In this paper, an efficient euclidean decoding algorithm is presented to solve the Berlekamp's key equation of Reed-Solomon (RS) code for correcting erasures as well as errors by replacing the initial condition of...
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ISBN:
(纸本)0780379780
In this paper, an efficient euclidean decoding algorithm is presented to solve the Berlekamp's key equation of Reed-Solomon (RS) code for correcting erasures as well as errors by replacing the initial condition of the euclidean algorithm with the erasure locator polynomial and the Forney syndrome polynomial. By this proposed algorithm, the errata locator polynomial and errata evaluator polynomial can be obtained simultaneously without the computations of polynomial division and field element inversion. Moreover, the whole recursive decoding produce for solving Berlekamp's key equation could be performed with a fixed number of iterations. And, the weights used to reduce the degree of the errata evaluator polynomial at each iteration can be extracted from the coefficient of fixed degree. As a consequence, the complexity of RS decoder to correct both errors and erasures is reduced substantially. Therefore, this Proposed algorithm provides more modular, regular and simple for both software and hardware implementation. An example using this proposed algorithm is given for a (255, 239) RS code for correcting erasures and errors with s + 2v less than or equal to 16.
Over-speeding is one of the problems that contribute to the causes of road accidents which leads to traffic. As many automated systems are currently emerging to detect the speed of the vehicles to prevent accidents, t...
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ISBN:
(纸本)9781450385930
Over-speeding is one of the problems that contribute to the causes of road accidents which leads to traffic. As many automated systems are currently emerging to detect the speed of the vehicles to prevent accidents, the growing number of vehicles puts itself as another factor that affects the improvement of our current systems which can affect both accuracy and performance. The proposed method aims to improve the classification model to handle a large input to further improve the speed estimation system. A YOLOv3 model was utilized to detect and classify vehicles which gained a 96.69% accuracy, and the application of the euclidean algorithm for speed estimation yielded a +/- 0.00286494m/s (0.010313784 km/h) margin of sampling error with a 95% level of confidence.
In this paper, a novel-decoding algorithm based on euclidean method is developed correct errors for RS codes. This new decoding algorithm can solve the Berlekamp's key equation to find the error locator and evalua...
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ISBN:
(纸本)0780377656
In this paper, a novel-decoding algorithm based on euclidean method is developed correct errors for RS codes. This new decoding algorithm can solve the Berlekamp's key equation to find the error locator and evaluator polynomials simultaneously without performing the computation of polynomial division and finite field element inversion. Moreover, the number of iterations is fixed, which equals the minimum distance minus one. Also, it saves many extra controlling circuits. Therefore this novel-decoding algorithm is regular, efficient, simple and easy to implement.
This paper presents a method to merge Generalized Minimum Distance decoding of Reed-Solomon codes with the extended euclidean algorithm. By merge, we mean that the steps performed in Generalized Minimum Distance decod...
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ISBN:
(纸本)9781424482641
This paper presents a method to merge Generalized Minimum Distance decoding of Reed-Solomon codes with the extended euclidean algorithm. By merge, we mean that the steps performed in Generalized Minimum Distance decoding are similar to those of the extended euclidean algorithm. The resulting algorithm has a complexity of O(n(2)).
We show how Gabidulin codes can be list decoded by using a parametrization approach. For this we consider a certain module in the ring of linearized polynomials and find a minimal basis for this module using the Eucli...
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ISBN:
(纸本)9784885522925
We show how Gabidulin codes can be list decoded by using a parametrization approach. For this we consider a certain module in the ring of linearized polynomials and find a minimal basis for this module using the euclidean algorithm with respect to composition of polynomials. For a given received word, our decoding algorithm computes a list of all codewords that are closest to the received word with respect to the rank metric.
Volume holography is currently the subject of widespread interest as a fast-readout-rate, high-capacity digital data-storage technology. However, due to the effect of cross-talk noise, scattering. noise, noise grating...
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ISBN:
(纸本)0819448664
Volume holography is currently the subject of widespread interest as a fast-readout-rate, high-capacity digital data-storage technology. However, due to the effect of cross-talk noise, scattering. noise, noise gratings formed during a multiple exposure. schedule, it brings a lot of burst errors and random, errors in the system. Reed-Solomon error-correction codes have been widely used to protect digital data against errors. This paper presents VLSI implementations of an 16 errors correcting (255,223) Reed-Solomon decoder architecture for volume holographic storage. We describe the Reed-Solomon decoders using modified euclidean algorithms which are regular and simple, and naturally suitable for VLSI implementations. We design the speedily multiplication for GF(28) and pipeline structure to solve hardware complexity and high data processing rate for the Reed-Solomon decoders. We adopt high speed FPGA and have a data processing rate of 200 Mbit/s.
It is shown that a real Hankel matrix admits an approximate block diagonalization in which the successive transformation matrices are upper triangular Toeplitz matrices. The structure of this factorization was first f...
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It is shown that a real Hankel matrix admits an approximate block diagonalization in which the successive transformation matrices are upper triangular Toeplitz matrices. The structure of this factorization was first fully discussed in [1]. This approach is extended to obtain the quotients and the remainders appearing in the euclidean algorithm applied to two polynomials u(x) and v(x) of degree n and m, respectively, whith m < n.
In order to adapt the characteristic that the inter-cepted code sequence is not complete, the polynomial model in [6] has been amended. Based on the model, a scheme is proposed to improve the capability of classical E...
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ISBN:
(纸本)9781467321969
In order to adapt the characteristic that the inter-cepted code sequence is not complete, the polynomial model in [6] has been amended. Based on the model, a scheme is proposed to improve the capability of classical euclidean algorithm, and a new method for blind identification of rate 1/2 convolutional code is proposed .The validity of algorithm is verified by the simulation results, and it has less computational load compared to the references.
Borrowing inspiration from Marcone and Montalban's one-one correspondence between the class of signed trees and the equimorphism classes of indecomposable scattered linear orders, we find a subclass of signed tree...
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Borrowing inspiration from Marcone and Montalban's one-one correspondence between the class of signed trees and the equimorphism classes of indecomposable scattered linear orders, we find a subclass of signed trees which has an analogous correspondence with equimorphism classes of indecomposable finite rank discrete linear orders. We also introduce the class of finitely presented linear orders-the smallest subclass of finite rank linear orders containing 1, omega and omega* and closed under finite sums and lexicographic products. For this class we develop a generalization of the euclidean algorithm where the width of a linear order plays the role of the euclidean norm. Using this as a tool we classify the isomorphism classes of finitely presented linear orders in terms of an equivalence relation on their presentations using 3-signed trees.(c) 2023 Elsevier B.V. All rights reserved.
The minimum, maximum and average computing times of the classical euclidean algorithm are derived. With positive integer inputs of lengths m and n, and with output (greatest common divisor) of length k, m≧n≧km≧n≧k...
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The minimum, maximum and average computing times of the classical euclidean algorithm are derived. With positive integer inputs of lengths m and n, and with output (greatest common divisor) of length k, m≧n≧k
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