Read the abstract, see who wrote it and who cites it, and get the citation in APA, MLA, Chicago or Harvard.
About 408 papers for “binary BCH codes”
Robert Morelos-Zaragoza · 2002
This chapter contains sections titled: Binary cyclic codes General decoding of cyclic codes Binary BCH codes Polynomial codes Decoding of binary BCH codes Weight distribution and performance bounds
Cited by 1
Xinmei Huang, Qin Yue, Yansheng Wu et al. · Designs Codes and Cryptography · 2020
Cited by 16
Zhi Ma, Xin Lü, Keqin Feng et al. · Lecture notes in computer science · 2006
Cited by 29
H. Burton · IEEE Transactions on Information Theory · 1971
The iterative algorithm for decoding binary BCH codes presented by Berlekamp and, in an alternative form, by Massey is modified to eliminate inversion. Because inversion in a finite field is time consuming and requires relatively complex circuitry, this new algorithm should he useful in practical applications of multiple-error-correcting binary BCH codes.
Cited by 105
Min Yin, Menwang Xie, Bo Yi · 2013
Although various universal algorithms have been proposed for Key Equation Solver(KES), the most critical part of Reed-Solomon(RS) codes, little optimization has been done for their binary sibling-binary BCH codes. This paper presents two binary versions of reformulated inverse-free Berlekamp-Massey (riBM) algorithm. The proposed algorithms halve iteration cycles and arrange variables more flexibly and effectively. The first simplified algorithm reduces about 1/3 fewer process elements and registers, while the second requires only one half of gate counts compared to the original riBM algorithm. Also folded architectures can be adopted because both of the two optimized algorithms are symmetrical and regular.
Cited by 14
F. Levy-dit-Vehel · 1993
Cited by 2
Tsung‐Ching Lin, Chong‐Dao Lee, Yaotsu Chang et al. · IEEE Transactions on Information Theory · 2022
For the recently developed quasi-reversible BCH codes with long lengths and high error-correcting capability, this paper is aimed at proposing a new and faster decoding procedure. It consists of four steps: 1) compute the consecutive syndromes; 2) calculate the syndrome functions by the forward and backward recursions; 3) solve a linear subsystem together with one matrix multiplication in order to find an error-locator polynomial; 4) determine the errors from the obtained polynomial by using the root-finding algorithm. This procedure, especially in Steps 2 and 3, differs greatly from the conventional procedures, which determine an error-locator polynomial directly from solving a linear system with the aid of the consecutive syndromes. The key idea behind this decoding technique is that the computational complexity of such a small subsystem instead of an originally large linear system can be significantly reduced, although there are additional forward and backward syndrome calculations with low complexity increasing. Finally, the illustrative examples and numerical simulations can be helpful to demonstrate the accuracy and efficacy of the presented decoding technique at different error-correcting capabilities.
Cited by 2
José Felipe Voloch · IEEE Transactions on Information Theory · 2001
We give bounds for the minimal distance of duals of binary Bose-Chaudhuri-Hocquenghem (BCH) codes in a range where the Carlitz-Uchiyama bound is trivial. This is done by estimating the number of points on certain curves over finite fields.
Cited by 4
Iiro Honkala, Y. Kaipainen, Aimo Tietäväinen · Applicable Algebra in Engineering Communication and Computing · 1997
Cited by 1
Lu, Chung-Chin (author) · University of Southern California Digital Library · 2015
Cited by 0Open access
W.T. Penzhorn · 2005
Recently, it was shown how to determine the error locator polynomial of a primitive, binary t-error correcting BCH code in a single step [3]. For this purpose it is necessary to transform the set of t syndrome polynomial equations to an equivalent set of polynomial equations, leading to an analytic expression for the error locator polynomial, /spl sigma/(x). These results facilitate decoding beyond the BCH bound, i.e. correcting more than t errors. This requires the resolving of additional syndromes coefficients, which is achieved in a simple and elegant way by means of the expression derived for the syndrome polynomial /spl sigma/(x).
Cited by 4
Tadao Kasami, N. Tokura · IEEE Transactions on Information Theory · 1969
It is shown that if <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m \neq 8, 12</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m > 6</tex> , there are some binary primitive BCH codes (BCH codes in a narrow sense) of length <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2^{m} - 1</tex> whose minimum weight is greater than the BCH bound. This gives a negative answer to the question posed by Peterson [1] of whether or not the BCH bound is always the actual minimum weight of a binary primitive BCH code. It is also shown that for any even <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m \geq 6</tex> , there are some binary cyclic codes of length <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2^{m} - 1</tex> that have more information digits than the primitive BCH codes of length <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2^{m} - 1</tex> with the same minimum weight.
Cited by 65
Yang Liu, Ruihu Li, Qiang Fu et al. · Finite Fields and Their Applications · 2018
Cited by 41Open access
Eric Hsueh-Chan Lu, Tofar C.-Y. Chang · IEE Proceedings - Communications · 1996
A step-by-step decoding algorithm is presented for double-error-correcting binary BCH codes of length n = 2m – 1. The decoding algorithm can directly determine whether any received bit is correct or not without knowing the number of errors which have occurred in the received vector and also without determining the corresponding error location polynomial. The merits of the hardware decoder based on the algorithm are that it is very simple and fast. In addition, it is suitable for decoding long block codes.
Cited by 14
A Tietäinen · Discrete Applied Mathematics · 1987
Cited by 36
C. Kraft · 2002
A very fast, parallel, combinatorial Berlekamp decoder that can perform the second step in binary BCH decoding at rates exceeding 300 Mb/s is presented. The circuit given is for the t=3 case. It is possible to build a t=5 decoder that can operate faster than 100 Mb/s. In addition to the Berlekamp section, the complete BCH decoder also requires a syndrome generator and a root finder. These can be implemented in a straightforward way with sequential circuits and ROMs or fast static RAMs. For the t=3 code, there are only three syndrome components yielding 48 clock cycles for 255 incoming bits.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
Cited by 1
E.M. Gabidulin, Juriaan Simonis · 2002
For any positive integer m, a metric on F/sub 2//sup 2m/ is considered which is induced by the quasi-perfect [2/sup m/-1,2/sup m/-2m-1,5] binary BCH code. Constructions of codes are given which are perfect with respect to this metric. In addition, easy decoding methods for these codes are proposed.
Cited by 0
T. Aaron Gulliver, Wen Ching Lin, F. Dehne · Applied Mathematics Letters · 1998
Cited by 2
J. van der Horst · IEEE Transactions on Information Theory · 1973
Cited by 1
Ta-Hsiang Hu, Ming-Hua Chang, Ming-hua Chang · 2015
Abstract — This study presents a modified and conceptually simple step-by-step decoding algorithm for binary cyclic BCH codes. Step-by-step decoding temporarily changes one information bit value at a time and then checks weather the weight of the error pattern decreases by computing the corresponding syndrome matrix determinant. Based on the channel information, this study propose a modified step-by-step decoding, which locates a test set and checks the weight of the error pattern in the decoding procedure. Rather than testing all information bits, the bit positions listed in the test set are examined in the proposed step-by-step decoding. The error performance of the proposed decoding is very close to that of the conventional step-by-step decoding with a low decoding complexity, as in simulations of a BPSK coherent system over AWGN channels. Key Words —step-by-step decoding, BCH codes. I.
Cited by 0