Efficient calculation of cyclic convolution by means of fast Fourier transform in a finite field

Amerbaev, V.M.; Solovyev, Roman; Stempkovskiy, Alexander; Telpukhov, Dmitry

doi:10.1109/ewdts.2014.7027043

Cited by 5 publications

(4 citation statements)

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“…The mathematical apparatus of the discrete Fourier transform in Galois fields is used in the modern theory of noiseless coding both for describing the most important block codes in the frequency domain and for building new code constructions with improved properties [1][2][3][4][5][6][7][8][9]. Application of fast Fourier transform algorithms allows significantly reduce the computational complexity of coding and decoding algorithms, and also implement some computational processes in parallel [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27].…”

Section: Challenge Problem In General and Previous Researchmentioning

confidence: 99%

“…The Fourier transform plays an important role in the development of modern methods of the theory of information processing and transmission. In particular, the integral Fourier transform is used to process and study signals that are time-continuous and take real and complex values [6][7][8][9][10][11][12][13][14][15][16][17]. For digital processing of discretely-timed a discrete Fourier transform [3,[18][19][20] is used:…”

Section: Discrete Fourier Transform In Finite Fieldsmentioning

confidence: 99%

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Representation of Cascade Codes in the Frequency Domain

Кuznetsov

Pushkar'ov

Serhiienko

et al. 2020

Data-Centric Business and Applications

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The mathematical apparatus of the multidimensional discrete Fourier transform over finite fields is considered. Methods for the description of linear block codes in the frequency domain are investigated. It is shown that, in contrast to iterative codes (code-products), cascade codes in the general case cannot be described in the frequency domain in terms of multidimensional spectra. Analytic expressions are obtained that establish a one-to-one functional correspondence between the spectrum of a sequence over a finite field and the spectra of the corresponding words obtained by limiting this word to a subfield. A general solution of the problem of representation of cascade codes in the frequency domain is obtained, which allows constructing in the frequency domain using computationally efficient algorithms of encoding and decoding, and the derived analytic dependences of components of multidimensional spectra.

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Section: Challenge Problem In General and Previous Researchmentioning

confidence: 99%

Section: Discrete Fourier Transform In Finite Fieldsmentioning

confidence: 99%

Representation of Cascade Codes in the Frequency Domain

Кuznetsov

Pushkar'ov

Serhiienko

et al. 2020

Data-Centric Business and Applications

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“…In this case the result corresponds to the cyclic convolution [4]. Moreover, if we add zeros to the sequences, cyclic convolution calculation becomes equivalent to calculation of the required linear convolution.…”

Section: Implementation Of Fir Filters In Frequency Domainmentioning

confidence: 99%

“…[4] The RNS-based FIR filter implementation with the use of number-theoretic fast Fourier transform is presented in the (Fig. 3).…”

Section: Development Of Rns-based Fir Filter Us-ing the Convolution Tmentioning

confidence: 99%

Hardware Implementation of Fir Filter Based on Number-theoretic Fast Fourier Transform in Residue Number System

Amerbaev¹,

Soloviev²,

Telpukhov³

2014

ENG

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New approach to hardware FIR filter implementation is described in this paper. Method includes the conversion to the frequency domain, as well as the principles of residue number systems and number-theoretic transforms. Parameterized RTL IP-core generators were implemented for both conventional and developed methods. These IP generators were used to implement different devices for different filter orders and input widths. Filters were synthesized, and resulting time and hardware evaluation allow one to consider the effectiveness of the method compared with the conventional realization of FIR filter.

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