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Исследование корректирующих свойств кодов с малой плотностью проверок, основанных на кодах с повторением и матрицах перестановок
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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
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 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
Rybin P., Ivanov F., Journal of Communications Technology and Electronics 2018 Vol. 63 No. 12 P. 1518–1523
The error exponent of the regular graph-based binary low-density parity-check (LDPC) codes under the maximum likelihood (ML) decoding algorithm in the binary symmetric channel (BSC) is analyzed. Unlike most other papers where error exponents are considered for the case when the length of LDPC codes tends to infinity (asymptotic analysis), the finite length case (finite ...
Added: March 1, 2019
Ivanov F., Rybin P., , in: Proceedings of 2017 VI-th International Conference on Engineering and Telecommunication (EnT) 29-30 Nov. 2017.: IEEE Computer Society, 2017. P. 67–71.
In this paper we present a new ensemble of Low- Density Parity-Check codes (LDPC Codes) based on modular Golomb rulers and permutation matrices. We suggest a designing rule for these codes that allows obtaining a nested family of LDPC codes with wide range of rates from one matrix of lowest rate code. Moreover, the regular ...
Added: October 4, 2018
Frolov A., Rybin P., Ivanov F., , in: Proceedings of the 2016 XV International Symposium «Problems of Redundancy in Information and Control Systems.: Institute of Electrical and Electronics Engineers ( IEEE ), 2016. P. 48–52.
Non-orthogonal multiple access schemes are of great interest for next generation wireless systems, as such schemes allow to reduce the total number of resources (frequencies or time slots) in comparison to orthogonal transmission (TDMA, FDMA, CDMA). In this paper we consider an iterative LDPC-based joint decoding scheme suggested in [1]. We investigate the most difficult ...
Added: October 4, 2018
[б.и.], 2018.
«Информационные технологии и системы» (ИТиС) – междисциплинарная школа-конференция Института проблем передачи информации им. А. А. Харкевича Российской академии наук (ИППИ РАН). Она зародилась в далеком 1966 году как ежегодная конференция молодых ученых Института. Прерванная в трудные 90-ые, традиция была возобновлена в 2007 году и с тех пор вышла далеко за пределы ИППИ РАН, каждый год собирая на ...
Added: October 4, 2018
Rybin P., Ivanov F., Информационные процессы 2017 Т. 17 № 4 С. 284–293
This paper deals with the error exponent of the regular graph-based binary low-density parity-check (LDPC) codes under the maximum likelihood (ML) decoding algorithm in the binary symmetric channel (BSC). Unlike other papers where error exponents are considered for the case when the length of LDPC codes tends to infinity (asymptotic analysis) we considered the finite ...
Added: October 4, 2018
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
Ivanov F., Проблемы передачи информации 2017 Т. 53 № 3 С. 30–43
We propose a new ensemble of binary low-density parity-check codes with paritycheck matrices based on repetition codes and permutation matrices. The proposed class of codes is a subensemble of quasi-cyclic codes. For the constructed ensemble, we obtain minimum distance estimates. We present simulation results for the proposed code constructions under the (Sum-Product) iterative decoding algorithm ...
Added: February 1, 2018
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
Ivanov F., Zyablov V., Потапов В. Г., Информационные процессы 2012 Т. 12 № 1 С. 68–83
Methods for constructing a mapping of the elements of a multiplicative group of a Galois field onto a symmetric group of permutation matrices are proposed. A technique minimizing the order of the symmetric group is suggested. The results are used for constructing an ensemble of low-density parity-check codes. The obtained code constructions are tested on ...
Added: December 11, 2017
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
Ivanov F., Зяблов В. В., Проблемы передачи информации 2013 Т. 49 № 4 С. 41–56
An algorithm for generating parity-check matrices of regular low-density paritycheck codes based on permutation matrices and Steiner triple systems S(v, 3, 2), v = 2m − 1, is proposed. Estimations of the rate, minimum distance, and girth for obtained code constructions are presented. Results of simulation of the obtained code constructions for an iterative “belief propagation” (Sum-Product) decoding algorithm ...
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