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On the Stopping Distance of array code Parity-Check Matrices

IEEE TRANSACTIONS ON INFORMATION THEORY 2009年第8期55卷 3488-3493页

作者： Esmaeili, Morteza Amoshahy, Mohammad Javad Isfahan Univ Technol Dept Math Sci Esfahan *** Iran

For q an odd prime and 1 3 and q > 3.

For q an odd prime and 1 <= m <= q, we study two binary qm x q(2) parity check matrices for binary array codes. For both parity check matrices, we determine the stopping distance and the minimum distance of the associated code for 2 <= m <= 3, and for (m, q) = (4, 5). In the case (m, q) = (4, 7), the stopping distance and the related minimum distance are also determined for one of the given parity check matrices. Moreover, we give a lower bound on the stopping distances for m > 3 and q > 3.

关键词： Stopping distance array code low-density parity-check (LDPC) code

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New MDS array code Correcting Multiple Disk Failures

New MDS Array Code Correcting Multiple Disk Failures

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IEEE Global Communications Conference (GLOBECOM)

作者： Hou, Hanxu Shum, Kenneth W. Chen, Minghua Li, Hui Peking Univ Shenzhen Grad Sch Shenzhen Key Lab Cloud Comp Tech & App Shenzhen Engn Lab Converged Networks Technol Beijing Peoples R China Chinese Univ Hong Kong Dept Informat Engn Hong Kong Hong Kong Peoples R China Chinese Univ Hong Kong Inst Network Coding Shenzhen Key Lab Network Coding Key Tech & Applic Hong Kong Hong Kong Peoples R China

ISBN: (纸本)9781479935123

We present a new family of maximal-distance separable (MDS) array codes which can tolerate five disk failures. The encoding is based on bit-wise exclusive OR (XOR) and bit-wise cyclic shifts, and hence is amenable to practical implementation. Efficient repair method for correcting up to two disk failures is also given. The proposed coding scheme provides a larger spectrum of parameters, with comparable encoding and repairing complexities in compare with existing MDS array codes, such as the row-diagonal parity (RDP) code and the EVENODD code.

关键词： array code RAID efficient repairing

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A decoding algorithm with restrictions for array codes

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IEEE TRANSACTIONS ON INFORMATION THEORY 1999年第7期45卷 2339-2344页

作者： Haslach, C Vinck, AJH Univ Essen Gesamthsch Inst Expt Math D-45326 Essen Germany

We present a simple and efficient error correction scheme for array-like data structures. We assume that the channel behaves such that each row of a received array is either error-free or corrupted by many symbol errors. Provided that row error vectors are linearly independent, the proposed decoding algorithm can correct asymptotically one erroneous row per redundant row, even without having reliability information from the channel output. This efficient decoding algorithm can be used for correction of error clusters and for decoding elf concatenated codes. We also derive a random access scheme that has many similarities with the Aloha system.

关键词： array code block-interleaving burst-correcting decoding of concatenated codes linear independency

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A Class of array codes Correcting a Cluster of Unidirectional Errors for Two-Dimensional Matrix Symbols

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2009年第6期E92A卷 1508-1519页

作者： Kaneko, Haruhiko Fujiwara, Eiji Tokyo Inst Technol Dept Comp Sci Tokyo 1528552 Japan

Two-dimensional (2D) matrix symbols have higher storage capacity than conventional bar-codes, and hence have been used in various applications, including parts management in factories and Internet site addressing in camera-equipped mobile phones. These symbols generally utilize strong error control codes to protect data from errors caused by blots and scratches, and therefore require a large number of check bits. Because 2D matrix symbols are expressed in black and white dot patterns, blots and scratches often induce clusters of unidirectional errors (i.e., errors that affect black but not white dots, or vice versa). This paper proposes a new class of unidirectional l(m) x l(n)-clustered error correcting codes capable of correcting unidirectional errors confined to a rectangle with l(m) rows and l(n) columns. The proposed code employs 2D interleaved parity-checks, as well as vertical and horizontal arithmetic residue checks. Clustered error pattern is derived using the 2D interleaved parity-checks, while vertical and horizontal positions of the error are calculated using the vertical and horizontal arithmetic residue checks. This paper also derives an upper bound on the number of codewords based on Hamming bound. Evaluation shows that the proposed code provides high code rate close to the bound. For example, for correcting a cluster of unidirectional 40 x 40 errors in 150 x 150 codeword, the code rate of the proposed code is 0.9272, while the upper bound is 0.9284.

关键词： unidirectional error burst error clustered error array code two-dimensional bar-code arithmetic residue check QR code

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More on the Stopping and Minimum Distances of array codes

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IEEE TRANSACTIONS ON COMMUNICATIONS 2011年第3期59卷 750-757页

作者： Esmaeili, M. Tadayon, M. H. Gulliver, T. A. Isfahan Univ Technol Dept Math Sci Esfahan *** Iran Univ Victoria Dept Elect & Comp Engn Victoria BC V8W 3P6 Canada ITRC Tehran Iran

For q an odd prime and 1 = 4,q > 5) is also determined.

For q an odd prime and 1 <= m <= q, two specific binary qm x q(2) parity-check matrices denoted by H (P) (m, q) and H (I) (m, q) are considered. The corresponding binary codes, C (P) (m, q) and C (I) (m, q), respectively, are called proper and improper array codes with parameters m and q. Given a parity-check matrix H representing a binary code C, let s (H) denote the stopping distance of H and d(C) be the minimum Hamming distance of C. It is known that that s (H (I)(m, q)) = s (H (P)(m, q)) = d(C I (m, q)) = d(C (P) (m, q)) for m <= 3. In this paper, we show that these equalities do not hold for all values of m and q. In particular, although s(H (P)(4, 7)) = d(C (P)(4, 7)) = 8 we have s(H (T)(4, 7)) = 9 and d(C (T)(4, 7)) = 10. It is also shown that s(C (I)(5, 11)) = d(C (P)(5, 11)) = 10 while s(H (I)(5, 11)) = 11 and d(C (I)(5, 11)) = 12. This suggests that in many cases the improper array codes would perform better than the proper array codes over the AWGN and binary erasure channels. Performance results are given which confirm this claim. The combinatorial structure of the eight- element stopping sets for H (m >= 4,q > 5) is also determined.

关键词： Stopping distance array code LDPC code

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An efficient QoS enhancement mechanism of VoIP using erasure array codes

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High Technology Letters 2017年第4期23卷 390-398页

作者：李真 Zhang Qin Ren Hui Liu Wenbo Gao Xinyan School of Information Engineering Communication University of China School of Software Dalian University of Technology

In order to solve the problem of losing voice packets in voice over internet protocol(VoIP),a kind of lost packets double recovery algorithm is proposed. The algorithm is based on erasure coding technique which comes from highly available data storage systems. An efficient coding scheme with higher tolerance based on STAR and Reed-Solomon( RS) erasure code is described. An efficient method is also provided which could transform the voice data packets of one dimensional bit stream into two dimensional array according to given window size. If the lost rate has increased beyond the error correction capability,packet-loss concealment will be adopted. Under various conditions of packet-loss simulation during the experiments,the algorithm has proved its better performance on MOS rating and coding rate.

关键词： packet loss recovery voice over internet protocol(VoIP) quality of service(QoS) array code

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Optimal Repair Algorithm of Single-Disk Failure for array codes with Local Properties

Optimal Repair Algorithm of Single-Disk Failure for Array Co...

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2023 IEEE International Conference on Big Data, BigData 2023

作者： Luo, Chuang Hou, Hanxu Zhang, Peng Li, Hui ShenZhen University School of Electronics & Information Engineering Shenzhen China Dongguan University of Technology School of Electrical Engineering & Intelligentization Dongguan China Peking University Shenzhen Graduate School Shenzhen China

ISBN: (纸本)9798350324457

Distributed storage systems ensure data reliability and availability in the event of a disk failure by employing array codes. Generalized Expanded Blaum-Roth (GEBR) codes and Generalized Expanded Independent Parity(GEIP) codes are MDS array codes with local properties that can tolerate multiple disk failures while maintaining good repair performance. However, when repairing a single-disk failure, the repair bandwidth (defined as the total number of symbols downloaded from other surviving disks in repairing the single-disk failure) is not optimal. To address this issue, we propose a random search algorithm that uses a simulated annealing algorithm to optimize the repair strategy. It starts with a viable repair strategy and gradually replaces the current strategy with another that downloads less data. Experimental results demonstrate that our proposed algorithm can significantly reduce the data required to repair single-disk failure for both GEBR and GEIP codes by 25%-38%, under the selection of suitable parameters, when compared with traditional repair methods. Moreover, our repair algorithm can be done in polynomial time. © 2023 IEEE.

关键词： array code Distributed storage system repair bandwidth single-disk failure

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LINEAR BLOCK AND array codeS CORRECTING REPEATED CT BURST ERRORS

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Albanian Journal of Mathematics 2013年第2期7卷 77-92页

作者： Fatih Temiz Vedat Şiap Department of Mathematics Yildiz Technical University Turkey Department of Mathematical Engineering Yildiz Technical University Turkey

Burst errors are very common in practice. There have been many designs in order to correct or at least detect such errors. Recently, a new kind of burst error which is termed as repeated burst error has been introduced in order to detect or correct errors that occurs in very busy communication channels. In this paper, we extend the definition of repeated burst errors for block and array codes endowed with a homogeneous metric. We also obtain some upper bounds on the number of parity check digits for these codes correcting all repeated burst errors.

关键词： 94B05 94B20 2−repeated burst error array code burst error Chieng-Tang burst error linear code

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On the construction of quasi-cyclic low-density parity-check codes based on girth

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2004年第9期E87A卷 2432-2439页

作者： Okamura, T NEC Corp Ltd Internet Syst Res Labs Kawasaki Kanagawa 2118666 Japan

In this paper, we propose a method for constructing quasicyclic low-density parity-check codes randomly using cyclic shift submatrices on the basis of the girth of the Tanner graphs of these codes. We consider (3, K)-regular codes and first derive the necessary and sufficient conditions for weight-4 and weight-6 codewords to exist. On the basis of these conditions, it is possible to estimate the probability that a random method will generate a (3, K)-regular code with a minimum distance less than or equal to 6, and the proposed method is shown to offer a lower probability than does conventional random construction. Simulation results also show that it is capable of generating good codes both regular and irregular.

关键词： low-density parity-check code quasi-cyclic code Tanner graph girth array code irregular code

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On the Minimum-Weight codewords of array LDPC codes with Column Weight 4

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2014年第11期E97A卷 2236-2246页

作者： Liu, Haiyang Deng, Gang Chen, Jie Chinese Acad Sci Inst Microelect Beijing 100029 Peoples R China

In this paper, we investigate the minimum-weight codewords of array LDPC codes C(m, q), where q is an odd prime and m 19. In other words, C(4, q) has 4q(2)(q - 1) minimum-weight codewords for all q > 19. In additi... 详细信息

In this paper, we investigate the minimum-weight codewords of array LDPC codes C(m, q), where q is an odd prime and m <= q. Using some analytical approaches, the lower bound on the number of minimum-weight codewords of C(m, q) given by Kaji (IEEE Int. Symp. Inf. Theory, June/July 2009) is proven to be tight for m = 4 and q> 19. In other words, C(4, q) has 4q(2)(q - 1) minimum-weight codewords for all q > 19. In addition, we show some interesting universal properties of the supports of generators of minimum-weight codewords of the code C(4, q)(q > 19).

关键词： low-density parity-check (LDPC) code array code minimum-weight codeword cyclic shift closure

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