the factorization of polynomials over finite fields are presented in the monograph [25,Chapter 14] and in [31], [2].…”

Section: Introductionmentioning

confidence: 99%

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Efficient Algorithm for Finding Roots of Error-Locator Polynomials

Fedorenko¹

2021

IEEE Access

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A novel method for finding roots of polynomials over finite fields has been proposed. This method is based on the cyclotomic discrete Fourier transform algorithm. The improvement is achieved by using the normalized cyclic convolutions, which have a small complexity and allow matrix decomposition, as well as methods of adapting the truncated normalized cyclic convolutions calculation. For small values of degree of the error-locator polynomial the novel method has not only the smallest multiplicative complexity, but the full computational complexity of this method is also less than with other methods. Thus, the multiplicative complexity of the novel method in comparison to the method of affine decomposition (the Fedorenko-Trifonov method) is up to ten times less, although the additive complexity is approximately 10-15% more. The novel method has matrix representation convenient for implementation.INDEX TERMS Convolution, decoding, discrete Fourier transforms, error correction codes, fast Fourier transforms, Galois fields, Reed-Solomon codes.

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“…The latter operation is executed recursively or we can apply short cyclic convolutions from [6,Fig. 11 11.1], [4], [12], [40], [41]. [7], [21].…”

Section: The Truncated Normalized Cyclic Convolution a Normalizementioning

confidence: 99%

Section: Examplementioning

confidence: 99%