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## A spectral algorithm for decoding systematic BCH codes

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.

Keywords: декодированиеdecodingбыстрое дискретное преобразование Фурьеdecoding algorithmалгоритм декодированияReed-Solomon codeserror correction codesкоды Рида-Соломонаdiscrete Fourier transformsFast Fourier transformsкоды, исправляющие ошибкиконечные поляdiscrete Fourier transforms over finite fieldsBCH codesдискретное преобразование ФурьеGalois fieldsБЧХ коды

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

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 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. ...

Added: September 4, 2019

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

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

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

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., Automation and Remote Control 2016 Vol. 77 No. 10 P. 1781-1791

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 speedup of modeling. ...

Added: October 3, 2018

Kurmukova A., Ivanov F., Zyablov V. V., Problems of Information Transmission 2022 Vol. 58 No. 2 P. 122-136

We propose a new approach to the analytical estimation of the error burst probability, the probability of erroneous decoding, and the probability of error per bit for convolutional codes with Viterbi decoding in a binary symmetric channel (BSC). Upper and lower estimates of the probability of error per bit and of the erroneous decoding probability ...

Added: November 19, 2022

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

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

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., Четвериков И. С., Kreshchuk A. et al., Proceedings of the IEEE 2022 P. 60-64

In this paper, an improvement for successive cancellation (SC) decoding is presented for polar codes. This improvement is based on applying Creeper approach that was used to decode convolutional codes. The proposed decoder combines a stack and a Fano approaches and allows to significantly decrease complexity of Successive Cancellation Fano decoder at the cost of ...

Added: January 26, 2023

Никольская Т. Е., Павлина С. Ю., Вестник Волгоградского государственного университета. Серия 2: Языкознание 2019 Т. 18 № 1 С. 132-145

The article investigates inter-cultural artistic communication which occurs through multimodal texts in general and feature films in particular. Artistic communication faces a challenge when its source and target belong to different ethnic and/or generational cohorts. The similarity or difference of communication codes depends on the level of adequacy of the sender’s and the recipient’s discursive ...

Added: September 19, 2023

A. M. Veresova, A. A. Ovchinnikov, , in : 2022 Wave Electronics and its Application in Information and Telecommunication Systems (WECONF) 30 May - 3 June 2022, St. Petersburg, Russia. : IEEE, 2022. P. 1-4.

Channels with memory can be described using the Gilbert–Elliott model. To correct errors in such channels, non–
binary Reed-Solomon codes are used, as well as low-density parity-check codes together with interleaving procedure or modifications of classical decoding algorithms. The purpose of this study is to compare the effectiveness of these codes when using different decoding algorithms in channels with memory. The probability ...

Added: October 27, 2022

Иваничкина Л. В., Непорада А. Л., Vinnikov V., Contemporary Engineering Sciences 2016 Vol. 9 No. 21 P. 1015-1029

This paper is concerned with the properties of local reconstruction codes (LRC) both hierarchical and nonuniform, providing the reliability of data storages. The LRCs belong to erasure codes, which recover initial data from corruption at the cost of storage overhead due to introduced redundancy. The study is carried out via Markov chain solutions to reveal ...

Added: December 28, 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

Monterey : IEEE, 2016

Added: January 9, 2019

Terry S. C., Ivanov F., Muhammad R. K. et al., Journal of Information Security and Applications 2023 Vol. 76 Article 103530

One main construct for code-based public key cryptosystems is the McEliece framework that hedges upon the hardness of decoding arbitrary linear codes. Based on Goppa codes, the original McEliece cryptosystem however, suffers from having very large public keys. To alleviate this problem, we define a new IKKR problem that is is NP-complete and use this assumption of the intracability if the ...

Added: December 28, 2022

Lazarevich I., Prokin I., Гуткин Б. С. et al., PLoS Computational Biology 2023 Vol. 19 No. 1 P. 1-18

Modern well-performing approaches to neural decoding are based on machine learning
models such as decision tree ensembles and deep neural networks. The wide range of algorithms
that can be utilized to learn from neural spike trains, which are essentially time-series
data, results in the need for diverse and challenging benchmarks for neural decoding, similar
to the ones in the ...

Added: March 18, 2024

Vlasenko S. V., Мир русского слова 2014 № 3 С. 16-28

The article marks the 90-th anniversary of Prof. Alexander D. Shveitser, thus honoring the memory of the Soviet and Russian translation studies Patriarch and an authority in translation/interpretation practices, who excelled in American studies and sociolinguistics as well. The focus is made on Shveitser’s professional approaches to a number of translation/interpretation problem areas associated with ...

Added: November 12, 2014

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

Krouk E., СПб. : ГУАП, 2007

В монографии рассмотрены вопросы комбинаторного декодирования линейных кодов в дикретных каналах. Монография может быть использована студентами обучающимися по специальности 09.01.04 ...

Added: August 7, 2017