127 results
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2. Mutually disjoint Steiner systems from BCH codes
- Author
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Yan, Qianqian and Zhou, Junling
- Published
- 2024
- Full Text
- View/download PDF
3. On Infinite Families of Narrow-Sense Antiprimitive BCH Codes Admitting 3-Transitive Automorphism Groups and Their Consequences.
- Author
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Liu, Qi, Ding, Cunsheng, Mesnager, Sihem, Tang, Chunming, and Tonchev, Vladimir D.
- Subjects
AUTOMORPHISM groups ,ALGEBRAIC coding theory ,REPRESENTATIONS of groups (Algebra) ,DATA transmission systems ,QUANTUM information science ,GROUP theory ,LINEAR codes ,CYCLIC codes - Abstract
The Bose-Chaudhuri-Hocquenghem (BCH) codes are a well-studied subclass of cyclic codes that have found numerous applications in error correction and notably in quantum information processing. They are widely used in data storage and communication systems. A subclass of attractive BCH codes is the narrow-sense BCH codes over the Galois field ${\mathrm {GF}}(q)$ with length $q+1$ , which are closely related to the action of the projective general linear group of degree two on the projective line. Despite its interest, not much is known about this class of BCH codes. This paper aims to study some of the codes within this class and specifically narrow-sense antiprimitive BCH codes (these codes are also linear complementary duals (LCD) codes that have interesting practical recent applications in cryptography, among other benefits). We shall use tools and combine arguments from algebraic coding theory, combinatorial designs, and group theory (group actions, representation theory of finite groups, etc.) to investigate narrow-sense antiprimitive BCH Codes and extend results from the recent literature. Notably, the dimension, the minimum distance of some $q$ -ary BCH codes with length $q+1$ , and their duals are determined in this paper. The dual codes of the narrow-sense antiprimitive BCH codes derived in this paper include almost MDS codes. Furthermore, the classification of ${\mathrm {PGL}}(2, p^{m})$ -invariant codes over ${\mathrm {GF}}(p^{h})$ is completed. As an application of this result, the $p$ -ranks of all incidence structures invariant under the projective general linear group ${\mathrm {PGL}}(2, p^{m})$ are determined. Furthermore, infinite families of narrow-sense BCH codes admitting a 3-transitive automorphism group are obtained. Via these BCH codes, a coding-theory approach to constructing the Witt spherical geometry designs is presented. The BCH codes proposed in this paper are good candidates for permutation decoding, as they have a relatively large group of automorphisms. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
4. Infinite Families of Linear Codes Supporting More t -Designs.
- Author
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Yan, Qianqian and Zhou, Junling
- Subjects
AUTOMORPHISM groups ,CYBERNETICS ,AUTOMORPHISMS ,LINEAR codes - Abstract
Tang and Ding [IEEE IT 67 (2021) 244-254] studied the class of BCH codes $\mathcal {C}_{(q,q+1,4,1)}$ and their dual codes with $q=2^{m}$ and established that the codewords of the minimum (or the second minimum) weight in these codes support 4-designs or 3-designs. Motivated by this, we further investigate the codewords of the next adjacent weight in such codes and discover more infinite classes of $t$ -designs with $t=3,4$. In particular, we prove that codewords of weight 7 in $\mathcal {C}_{(q,q+1,4,1)}$ support 4-designs for odd $m \geqslant 5$ and they support 3-designs for even $m \geqslant 4$ , which provide infinite classes of simple $t$ -designs with new parameters. Another significant class of $t$ -designs we produce in this paper has complementary designs with parameters 4- $(2^{2s+1}+ 1,5,5)$ ; these designs have the smallest index among all the known simple 4- $(q+1,5,\lambda)$ designs derived from codes for prime powers $q$ ; and they are further proved to be isomorphic to the 4-designs admitting the projective general linear group PGL $(2,2^{2s+1})$ as the automorphism group constructed by Alltop in 1969. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
5. The q -Ary Antiprimitive BCH Codes.
- Author
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Zhu, Hongwei, Shi, Minjia, Wang, Xiaoqiang, and Helleseth, Tor
- Subjects
CYCLIC codes ,LINEAR codes ,DECODING algorithms ,LIQUID crystal displays - Abstract
It is well-known that cyclic codes have efficient encoding and decoding algorithms. In recent years, antiprimitive BCH codes have attracted a lot of attention. The objective of this paper is to study BCH codes of this type over finite fields and analyse their parameters. Some lower bounds on the minimum distance of antiprimitive BCH codes are given. The BCH codes presented in this paper have good parameters in general, containing many optimal linear codes. In particular, two open problems about the minimum distance of BCH codes of this type are partially solved in this paper. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
6. Two Families of Optimal Linear Codes and Their Subfield Codes.
- Author
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Heng, Ziling, Wang, Qiuyan, and Ding, Cunsheng
- Subjects
LINEAR codes ,CYCLIC codes ,FAMILIES - Abstract
In this paper, a family of $[{q}^{2}-1, 4, {q}^{2}-{q}-2]$ cyclic codes over ${\mathbb F}_{{q}}$ meeting the Griesmer bound is presented. Their duals are $[{q}^{2}-1,{q}^{2}-5,4]$ almost MDS codes and are optimal with respect to the sphere-packing bound. The ${q}_{0}$ -ary subfield codes of this family of cyclic codes are also investigated, where ${q}_{0}$ is any prime power such that q is power of ${q}_{0}$. Some of the subfield codes are optimal and some have the best known parameters. It is shown that the subfield codes are equivalent to a family of primitive BCH codes and thus the parameters of the BCH codes are solved. The duals of the subfield codes are also optimal with respect to the sphere-packing bound. A family of $[{q}^{2}, 4, {q}^{2}-{q}-1]$ linear codes over ${\mathbb F}_{{q}}$ meeting the Griesmer bound is presented. Their duals are $[{q}^{2},{q}^{2}-4,4]$ almost MDS codes and are optimal with respect to the sphere-packing bound. The ${q}_{0}$ -ary subfield codes of this family of linear codes are also investigated, where ${q}_{0}$ is any prime power such that q is power of ${q}_{0}$. Five infinite families of 2-designs are also constructed with three families of linear codes of this paper. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
7. On Hulls of Some Primitive BCH Codes and Self-Orthogonal Codes.
- Author
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Gan, Chunyu, Li, Chengju, Mesnager, Sihem, and Qian, Haifeng
- Subjects
ORTHOGONALIZATION ,FINITE fields ,LINEAR codes ,LIQUID crystal displays - Abstract
Self-orthogonal codes are an important type of linear codes due to their wide applications in communication and cryptography. The Euclidean (or Hermitian) hull of a linear code is defined to be the intersection of the code and its Euclidean (or Hermitian) dual. It is clear that the hull is self-orthogonal. The main goal of this paper is to obtain self-orthogonal codes by investigating the hulls. Let $\mathcal {C}_{(r,r^{m}-1,\delta,b)}$ be the primitive BCH code over $\mathbb {F}_{r}$ of length $r^{m}-1$ with designed distance $\delta $ , where $\mathbb {F}_{r}$ is the finite field of order $r$. In this paper, we will present Euclidean (or Hermitian) self-orthogonal codes and determine their parameters by investigating the Euclidean (or Hermitian) hulls of some primitive BCH codes. Several sufficient and necessary conditions for primitive BCH codes with large Hermitian hulls are developed by presenting lower and upper bounds on their designed distances. Furthermore, some Hermitian self-orthogonal codes are proposed via the hulls of BCH codes and their parameters are also investigated. In addition, we determine the dimensions of the code $\mathcal {C}_{(r,r^{2}-1,\delta,1)}$ and its hull in both Hermitian and Euclidean cases for $2 \le \delta \le r^{2}-1$. We also present two sufficient and necessary conditions on designed distances such that the hull has the largest dimension. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
8. Binary [ n , (n + 1)/2] Cyclic Codes With Good Minimum Distances.
- Author
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Tang, Chunming and Ding, Cunsheng
- Subjects
CYCLIC codes ,REED-Muller codes ,BINARY codes ,LINEAR codes - Abstract
The binary quadratic-residue codes and the punctured Reed-Muller codes ${\mathcal {R}}_{2}((m-1)/2, m))$ are two families of binary cyclic codes with parameters $[n, (n+1)/2, d \geq \sqrt {n}]$. These two families of binary cyclic codes are interesting partly due to the fact that their minimum distances have a square-root bound. The objective of this paper is to construct two families of binary cyclic codes of length $2^{m}-1$ and dimension near $2^{m-1}$ with good minimum distances. When $m \geq 3$ is odd, the codes become a family of duadic codes with parameters $[2^{m}-1, 2^{m-1}, d]$ , where $d \geq 2^{(m-1)/2}+1$ if $m \equiv 3 \pmod {4}$ and $d \geq 2^{(m-1)/2}+3$ if $m \equiv 1 \pmod {4}$. The two families of binary cyclic codes contain some optimal binary cyclic codes. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
9. The Subfield Codes and Subfield Subcodes of a Family of MDS Codes.
- Author
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Tang, Chunming, Wang, Qi, and Ding, Cunsheng
- Subjects
CYCLIC codes ,LIQUID crystal displays ,LINEAR codes - Abstract
Maximum distance separable (MDS) codes are very important in both theory and practice. There is a classical construction of a family of $[{2^{m}+1, 2u-1, 2^{m}-2u+3}]$ MDS codes for $1 \leq u \leq 2^{m-1}$ , which are cyclic, reversible and BCH codes over ${\mathrm {GF}}(2^{m})$. The objective of this paper is to study the quaternary subfield subcodes and quaternary subfield codes of a subfamily of the MDS codes for even $m$. A family of quaternary cyclic codes is obtained. These quaternary codes are distance-optimal in some cases and very good in general. Furthermore, two infinite families of 3-designs from these quaternary codes and their duals are presented. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
10. The dual-containing primitive BCH codes with the maximum designed distance and their applications to quantum codes
- Author
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Shi, Xueying, Yue, Qin, and Wu, Yansheng
- Published
- 2019
- Full Text
- View/download PDF
11. Parameters and characterizations of hulls of some projective narrow-sense BCH codes
- Author
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Huang, Yuwen, Li, Chengju, Wang, Qi, and Du, Zongrun
- Published
- 2022
- Full Text
- View/download PDF
12. The Dual Codes of Several Classes of BCH Codes.
- Author
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Gong, Binkai, Ding, Cunsheng, and Li, Chengju
- Subjects
LINEAR codes ,HAMMING distance ,TELECOMMUNICATION systems ,CYCLIC codes - Abstract
As a special subclass of cyclic codes, BCH codes have wide applications in communication and storage systems. A BCH code of length $n$ over $\mathbb {F}_{q}$ is always relative to an $n$ -th primitive root of unity $\beta $ in an extension field of $\mathbb {F}_{q}$ , and is called a dually-BCH code if its dual is also a BCH code relative to the same $\beta $. The question as to whether a BCH code is a dually-BCH code is in general very hard to answer. In this paper, an answer to this question for primitive narrow-sense BCH codes and projective narrow-sense ternary BCH codes is given. Sufficient and necessary conditions in terms of the designed distances $\delta $ will be presented to ensure that these BCH codes are dually-BCH codes. In addition, the parameters of the primitive narrow-sense BCH codes and their dual codes are investigated. Some lower bounds on minimum distances of the dual codes of primitive and projective narrow-sense BCH codes are developed. Especially for binary primitive narrow-sense BCH codes, the new bounds on the minimum distances of the dual codes improve the classical Sidel’nikov bound, and are also better than the Carlitz and Uchiyama bound for large designed distances $\delta $. The question as to what subclasses of cyclic codes are BCH codes is also answered to some extent. As a byproduct, the parameters of some subclasses of cyclic codes are also investigated. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
13. A 5.4 \muW Soft-Decision BCH Decoder for Wireless Body Area Networks.
- Author
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Yang, Chia-Hsiang, Huang, Ting-Ying, Li, Mao-Ruei, and Ueng, Yeong-Luh
- Subjects
BODY area networks ,IEEE 802 standard ,INTEGRATED circuits ,BIT error rate ,ERROR-correcting codes ,DECODERS (Electronics) - Abstract
This paper presents an IEEE 802.15.6 compliant soft-decision BCH decoder for energy-constrained wireless body area networks. The proposed soft-decision decoder (SDD) provides a 1 dB coding gain compared to the hard-decision decoder (HDD). The improvement in BER performance can translate into power savings at the transmitter. The energy dissipation and area of the soft-decision BCH decoder is minimized by jointly considering the algorithm, architecture, and circuit parameters. An early termination strategy is proposed to reduce the number of redundant test patterns. Probabilistic sorting is proposed to determine the test patterns, and its hardware complexity is only 54.7% of the conventional sorting method. The HDD kernel is implemented by adopting the Peterson rule, reducing the area by 44.2%. A pass-transistor logic based Chien search circuit consumes 33.3% less energy compared to the standard-cell based implementation. The chip is designed to operate at the minimum energy point of 0.29 V, yielding an energy reduction of 94% compared to a direct-mapped SDD at SNR=5\ dB. Fabricated in 90 nm CMOS, the chip dissipates 5.4 \muW at 500 kHz, achieving a throughput of 6.38 Mbps. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
14. BCH Codes for the Rosenbloom–Tsfasman Metric.
- Author
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Zhou, Wei, Lin, Shu, and Abdel-Ghaffar, Khaled A. S.
- Subjects
BCH codes ,CYCLIC codes ,HASSE diagrams ,PARTIALLY ordered sets -- Graphic methods ,HAMMING codes - Abstract
The Rosenbloom–Tsfasman metric has attracted the attention of many researchers as a generalization of the Hamming metric that is relevant to practical problems. Codes for this metric were considered. In particular, Reed–Solomon codes were generalized to be compatible with this metric. In this paper, a generalization of BCH codes for the Rosenbloom–Tsfasman metric is proposed. This generalization is based on considering BCH codes as subfield subcodes of Reed–Solomon codes. By characterizing these subfield subcodes, an explicit construction of BCH codes for the Rosenbloom–Tsfasman metric is provided. Two important properties of Reed–Solomon codes and BCH codes for the Rosenbloom–Tsfasman metric are studied and compared with those for the Hamming metric. These properties are cyclic structure and duality. The approach is based on Galois-Fourier transforms associated with Hasse derivatives. [ABSTRACT FROM PUBLISHER]
- Published
- 2016
- Full Text
- View/download PDF
15. A class of narrow-sense BCH codes over Fq of length qm-12.
- Author
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Ling, Xin, Mesnager, Sihem, Qi, Yanfeng, and Tang, Chunming
- Subjects
LINEAR codes ,QUADRATIC forms ,DECODING algorithms ,CIPHERS - Abstract
BCH codes with efficient encoding and decoding algorithms have many applications in communications, cryptography and combinatorial design. This paper studies a class of linear codes of length q m - 1 2 over F q with special trace representation, where q is an odd prime power. With the help of the inner distributions of some subsets of association schemes of quadratic forms, we determine the weight enumerators of these codes. Determining some cyclotomic coset leaders δ i of cyclotomic cosets modulo q m - 1 2 , we prove that narrow-sense BCH codes of length q m - 1 2 with designed distance δ i = q m - q m - 1 2 - 1 - q ⌊ m - 3 2 ⌋ + i - 1 2 have the corresponding trace representation, and have the minimal distance d = δ i and the Bose distance d B = δ i , where 1 ≤ i ≤ ⌊ m + 11 6 ⌋ . [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
16. Reliable State Estimation of an Unmanned Aerial Vehicle Over a Distributed Wireless IoT Network.
- Author
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Noor-A-Rahim, Md., Khyam, M. O., Ali, G. G. Md. Nawaz, Liu, Zilong, Pesch, Dirk, and Chong, Peter H. J.
- Subjects
TELECOMMUNICATION systems ,WIRELESS Internet ,WIRELESS communications ,INTERNET of things ,WIRELESS sensor networks ,REMOTELY piloted vehicles - Abstract
Unmanned aerial vehicles (UAVs) have attracted a lot of attention due to their enormous potentiality in civil and military applications over the past years. In order to allow accurate control action of UAV, a robust and real-time state estimation technique is required. In this paper, we propose a Kalman filter based UAV state estimation technique when the communication takes place over wireless links in an Internet of Things (IoT) network. We consider that a set of sensors observes the state of the UAV and transmits the observation to a control center (central server) over a distributed wireless IoT network. To deal with the communication impairments due to wireless communication links between the UAV's sensors and the IoT system components, e.g., IoT gateways, a Bose–Chaudhuri–Hocquenghem coded communication system is presented. Based on the received signals at the IoT gateways, a global state estimation technique is proposed. Performance of the proposed communication and estimation scheme is demonstrated through numerical results for different conditions. From the comparison with a conventional estimation scheme, it is observed that the proposed scheme significantly outperforms the conventional scheme in terms of state estimation and error performance. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
17. The covering radii of a class of binary cyclic codes and some BCH codes
- Author
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Kavut, Selçuk and Tutdere, Seher
- Published
- 2019
- Full Text
- View/download PDF
18. A class of negacyclic BCH codes and its application to quantum codes
- Author
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Zhu, Shixin, Sun, Zhonghua, and Li, Ping
- Published
- 2018
- Full Text
- View/download PDF
19. Optimization of a Systolic Array BCH encoder with Tree-Type Structure.
- Author
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Lim, Duk-Gyu, Shakya, Sharad, and Lee, Je-Hoon
- Subjects
SYSTOLIC array circuits ,ERROR-correcting codes ,PARALLEL processing ,ALGORITHMS ,COMPARATIVE studies ,FIELD programmable gate arrays - Abstract
BCH code is one of the most widely used error correcting code for the detection and correction of random errors in the modern digital communication systems. The conventional BCH encoder that is operated in bit-serial manner cannot adequate with the recent high speed appliances. Therefore, parallel encoding algorithms are always a necessity. In this paper, we introduced a new systolic array type BCH parallel encoder. To study the area and speed, several parallel factors of the systolic array encoder is compared. Furthermore, to prove the efficiency of the proposed algorithm using tree-type structure, the throughput and the area overhead was compared with its counterparts also. The proposed BCH encoder has a great flexibility in parallelization and the speed was increased by 40% than the original one. The results were implemented on synthesis and simulation on FPGA using VHDL. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
20. Decoding of QOSTBC Concatenates BCH Code Based on Parallel Interference Cancellation.
- Author
-
Yan Zheng-Hang, Yang Yu-Hang, Ma Maode, and Lu Yilong
- Subjects
MAXIMUM likelihood statistics ,ALGORITHMS ,SIGNAL-to-noise ratio ,ANTENNAS (Electronics) ,FORWARD error correction - Abstract
It has been shown that quasi orthogonal space time block code (QOSTBC) can achieve high transmission rate with partial diversity. In this paper, a QOSTBC concatenating Bose-Chaudhuri- Hocquenghem (BCH) code structure is presented. At the receiver, pairwise detection and error correction are first implemented. The decoded data are regrouped. Parallel interference cancellation (PIC) and dual orthogonal space time block code (OSTBC) decoding are deployed to the regrouped data. The pure concatenated scheme is shown to have higher diversity order and better error performance at high signal-to-noise ratio (SNR) scenario than both QOSTBC and OSTBC schemes. The PIC and dual OSTBC decoding algorithm can further obtain approximate 1.2 dB gains than the pure concatenated scheme at 10
-6 bit error probability. [ABSTRACT FROM AUTHOR]- Published
- 2011
21. Coding Schemes for Noiseless and Noisy Asynchronous CDMA Systems.
- Author
-
Ying-Wah Wu and Shih-Chun Chang
- Subjects
ASYNCHRONOUS transfer mode ,WIRELESS communications ,CODE division multiple access ,SPREAD spectrum communications ,INFORMATION theory - Abstract
Novel coding schemes for noiseless and noisy asynchronous code division multiple access (A-CDMA) systems are presented in this paper. The schemes use Wu-Chang spreading code, block interleaver, and synchronizable channel codes to support A-CDMA communications with random delays. For the noiseless case, each active user generates one of M messages, M = ⌊(2
T-D - 1)/(D + 1)⌋, and a (T - D)-stage MLSR encoder encodes the message into a codeword of length T. Given a maximum random delay of D chips, the receiver can decode messages of all active users without ambiguity. For the noisy case, extended Bose-Caldwell cyclic codes are used to encode messages. The extended cyclic codes provide error correction and delay recovery effectively. By using a BCH code of length n as the cyclic code, the extended code can correct up to τ ≤ ⌊n/4⌋ errors and recover a maximum random delay of n - 1 chips. [ABSTRACT FROM AUTHOR]- Published
- 2010
- Full Text
- View/download PDF
22. Cancelable Fingerprint Cryptosystem Using Multiple Spiral Curves and Fuzzy Commitment Scheme.
- Author
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Sandhya, Mulagala and Prasad, Munaga V. N. K.
- Subjects
BIOMETRIC identification ,HUMAN fingerprints ,FUZZY algorithms ,CURVILINEAR motion ,PARAMETRIC equations ,ANTHROPOMETRY ,FUZZY sets - Abstract
The increased use of biometric-based authentication systems in a variety of applications has made biometric template protection an important issue. Unlike conventional systems, biometric cannot be revoked or changed. This made template protection a critical issue to be considered in the recent years. This paper proposes a cancelable fingerprint cryptosystem using multiple spiral curves and fuzzy commitment scheme. The method is built by combining cancelable biometrics and biometric cryptosystems. First, we compute transformed minutiae features using multiple spiral curves. Further, these transformed features are encrypted using fuzzy commitment scheme. Hence, a secure template is obtained. Experimental results and analysis prove the credibility of proposed method with recently presented methods of fingerprint template protection. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
23. A class of narrow-sense BCH codes over Fqqm-12 of length Fqqm-12
- Author
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Ling, Xin, Mesnager, Sihem, Qi, Yanfeng, and Tang, Chunming
- Published
- 2020
- Full Text
- View/download PDF
24. New Quantum BCH Codes of Length n=2(q4−1).
- Author
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Wang, Jun Li, Li, Rui Hu, Ma, Yue Na, and Liu, Yang
- Subjects
CIPHERS ,NANOELECTRONICS ,DIMENSIONS - Abstract
In this paper, narrow-sense and non-narrow-sense BCH codes of length n =2(q
4 −1) that contain their Hermitian duals over Fq2 are studied, where q is an odd prime power. Theory of cyclotomic coset is applied to confirm the maximum designed distances and dimensions of these BCH codes. Finally, some new quantum codes are obtained from such BCH codes, many of our quantum codes are much better than those from narrow-sense BCH codes in [12]. [ABSTRACT FROM AUTHOR]- Published
- 2019
- Full Text
- View/download PDF
25. Some binary BCH codes with length n = 2m + 1.
- Author
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Liu, Yang, Li, Ruihu, Fu, Qiang, Lu, Liangdong, and Rao, Yi
- Subjects
- *
BCH codes , *BINARY codes , *CYCLOTOMIC fields , *CYCLIC codes , *FINITE fields - Abstract
Abstract Under research for nearly sixty years, Bose–Chaudhuri–Hocquenghem (BCH) codes have played increasingly important roles in many applications such as communication, data storage and information security. However, the dimension and minimum distance of BCH codes have been seldom solved by now because of their intractable characteristics. The objective of this paper is to study the dimensions of some binary BCH codes with length n = 2 m + 1. Many new techniques are employed to investigate the coset leaders modulo n. For m = 2 t + 1 , 4 t + 2 , 8 t + 4 and m ≥ 10 , the first five largest coset leaders modulo n are determined, and the dimensions of some BCH codes of length n with designed distance δ > 2 ⌈ m 2 ⌉ are presented. These new skills and results may be helpful to study other types of cyclic codes over finite fields. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
26. On the dimension and minimum distance of BCH codes over GF( q).
- Author
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Dianwu, Yue and Zhengming, Hu
- Abstract
In this paper, only narrow-sense primitive BCH codes over GF( q) are considered. A formula, that can be used in many cases, is first presented for computing the dimension of BCH codes. It improves the result given by MacWilliams and Sloane in 1977. A new method for finding the dimension of all types of BCH codes is proposed. In second part, it is proved that the BCH bound is the leader of some cyclotomic coset, and we guess that the minimum distance for any BCH code is also the leader of some cyclotomic coset. [ABSTRACT FROM AUTHOR]
- Published
- 1996
- Full Text
- View/download PDF
27. Efficient image tampering localization using semi-fragile watermarking and error control codes
- Author
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Pascal Lefèvre, Caroline Fontaine, Jiwu Huang, Philippe Gaborit, Philippe Carré, College of Information Engineering [Shenzhen], Shenzhen Univerisity [Shenzhen], Synthèse et analyse d'images (XLIM-ASALI), XLIM (XLIM), Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS)-Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Méthodes Formelles (LMF), Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Ecole Normale Supérieure Paris-Saclay (ENS Paris Saclay), and Mathématiques & Sécurité de l'information (XLIM-MATHIS)
- Subjects
Block code ,Image quality ,Computer science ,02 engineering and technology ,Image (mathematics) ,[INFO.INFO-CR]Computer Science [cs]/Cryptography and Security [cs.CR] ,020401 chemical engineering ,[INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing ,Computer Science::Multimedia ,0202 electrical engineering, electronic engineering, information engineering ,Code (cryptography) ,0204 chemical engineering ,Electrical and Electronic Engineering ,Digital watermarking ,ComputingMilieux_MISCELLANEOUS ,[INFO.INFO-MM]Computer Science [cs]/Multimedia [cs.MM] ,020206 networking & telecommunications ,Control and Systems Engineering ,[INFO.INFO-IT]Computer Science [cs]/Information Theory [cs.IT] ,Signal Processing ,Computer Vision and Pattern Recognition ,Error detection and correction ,Algorithm ,Software ,Decoding methods ,BCH code - Abstract
In this paper, we propose an image tampering localization algorithm using semi-fragile watermarking and Error-Locating codes in the DWT domain. By introducing different families of codes, we show the benefit in terms of image tampering localization and complexity of using control code error localization as an authentication function. Indeed, we first experimentally show that error localization block codes is as precise as using classical error correcting codes (Reed-Solomon and BCH codes) to locate image tampering. However, their corresponding decoding algorithms complexity is at least quadratic which make them impractical for some real time applications. To solve this problem, we introduce error-control codes called Error-Locating codes where error localization is reduced to a single syndrome computation performed with low number of binary operations (detailed later in the paper). We provide comparisons of image quality and tampering localization performances using error-detection, error-localization and error-correction approaches with different error control codes.
- Published
- 2022
28. Dimensions of three types of BCH codes over [formula omitted].
- Author
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Liu, Hao, Ding, Cunsheng, and Li, Chengju
- Subjects
- *
BCH codes , *FINITE fields , *MATHEMATICAL formulas , *INFORMATION storage & retrieval systems , *COMMUNICATION - Abstract
BCH codes have been studied for over fifty years and widely employed in consumer devices, communication systems, and data storage systems. However, the dimension of BCH codes is settled only for a very small number of cases. In this paper, we study the dimensions of BCH codes over finite fields with three types of lengths n , namely n = q m − 1 , n = ( q m − 1 ) ∕ ( q − 1 ) and n = q m + 1 . For narrow-sense primitive BCH codes with designed distance δ , we investigate their dimensions for δ in the range 1 ≤ δ ≤ q ⌈ m 2 ⌉ + 1 . For non-narrow sense primitive BCH codes, we provide two general formulas on their dimensions and give the dimensions explicitly in some cases. Furthermore, we settle the minimum distances of some primitive BCH codes. We also explore the dimensions of the BCH codes of lengths n = ( q m − 1 ) ∕ ( q − 1 ) and n = q m + 1 over finite fields. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
29. Construction and decoding of BCH codes over chain of commutative rings
- Author
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Shah, Tariq, Qamar, Attiq, and de Andrade, Antonio Aparecido
- Published
- 2012
- Full Text
- View/download PDF
30. A new efficient way based on special stabilizer multiplier permutations to attack the hardness of the minimum weight search problem for large BCH codes
- Author
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Said Nouh, Mohamed Azouazi, Abdelwahed Namir, and Issam Abderrahman Joundan
- Subjects
Discrete mathematics ,General Computer Science ,05 social sciences ,Code word ,050301 education ,Minimum weight ,02 engineering and technology ,Coding theory ,Data_CODINGANDINFORMATIONTHEORY ,Zimmermann algorithm ,BCH codes ,Permutation ,Canteaut-chabaud algorithm ,Dimension (vector space) ,0202 electrical engineering, electronic engineering, information engineering ,Code (cryptography) ,020201 artificial intelligence & image processing ,Multiplier (economics) ,Electrical and Electronic Engineering ,Minimum distance ,0503 education ,BCH code ,Multiplier ,Mathematics - Abstract
BCH codes represent an important class of cyclic error-correcting codes; their minimum distances are known only for some cases and remains an open NP-Hard problem in coding theory especially for large lengths. This paper presents an efficient scheme ZSSMP (Zimmermann Special Stabilizer Multiplier Permutation) to find the true value of the minimum distance for many large BCH codes. The proposed method consists in searching a codeword having the minimum weight by Zimmermann algorithm in the sub codes fixed by special stabilizer multiplier permutations. These few sub codes had very small dimensions compared to the dimension of the considered code itself and therefore the search of a codeword of global minimum weight is simplified in terms of run time complexity. ZSSMP is validated on all BCH codes of length 255 for which it gives the exact value of the minimum distance. For BCH codes of length 511, the proposed technique passes considerably the famous known powerful scheme of Canteaut and Chabaud used to attack the public-key cryptosystems based on codes. ZSSMP is very rapid and allows catching the smallest weight codewords in few seconds. By exploiting the efficiency and the quickness of ZSSMP, the true minimum distances and consequently the error correcting capability of all the set of 165 BCH codes of length up to 1023 are determined except the two cases of the BCH(511,148) and BCH(511,259) codes. The comparison of ZSSMP with other powerful methods proves its quality for attacking the hardness of minimum weight search problem at least for the codes studied in this paper.
- Published
- 2019
31. Two bit overlap: a class of double error correction one step majority logic decodable codes
- Author
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Ori Rottenstreich, Shanshan Liu, Pedro Reviriego, and Fabrizio Lombardi
- Subjects
Telecomunicaciones ,Computer science ,One step majority logic decoding ,02 engineering and technology ,Code rate ,020202 computer hardware & architecture ,Theoretical Computer Science ,Parity-check matrix ,Computational Theory and Mathematics ,Hardware and Architecture ,Memory ,0202 electrical engineering, electronic engineering, information engineering ,Error correction codes ,Orthogonal Latin square codes ,Arithmetic ,Error detection and correction ,Software ,Decoding methods ,BCH code ,Block (data storage) ,Parity bit - Abstract
Error Correction Codes (ECCs) are commonly used to protect memories against soft errors with an impact on memory area and delay. For large memories, the area overhead is mostly due to the additional cells needed to store the parity check bits. In terms of delay, the overhead is mostly needed to detect and correct errors when the data is read from the memory. Most ECCs that can correct more than one error have a complex decoding process and so are limited in high speed memory applications. One exception is One Step Majority Logic Decodable (OS-MLD) codes for which decoding can be done in parallel at high speed. Unfortunately, there are only a few OS-MLD codes that provide a limited choice in terms of block sizes, error correction capabilities and code rate. Therefore, there is considerable interest in a novel construction of OS-MLD codes to provide additional choices for protecting memories. In this paper, a new method to construct Double Error Correction (DEC) OS-MLD codes is presented. This method is based on the use of parity check matrices in which two bits have at most two parity check equations in common; the proposed method provides codes that require a smaller number of parity check bits than existing codes like Orthogonal Latin Square (OLS) codes. The drawback of the proposed Two Bit Overlap (TBO) codes is that they require slightly more complex decoding than OLS codes. Therefore, they provide an intermediate solution between OLS and non OS-MLD codes in terms of decoding delay and number of parity check bits. The proposed TBO codes have been implemented for some block sizes and compared to both OLS and BCH codes to illustrate the trade off in delay and memory overhead. Finally, this paper discusses the generalization of the proposed scheme to codes with larger error correction capabilities. Publicado
- Published
- 2019
32. On cyclic caps in 4-dimensional projective spaces
- Author
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Giulietti, Massimo
- Published
- 2008
- Full Text
- View/download PDF
33. A Scheme for Collective Encoding and Iterative Soft-Decision Decoding of Cyclic Codes of Prime Lengths: Applications to Reed–Solomon, BCH, and Quadratic Residue Codes.
- Author
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Lin, Shu, Abdel-Ghaffar, Khaled, Li, Juane, and Liu, Keke
- Subjects
CYCLIC codes ,ITERATIVE decoding ,CONGRUENCES & residues ,REED-Solomon codes ,PARITY-check matrix - Abstract
A novel scheme is presented for encoding and iterative soft-decision decoding of cyclic codes of prime lengths. The encoding of a cyclic code of a prime length is performed on a collection of codewords which are mapped through Galois Fourier transform into a codeword in a low-density parity-check code with a binary parity-check matrix for transmission. Using this matrix, binary iterative soft-decision decoding algorithm is applied to jointly decode a collection of codewords from the cyclic code. The joint-decoding allows for information sharing among the received vectors corresponding to the codewords in the collection during the iterative decoding process. For decoding Reed-Solomon and BCH codes of prime lengths, the proposed decoding scheme not only requires much lower decoding complexity than other soft-decision decoding algorithms for these codes, but also yields superior performance. The proposed decoding scheme can also achieve a joint-decoding gain over the maximum likelihood decoding of individual codewords. The decoding scheme is also applied to quadratic residue codes. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
34. A Correlation-Breaking Interleaving of Polar Codes in Concatenated Systems
- Author
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Ya Meng, Liping Li, and Chuan Zhang
- Subjects
FOS: Computer and information sciences ,General Computer Science ,Interleaving ,Computer science ,Information Theory (cs.IT) ,Concatenated error correction code ,Computer Science - Information Theory ,Concatenation ,Data_CODINGANDINFORMATIONTHEORY ,Bit error rate ,Low-density parity-check code ,Error detection and correction ,Algorithm ,BCH code ,Decoding methods ,Computer Science::Information Theory - Abstract
It is known that the bit errors of polar codes with successive cancellation (SC) decoding are coupled. However, existing concatenation schemes of polar codes with other error correction codes rarely take this coupling effect into consideration. To achieve a better error performance of concatenated systems with polar codes as inner codes, one can divide all bits in an outer block into different polar blocks to completely de-correlate the possible coupled errors in the transmitter side. We call this interleaving a blind interleaving (BI) which serves as a benchmark. Two BI schemes, termed BI-DP and BI-CDP, are proposed in the paper. To better balance performance, memory size, and the decoding delay from the de-interleaving, a novel interleaving scheme, named the correlation-breaking interleaving (CBI), is proposed. The CBI breaks the correlated information bits based on the error correlation pattern proposed and proven in this paper. The proposed CBI scheme is general in the sense that any error correction code can serve as the outer code. In this paper, Low-Density Parity-Check (LDPC) codes and BCH codes are used as two examples of the outer codes of the interleaving scheme. The CBI scheme 1) can keep the simple SC polar decoding while achieving a better error performance than the state-of-the-art (SOA) direct concatenation of polar codes with LDPC codes and BCH codes; 2) achieves a comparable error performance as the BI-DP scheme with a smaller memory size and a shorter decoding delay. Numerical results are provided to verify the performance of the BI schemes and the CBI scheme.
- Published
- 2017
35. Some new results on dimension and Bose distance for various classes of BCH codes.
- Author
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Cherchem, Ahmed, Jamous, Abdelillah, Liu, Hongwei, and Maouche, Youcef
- Subjects
- *
DISTANCES , *CYCLIC codes , *BINARY codes , *CIPHERS - Abstract
In this paper, we give the dimension and the minimum distance of two subclasses of narrow-sense primitive BCH codes over F q with designed distance δ = a q m − 1 − 1 (resp. δ = a q m − 1 q − 1) for all 1 ≤ a ≤ q − 1 , where q is a prime power and m > 1 is a positive integer. As a consequence, we obtain an affirmative answer to two conjectures proposed by C. Ding in 2015. Furthermore, using the previous part, we extend some results of Yue and Hu [16] , and we give the dimension and, in some cases, the Bose distance for a large designed distance in the range a q m − 1 q − 1 , a q m − 1 q − 1 + T for 0 ≤ a ≤ q − 2 , where T = q m + 1 2 − 1 if m is odd, and T = 2 q m 2 − 1 if m is even. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
36. On components of the Kerdock codes and the dual of the BCH code [formula omitted].
- Author
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Mogilnykh, I. Yu. and Solov'eva, F.I.
- Subjects
- *
LINEAR codes , *CIPHERS - Abstract
In the paper we investigate the structure of i -components of two classes of codes: the Kerdock codes and the duals of the linear uniformly packed codes with parameters of the primitive double-error-correcting BCH code. We prove that for any admissible length the punctured Kerdock code consists of two i -components and the duals of the linear uniformly packed codes with parameters of the primitive double-error-correcting BCH code is an i -component for any i. We give an alternative proof for the fact presented by De Caen and van Dam in 1999 that the restrictions of the Hamming scheme to the doubly shortened Kerdock codes are association schemes. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
37. Tensor-Product Parity Code for Magnetic Recording.
- Author
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Panu Chaichanavong and Siegel, Paul H.
- Subjects
- *
DATA tapes , *BAR codes , *PRODUCT coding , *AUTOMATIC identification , *PARITY nonconservation , *QUANTUM theory - Abstract
In magnetic recording, a standard code architecture consists of an outer Reed-Solomon code in concatenation with an inner parity code. The inner parity code is used to detect and correct common error events. Generally, a parity code with short block length performs better, as multiple error events within one block and, consequently, miscorrection are less likely. In this paper, we study an inner code that offers the same system performance as a parity code with very short block length, even as short as the symbol length (in bits) of the outer Reed-Solomon code, but with higher code rate. This code is a tensor-product code, with a Bose-Chauduri-Hocquenghem (BCH) code and a short parity code as constituent codes. The decoder for this code is not much more complex than the optimal decoder of the baseline parity-coded channel; in fact, the only additional steps are Viterbi detection matched to the channel and decoding of the BCH code. [ABSTRACT FROM AUTHOR]
- Published
- 2006
- Full Text
- View/download PDF
38. On some cyclic codes of length [formula omitted].
- Author
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Wu, Peng, Li, Chengju, and Peng, Wei
- Subjects
- *
CYCLIC codes , *LINEAR codes , *TELECOMMUNICATION systems , *DECODING algorithms - Abstract
Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. The objective of this paper is to investigate the parameters of some q -ary cyclic codes of length n = q 2 m − 1 q + 1. The dimensions of these codes are settled and the lower bounds on their minimum distances are presented by employing the Hartmann-Tzeng bound or BCH bound. Moreover, when q = 2 , 3 , we give the largest coset leaders δ 1 modulo n and investigate the parameters of the BCH codes C (q , n , δ 1 , 1). [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
39. Wavelet Packets-Based Blind Watermarking for Medical Image Management
- Author
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Salwa A. K. Mostafa, A. S. Tolba, Naser El-Sheimy, F. M. Abdel-Kader, and Hisham M. Elhindy
- Subjects
Biomedical Engineering ,ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION ,Medical image watermarking (MIW) ,Medicine (miscellaneous) ,Bioengineering ,computer.software_genre ,Article ,Wavelet packet decomposition ,Robustness (computer science) ,Medicine ,Computer vision ,Digital watermarking ,Histogram equalization ,business.industry ,Watermark ,computer.file_format ,JPEG ,Gamma correction ,BCH code ,Data mining ,Artificial intelligence ,business ,Error detection and correction ,computer ,discrete wavelet packet transform DWPT ,electronic patient record (EPR) - Abstract
The last decade has witnessed an explosive use of medical images and Electronics Patient Record (EPR) in the healthcare sector for facilitating the sharing of patient information and exchange between networked hospitals and healthcare centers. To guarantee the security, authenticity and management of medical images and information through storage and distribution, the watermarking techniques are growing to protect the medical healthcare information. This paper presents a technique for embedding the EPR information in the medical image to save storage space and transmission overheads and to guarantee security of the shared data. In this paper a new method for protecting the patient information in which the information is embedded as a watermark in the discrete wavelet packet transform (DWPT) of the medical image using the hospital logo as a reference image. The patient information is coded by an error correcting code (ECC), BCH code, to enhance the robustness of the proposed method. The scheme is blind so that the EPR can be extracted from the medical image without the need of the original image. Therefore, this proposed technique is useful in telemedicine applications. Performance of the proposed method was tested using four modalities of medical images; MRA, MRI, Radiological, and CT. Experimental results showed no visible difference between the watermarked and the original image. Moreover, the proposed watermarking method is robust against a wide range of attacks such as JPEG coding, Gaussian noise addition, histogram equalization, gamma correction, contrast adjustment, and sharpen filter and rotation.
- Published
- 2010
40. Implementation and verification of different ECC mitigation designs for BRAMs in flash-based FPGAs
- Author
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Hong Su, Jie Liu, Zhang Zhangang, Zhen-Lei Yang, and Xiaohui Wang
- Subjects
Nuclear and High Energy Physics ,Physics - Instrumentation and Detectors ,Computer science ,Event (computing) ,FOS: Physical sciences ,Astronomy and Astrophysics ,Parallel computing ,Instrumentation and Detectors (physics.ins-det) ,Flash (photography) ,Error correcting ,Field-programmable gate array ,Instrumentation ,Hamming code ,BCH code - Abstract
Embedded RAM blocks (BRAMs) in field programmable gate arrays (FPGAs) are susceptible to single event effects (SEEs) induced by environmental factors such as cosmic rays, heavy ions, alpha particles and so on. As technology scales, the issue will be more serious. In order to tackle this issue, two different error correcting codes (ECCs), the shortened Hamming codes and shortened BCH codes, are investigated in this paper. The concrete design methods of the codes are presented. Also, the codes are both implemented in flash-based FPGAs. Finally, the synthesis report and simulation results are presented in the paper. Moreover, the heavy-ion experiments are performed, the experimental results indicate that the error cross-section using the shortened Hamming codes can be reduced by two orders of magnitude compared with the device without mitigation, and no errors are discovered in the experiments for the device using the shortened BCH codes.
- Published
- 2015
41. A single-bit and double-adjacent error correcting parallel decoder for multiple-bit error correcting BCH codes
- Author
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Kazuteru Namba, Salvatore Pontarelli, Marco Ottavi, and Fabrizio Lombardi
- Subjects
Computer science ,Detector ,MAXEkSAT ,Settore ING-INF/01 - Elettronica ,Electronic, Optical and Magnetic Materials ,Power (physics) ,Soft-decision decoder ,Logic gate ,Electrical and Electronic Engineering ,Safety, Risk, Reliability and Quality ,Error detection and correction ,Algorithm ,Decoding methods ,BCH code ,Computer Science::Information Theory - Abstract
This paper presents a novel high-speed BCH decoder that corrects double-adjacent and single-bit errors in parallel and serially corrects multiple-bit errors other than double-adjacent errors. Its operation is based on extending an existing parallel BCH decoder that can only correct single-bit errors and serially corrects double-adjacent errors at low speed. The proposed decoder is constructed by a novel design and is suitable for nanoscale memory systems, in which multiple-bit errors occur at a probability comparable to single-bit errors and double-adjacent errors occur at a higher probability (nearly two orders of magnitude) than other multiple-bit errors. Extensive simulation results are reported. Compared with the existing scheme, the area and delay time of the proposed decoder are on average 11% and 6% higher, but its power consumption is reduced by 9% on average. This paper also shows that the area, delay, and power overheads incurred by the proposed scheme are significantly lower than traditional fully parallelized BCH decoders capable of correcting any double-bit errors in parallel.
- Published
- 2014
42. On the decoding of quasi-BCH codes
- Author
-
Barbier, Morgan, Pernet, Clément, Quintin, Guillaume, Equipe AMACC - Laboratoire GREYC - UMR6072, Groupe de Recherche en Informatique, Image et Instrumentation de Caen (GREYC), Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Ingénieurs de Caen (ENSICAEN), Normandie Université (NU)-Normandie Université (NU)-Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Ingénieurs de Caen (ENSICAEN), Normandie Université (NU), PrograMming and scheduling design fOr Applications in Interactive Simulation (MOAIS), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire d'Informatique de Grenoble (LIG), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'informatique de l'École polytechnique [Palaiseau] (LIX), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X), Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU)-École Nationale Supérieure d'Ingénieurs de Caen (ENSICAEN), Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS)-Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS), and École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
FOS: Computer and information sciences ,BCH code ,quasi-BCH code ,Quasi-cyclic code ,[INFO.INFO-IT]Computer Science [cs]/Information Theory [cs.IT] ,Computer Science - Information Theory ,Information Theory (cs.IT) ,Reed-Solomon ,[MATH.MATH-IT]Mathematics [math]/Information Theory [math.IT] ,Data_CODINGANDINFORMATIONTHEORY ,interleaved code ,Hardware_ARITHMETICANDLOGICSTRUCTURES - Abstract
International audience; In this paper we investigate the structure of quasi-BCH codes. In the first part of this paper we show that quasi-BCH codes can be derived from Reed-Solomon codes over square matrices extending the known relation about classical BCH and Reed-Solomon codes. This allows us to adapt the Welch-Berlekamp algorithm to quasi-BCH codes. In the second part of this paper we show that quasi-BCH codes can be seen as subcodes of interleaved Reed-Solomon codes over finite fields. This provides another approach for decoding quasi-BCH codes.
- Published
- 2013
43. High throughput error correction in information reconciliation for semiconductor superlattice secure key distribution
- Author
-
Jianguo Xie, Song Helun, Xiaoming Chen, Han Wu, Chao Xia, Liwei Xu, and Peng Ding
- Subjects
Multidisciplinary ,Computer science ,Science ,Key distribution ,Information technology ,Data_CODINGANDINFORMATIONTHEORY ,010502 geochemistry & geophysics ,01 natural sciences ,Article ,0103 physical sciences ,Lookup table ,Key (cryptography) ,Medicine ,Low-density parity-check code ,010306 general physics ,Error detection and correction ,Algorithm ,Throughput (business) ,BCH code ,Decoding methods ,0105 earth and related environmental sciences ,Communication channel - Abstract
Semiconductor superlattice secure key distribution (SSL-SKD) has been experimentally demonstrated to be a novel scheme to generate and agree on the identical key in unconditional security just by public channel. The error correction in the information reconciliation procedure is introduced to eliminate the inevitable differences of analog systems in SSL-SKD. Nevertheless, the error correction has been proved to be the performance bottleneck of information reconciliation for high computational complexity. Hence, it determines the final secure key throughput of SSL-SKD. In this paper, different frequently-used error correction codes, including BCH codes, LDPC codes, and Polar codes, are optimized separately to raise the performance, making them usable in practice. Firstly, we perform multi-threading to support multi-codeword decoding for BCH codes and Polar codes and updated value calculation for LDPC codes. Additionally, we construct lookup tables to reduce redundant calculations, such as logarithmic table and antilogarithmic table for finite field computation. Our experimental results reveal that our proposed optimization methods can significantly promote the efficiency of SSL-SKD, and three error correction codes can reach the throughput of Mbps and provide a minimum secure key rate of 99%.
- Published
- 2021
44. Multirate Filter Bank Representations of RS and BCH Codes
- Author
-
Marc Moonen and Geert Van Meerbergen
- Subjects
Computer science ,Computer Networks and Communications ,Speech recognition ,lcsh:TK5101-6720 ,Signal Processing ,lcsh:Electronics ,lcsh:TK7800-8360 ,Filter bank ,Algorithm ,BCH code ,Computer Science Applications ,lcsh:Telecommunication - Abstract
This paper addresses the use of multirate filter banks in the context of error-correction coding. An in-depth study of these filter banks is presented, motivated by earlier results and applications based on the filter bank representation of Reed-Solomon (RS) codes, such as Soft-In Soft-Out RS-decoding or RS-OFDM. The specific structure of the filter banks (critical subsampling) is an important aspect in these applications. The goal of the paper is twofold. First, the filter bank representation of RS codes is now explained based on polynomial descriptions. This approach allows us to gain new insight in the correspondence between RS codes and filter banks. More specifically, it allows us to show that the inherent periodically time-varying character of a critically subsampled filter bank matches remarkably well with the cyclic properties of RS codes. Secondly, an extension of these techniques toward the more general class of BCH codes is presented. It is demonstrated that a BCH code can be decomposed into a sum of critically subsampled filter banks.
- Published
- 2008
45. Early-Stopped Approach and Analysis for the Berlekamp-Massey Algorithm
- Author
-
Chou, Hung-Pu and Hong-fu, Chou
- Subjects
Computer science [C05] [Engineering, computing & technology] ,BCH code ,BM algorithm ,low latency design ,Sciences informatiques [C05] [Ingénierie, informatique & technologie] - Abstract
BCH codes are being widely used in commercial NAND flash controllers, and the decoding algorithm based on the Berlekamp-Massey (BM) algorithm is a classic solution for solving the key equation used for error correction. The latency of BM decoding is the bottleneck of the Bose-Chaudhuri Hocquenghem (BCH) decoder when correcting a high number of bit errors. However, the flash memory has an error distribution that degrades with usage: few errors occur in the new memory and a low number of errors occur within a code block. With usage, the system performance degrades and BM decoding needs t iterations in order to correct a larger number t of errors. In an attempt to improve the system performance for high speed applications, early termination of the BM decoding is necessary to overcome this degradation. In this paper, a practical solution for early termination checking for BM algorithm is provided. The analysis of proposed method is presented by means of considering the weight distribution of BCH code and deriving the probability of malfunction as the event of undetectable error. The proposed method is presented to be effective by the numerical results and the probability of malfunction for the proposed method is lower than 10−26. As a result, the FPGA testing on a USB device validate the reliability of the proposed method for applying to a commercial product.
- Published
- 2022
46. Long Cyclic Codes Over GF(4) and GF(8) Better Than BCH Codes in the High-Rate Region.
- Author
-
Roth, Ron M. and Zeh, Alexander
- Subjects
BCH codes ,ERROR-correcting codes ,CYCLIC codes ,STATISTICAL matching ,DECODERS & decoding ,CODING theory - Abstract
An explicit construction of an infinite family of cyclic codes is presented which, over GF(4) (resp., GF(8)), have approximately 8/9 (resp., 48/49) the redundancy of BCH codes of the same minimum distance and length. As such, the new codes are the best codes currently known in a regime where the minimum distance is fixed and the code length goes to infinity. [ABSTRACT FROM PUBLISHER]
- Published
- 2017
- Full Text
- View/download PDF
47. VALIDATION OF THE BCH-ONTOLOGY
- Author
-
G. García and O. Zalamea
- Subjects
lcsh:Applied optics. Photonics ,Markup language ,Information retrieval ,Computer science ,lcsh:T ,lcsh:TA1501-1820 ,Data_CODINGANDINFORMATIONTHEORY ,Ontology (information science) ,lcsh:Technology ,Cultural heritage ,lcsh:TA1-2040 ,Ontology ,Use case ,CityGML ,CIDOC Conceptual Reference Model ,lcsh:Engineering (General). Civil engineering (General) ,Semantic Web ,BCH code - Abstract
In the heritage domain, capturing facts and knowledge for preventive conservation of Built Cultural Heritage (BCH) requires access to a large variety of data. It is a multidisciplinary activity and uses heterogeneous terminologies. In this regard, the BCH-ontology has been developed to facilitate integration and exchange of heterogeneous built cultural heritage information. The BCH-ontology reuses three already developed ontologies: Geneva City Geographic Markup Language (Geneva CityGML), Monument Damage ontology (Mondis), and CIDOC Conceptual Reference Model (CIDOC-CRM). Additionally, it provides a complete semantic framework by defining some classes and properties for improving BCH management. This paper presents the validation of the BCH-ontology ontological model to determine whether the ontology is able to represent BCH data under a preventive conservation approach. The San Luis seminary is a historical building built in the late XIX century in Cuenca-Ecuador and it is employed as use case. This validation allowed the identification of further use cases where the ontology offers a potential additional value in the BCH-domain.
- Published
- 2020
48. Quantum MDS and Synchronizable Codes From Cyclic and Negacyclic Codes of Length 2 ps Over F pm
- Author
-
Woraphon Yamaka, Bac T. Nguyen, and Hai Q. Dinh
- Subjects
Discrete mathematics ,General Computer Science ,General Engineering ,quantum synchronizable codes ,Hermitian matrix ,Prime (order theory) ,Separable space ,Finite field ,Hamming distance ,General Materials Science ,MDS codes ,lcsh:Electrical engineering. Electronics. Nuclear engineering ,Variety (universal algebra) ,quantum MDS codes ,Quantum ,Cyclic codes ,repeated-root codes ,lcsh:TK1-9971 ,BCH code ,Mathematics - Abstract
Let p be an odd prime, and Fp(m) is the finite field of pm elements. In this paper, all maximum distance separable (briefly, MDS) cyclic and negacyclic codes of length 2ps over Fp(m) are established. As an application, all quantum MDS (briefly, qMDS) codes are constructed from cyclic and negacyclic codes of length 2ps over finite fields using the Calderbank Shor-Steane (briefly, CSS) and Hermitian constructions. These codes are new in the sense that their parameters are different from all the previous constructions. Furthermore, quantum synchronizable codes (briefly, QSCs) are obtained from cyclic codes of length 2ps over Fp(m). To enrich the variety of available QSCs, many new QSCs are constructed to illustrate our results. Among them, there are QSCs codes with shorter lengths and much larger minimum distances than known primitive narrow-sense Bose-Chaudhuri-Hocquenghem (briefly, BCH) codes.
- Published
- 2020
49. Machine learning for decoding linear block codes: case of multi-class logistic regression model
- Author
-
Nouh Said, Chemseddine Idrissi Imrane, Bellfkih El Mehdi, Marzak Abdelaziz, and El Kasmi Alaoui Seddiq
- Subjects
Control and Optimization ,Computer Networks and Communications ,Computer science ,Logistic regression ,Data_CODINGANDINFORMATIONTHEORY ,Machine learning ,computer.software_genre ,BCH codes ,Error correction codes ,Syndrome decoding ,Electrical and Electronic Engineering ,business.industry ,SoftMax ,Linear code ,Support vector machine ,Hardware and Architecture ,Multilayer perceptron ,Signal Processing ,Softmax function ,Binary code ,Artificial intelligence ,business ,computer ,BCH code ,Decoding methods ,Information Systems - Abstract
Facing the challenge of enormous data sets variety, several machine learning-based algorithms for prediction (e.g, Support vector machine, multi layer perceptron and logistic regression) have been highly proposed and used over the last years in many fields. Error correcting codes (ECCs) are extensively used in practice to protect data against damaged data storage systems and against random errors due to noise effects. In this paper, we will use machine learning methods, especially multi-class logistic regression combined with the famous syndrome decoding algorithm. The main idea behind our decoding method which we call logistic regression decoder (LRDec) is to use the efficient multi-class logistic regression models to find errors from syndromes in linear codes such as bose, ray-chaudhuri and hocquenghem (BCH), and the quadratic residue (QR). Obtained results of the proposed decoder have a significant benefit in terms of bit error rate (BER) for random binary codes. The comparison of our decoder with many competitors proves its power. The proposed decoder has reached a success percentage of 100% for correctable errors in the studied codes.
- Published
- 2021
50. Primitive Rateless Codes
- Author
-
Mahyar Shirvanimoghaddam
- Subjects
FOS: Computer and information sciences ,Discrete mathematics ,Sequence ,Computer Science - Cryptography and Security ,Information Theory (cs.IT) ,Computer Science - Information Theory ,05 social sciences ,Code word ,050801 communication & media studies ,16. Peace & justice ,Upper and lower bounds ,0508 media and communications ,Primitive polynomial ,Code (cryptography) ,Dual polyhedron ,Electrical and Electronic Engineering ,Hamming weight ,Cryptography and Security (cs.CR) ,BCH code ,Mathematics - Abstract
In this paper, we propose primitive rateless (PR) codes. A PR code is characterized by the message length and a primitive polynomial over $\mathbf{GF}(2)$, which can generate a potentially limitless number of coded symbols. We show that codewords of a PR code truncated at any arbitrary length can be represented as subsequences of a maximum-length sequence ($m$-sequence). We characterize the Hamming weight distribution of PR codes and their duals and show that for a properly chosen primitive polynomial, the Hamming weight distribution of the PR code can be well approximated by the truncated binomial distribution. We further find a lower bound on the minimum Hamming weight of PR codes and show that there always exists a PR code that can meet this bound for any desired codeword length. We provide a list of primitive polynomials for message lengths up to $40$ and show that the respective PR codes closely meet the Gilbert-Varshamov bound at various rates. Simulation results show that PR codes can achieve similar block error rates as their BCH counterparts at various signal-to-noise ratios (SNRs) and code rates. PR codes are rate-compatible and can generate as many coded symbols as required; thus, demonstrating a truly rateless performance., Accepted for publication in IEEE Transaction on Communications, July 2021
- Published
- 2021
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