Efficient Syndrome Calculation via the Inverse Cyclotomic Discrete Fourier Transform

Fedorenko, Sergei V.

doi:10.1109/lsp.2019.2929408

Cited by 9 publications

(9 citation statements)

References 19 publications

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“…It is well known that both the WB algorithm and the Euclidean algorithm are capable of solving the WB key equation (10). However, the WB algorithm executes the polynomial evaluations and the polynomial updates in sequence during each iteration.…”

Section: Draft July 25 2022mentioning

confidence: 99%

“…, 2 µ−1 . Furthermore, because (λ(x), z(x)) satisfies the key equation (10), we must have z(ω i ) = u(ω i )λ(ω i ) for i = 0, 1, . .…”

Section: Frequency-domain Modular Approachmentioning

confidence: 99%

“…In this subsection, we present the FMA for solving (10). The idea behind the FMA is that φ j i and Ψ j 1 need not to be computed at each iteration until enough information has been collected.…”

Section: E Fast Modular Approachmentioning

confidence: 99%

“…Wu et al [8] used the partial composite cyclotomic Fourier transform (CFT) to derive fast syndrome-based decoders. Bellini et al [9] proposed a method to reduce the number of additions required in the CFT, and Fedorenko [10] further reduced the multiplicative complexity of the partial inverse CFT. Gao and Mateer [11] devised an additive FFT algorithm based on a Taylor expansion.…”

Section: Introductionmentioning

confidence: 99%

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New Decoding of Reed-Solomon Codes Based on FFT and Modular Approach

Tang¹,

Han²

2022

Preprint

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Decoding algorithms for Reed-Solomon (RS) codes are of great interest for both practical and theoretical reasons. In this paper, an efficient algorithm, called the modular approach (MA), is devised for solving the Welch-Berlekamp (WB) key equation. By taking the MA as the key equation solver, we propose a new decoding algorithm for systematic RS codes. For (n, k) RS codes, where n is the code length and k is the code dimension, the proposed decoding algorithm has both the best asymptotic computational complexity O(n log(n−k)+(n−k) log 2 (n−k)) and the smallest constant factor achieved to date. By comparing the number of field operations required, we show that when decoding practical RS codes, the new algorithm is significantly superior to the existing methods in terms of computational complexity. When decoding the (4096, 3584) RS code defined over F 2 12 , the new algorithm is 10 times faster than a conventional syndrome-based method. Furthermore, the new algorithm has a regular architecture and is thus suitable for hardware implementation.

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Section: Draft July 25 2022mentioning

confidence: 99%

“…, 2 µ−1 . Furthermore, because (λ(x), z(x)) satisfies the key equation (10), we must have z(ω i ) = u(ω i )λ(ω i ) for i = 0, 1, . .…”

Section: Frequency-domain Modular Approachmentioning

confidence: 99%

Section: E Fast Modular Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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New Decoding of Reed-Solomon Codes Based on FFT and Modular Approach

Tang¹,

Han²

2022

Preprint

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“…The extraction method in the time domain utilizes the periodic characteristics of the RCS measurement sequences [ 4 ]. The extraction method [ 3 ] in the transform domain includes the Fourier transform [ 5 , 6 ], wavelet transform [ 7 , 8 ], and the Merlin transform of the RCS measurement sequences [ 9 ]. Many methods have been attempted to establish the recognition criteria, such as the Bayesian method [ 10 , 11 , 12 ], the evidential reasoning method [ 13 , 14 , 15 , 16 ], the fuzzy classification method [ 17 , 18 , 19 ], and the neural network method [ 20 , 21 , 22 , 23 , 24 ].…”

Section: Introductionmentioning

confidence: 99%

Calibration of Radar RCS Measurement Errors by Observing the Luneburg Lens Onboard the LEO Satellite

Yang

et al. 2022

Sensors

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Accurate radar RCS measurements are critical to the feature recognition of spatial targets. A calibration method for radar RCS measurement errors is proposed for the first time in the context of special target tracking by observing the Luneburg Lens onboard the LEO satellite. The Luneburg Lens has favorable RCS scattering properties for the radar microwave. Thus, the laboratory RCS measurements of the Luneburg Lens, with some fixed incident frequency and with different incident orientations for the radar microwave, will be implemented in order to build a database. The incident orientation for the radar microwave in the satellite body frame will be calculated by taking advantage of the precise orbit parameters, with errors only at the magnitude of several centimeters and within the actual satellite attitude parameters. According to the incident orientation, the referenced RCS measurements can be effectively obtained by the bilinear interpolation in the database. The errors of actual RCS measurements can thus be calibrated by comparing the referenced and the actual RCS measurements. In the RCS measurement experiment, which lasts less than 400 s, the actual RCS measurement errors of the Luneburg Lens are nearly less than 0 dBsm, which indicates that the RCS measurement errors of the spatial targets can be effectively calculated by the proposed calibration method. After the elaborated calibration, the RCS measurements of the spatial targets can be accurately obtained by radar tracking.

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