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Efficient Syndrome Calculation via the Inverse Cyclotomic Discrete Fourier Transform
IEEE Signal Processing Letters. 2019. Vol. 26. No. 9. P. 1320-1324.
An effective calculation of the Reed-Solomon code syndrome is proposed. The method is based on the use of the partial normalized cyclic convolutions in the partial inverse cyclotomic discrete Fourier transform. The method is the best of the known algorithms, in terms of multiplicative complexity.
Keywords: конечное полеБыстрые алгоритмыдекодированиеsignal processingdigital signal processingdecodingDFTбыстрое дискретное преобразование Фурьеfinite fieldБПФлинейный кодпомехоустойчивый кодdecoding algorithmалгоритм декодированияReed-Solomon codesmultiplicative complexitydiscrete Fourier transformerror correction codesкоды Рида-Соломонаdecoding complexitydiscrete Fourier transforms over finite fields
Sergei Valentinovich Fedorenko, IEEE Signal Processing Letters 2016 Vol. 23 No. 6 P. 824-827
A novel method for computing the discrete Fourier transform (DFT) over a finite field based on the Goertzel-Blahut algorithm is described. The novel method is currently the best one for computing the DFT over even extensions of the characteristic two finite field, in terms of multiplicative complexity. ...
Added: January 26, 2018
Sergei Valentinovich Fedorenko, IEEE Access 2021 Vol. 9 P. 38673-38686
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 ...
Added: April 15, 2021
Fedorenko Sergei Valentinovich, IEEE Access 2022 Vol. 10 P. 110639-110645
A novel method of spectral decoding for systematic BCH codes has been proposed. This method has a simple description and a small computational complexity. ...
Added: October 26, 2022
Sergei Valentinovich Fedorenko, IEEE Access 2023 Vol. 11 P. 62771-62779
The novel methods for binary discrete Fourier transform (DFT) computation over the finite field have been proposed. The methods are based on a binary trace calculation over the finite field and use the cyclotomic DFT. The direct DFT computational complexity has been reduced due to using the binary trace function over the finite field and ...
Added: July 19, 2023
Avdoshin S. M., Набебин А. А., М. : ДМК Пресс, 2017
The textbook contains necessary information about universal and classical algebras, systems of axioms for the basic algebraic structures (groupoid, monoid, semi-groups, groups, partial orders, rings, fields). The basic cryptographic algorithms are described. Error-correcting codes - linear, cyclic, BCH are considered. Algorithms for designing of such codes are given. Many examples are shown. It is put ...
Added: August 19, 2016
Fedorenko S., СПб. : ГУАП, 2008
Fast algorithms for decoding of linear block codes. ...
Added: February 3, 2018
Sergei Valentinovich Fedorenko, IEEE Transactions on Signal Processing 2015 Vol. 63 No. 20 P. 5307-5317
A normalized cyclic convolution is a cyclic convolution when one of its factors is a fixed polynomial. Herein, a novel method for constructing a normalized cyclic convolution over a finite field is introduced. This novel method is the first constructive and best known method for even lengths. This method can be applied for computing discrete ...
Added: February 3, 2018
Fedorenko Sergei Valentinovich, IEEE Transactions on Signal Processing 2020 Vol. 68 P. 4813-4823
The new method for the discrete Fourier transform computation over a finite field is introduced.
This method is a nontrivial generalization of the Duhamel-Hollmann algorithm with replacement
of the Toeplitz convolution calculation by the normalized cyclic convolution calculation.
Both algorithms have the smallest multiplicative complexity. ...
Added: September 12, 2020
Sergei Valentinovich Fedorenko, / Preprint. Series Preprint "Preprint". 2016.
In this preprint, we present an example illustrating the novel method for the discrete Fourier transform (DFT) computation based on the Goertzel-Blahut algorithm introduced in the paper "Improving the Goertzel-Blahut algorithm" (IEEE Signal Processing Letters, vol. 23, no. 6, pp. 824-827, 2016). ...
Added: February 3, 2018
Ivanov F., Krouk E., Kabatiansky G. A. et al., Lecture Notes in Computer Science 2020 Vol. 12087 P. 41-49
Unlike most papers devoted to improvements of code-based cryptosystem, where original Goppa codes are substituted by some other codes, we suggest a new method of strengthening which is code-independent. We show (up to some limit) that the security of the new code-based cryptosystem is much closer to the hardness of maximum likelihood decoding than in the ...
Added: September 17, 2020
Ivanov F., Zhilin I., Автоматика и телемеханика 2016 Т. 10 С. 109-122
A modification of the decoding q-ary Sum Product Algorithm (q-SPA) was proposed for the nonbinary codes with small check density based on the permutation matrices. The algorithm described has a vector realization and operates over the vectors defined on the field GF(q), rather than over individual symbols. Under certain code parameters, this approach enables significant ...
Added: December 11, 2017
Rybin P., Journal of Communications Technology and Electronics 2016 Vol. 61 No. 12 P. 1432-1439
This paper deals with the irregular binary low-density parity-check (LDPC) codes and two iterative low-complexity decoding algorithms. The first one is the majority error-correcting decoding algorithm, and the second one is iterative erasure-correcting decoding algorithm. The lower bounds on correcting capabilities (the guaranteed corrected error and erasure fraction respectively) of irregular LDPC code under decoding ...
Added: December 11, 2017
Ivanov F., Zhilin I., Zyablov V., European Wireless 2015; 21th European Wireless Conference; Proceedings of 2015 P. 1-5
n this paper we propose to consider a generalized error-locating code (GEL-code) as a possible candidate for data transmission systems that require high code rates along with strict requirements on wrong decoding probability. The paper describes the construction of the GEL-code and the algorithms for encoding and decoding. The main idea is to implement a ...
Added: February 1, 2018
St. Petersburg : Institute of Electrical and Electronics Engineers, 2012
The volume contains proceedings of the XIII International symposium on problems of redundancy in information and control systems. ...
Added: January 31, 2013
Гриценко В. В., Maevsky A. E., Математические заметки 2014 Т. 96 № 5-6 С. 864-879
В статье изучается алгебра p(x)-циркулянтов над произвольным конечным полем и строятся алгоритмы случайного равновероятного выбора элементов из подмножества всех обратимых p(x)-циркулянтов или подмножества всех p(x)-циркулянтов с заданным значением определителя. Особенностью рассматриваемых алгоритмов является минимизация временной сложности и количества случайных элементов, используемых в процессе их работы. ...
Added: October 21, 2015
Osipov D., Titov D., Cybernetics and Information Technologies 2018 Vol. 18 No. 5 P. 77-86
The following paper adapts the classical Zigangirov-Jelinek algorithm to the decoding of nonbinary block codes under severe mixed jamming. To ensure reliable communications in this scenario we combine reception techniques based on distribution free statistical tests with sequential decoding on syndrome trellises. It will be shown that the proposed approach can ensure relatively high transmission ...
Added: July 6, 2018
NY : IEEE, 2019
The TSP 2019 Conference is organized by seventeen universities from Czech Rep., Hungary, Turkey, Taiwan, Japan, Slovak Rep., Spain, Bulgaria, France, Slovenia, Croatia, Greece, and Poland, for academics, researchers, and developers and it serves as a premier annual international forum to promote the exchange of the latest advances in telecommunication technology and signal processing. The ...
Added: July 29, 2019
Chennai : AIRCC Publishing Corporation, 2018
The 11th International Conference on Security and its Applications (CNSA 2018) was held in Zurich, Switzerland, during January 02~03, 2018. The 5th International Conference on Data Mining and Database (DMDB 2018) and The 5th International Conference on Artificial Intelligence and Applications (AIAP 2018) was collocated with The 11th International Conference on Security and its Applications ...
Added: January 10, 2018
А.А. Злотник, И.А. Злотник, Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2017 Т. 473 № 2 С. 131-137
Представлен новый быстрый прямой алгоритм реализации метода конечных элементов (МКЭ) порядка n>=2 на прямоугольниках для решения различных краевых задач для уравнений типа Пуассона. Он обобщает хорошо известный алгоритм для случая разностных схем или билинейных КЭ (n=1), использующий версии быстрого дискретного преобразования Фурье (БДПФ). Его ядром являются быстрые прямой и обратный алгоритмы разложения по собственным векторам ...
Added: October 25, 2016
NY : IEEE, 2018
In cooperation with the IEEE Region 8 (Europe, Middle East and Africa), IEEE Greece Section, IEEE Czechoslovakia Section, and IEEE Czechoslovakia Section SP/CAS/COM Joint Chapter, the TSP 2018 is organized by seventeen universities from Czech Republic, Hungary, Turkey, Taiwan, Japan, Slovak Republic, Spain, Bulgaria, France, Slovenia, Croatia, Greece, and Poland, for academics, researchers, and developers and it serves as ...
Added: September 3, 2018
Evsyutin O., Kokurina A., Мещеряков Р. В. et al., Multimedia Tools and Applications 2018 Vol. 77 No. 21 P. 28567-28599
Many effective methods of the data embedding into digital images are based on the frequency transformations. However use of similar transformations is connected to the following problem: the built-in message is distorted because of information losses in case of restoration of pixels’ integer values from the frequency domain. It represents a vital issue if the ...
Added: September 3, 2019
Fedorenko S., , in : Proceedings of Sixteenth International Workshop on Algebraic and Combinatorial Coding Theory at Svetlogorsk, Russia, September 02-08, 2018. : Skoltex, 2018. Ch. 43. P. 185-188.
Приведено доказательство теоремы об обратном циклотомическом DFT над конечным полем. ...
Added: September 25, 2018
Institute of Electrical and Electronics Engineers ( IEEE ), 2016
Proceedings of a meeting held 26-29 September 2016, Saint-Petersburg, Russia. ...
Added: October 4, 2018
IEEE, 2021
The conference “2021 Systems of signals generating and processing in the field of on board
communications” is organized with technical sponsorship of Russian (Moscow) IEEE Circuits
and Systems (CAS04) Chapter IEEE Region 8, Russian Section Chapter, MTT/ED and Institute of
Radio and Information Systems Association (IRIS), Vienna, Austria.
The conference featured invited researchers, educators, managers, and graduate students, whose
research ...
Added: May 19, 2021