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Keywords
(9)
Combinatorial Problems
Complete Graph
Equivalence Relation
Graph Theory
Mds Code
Low Density
Error Correction
Indexing Terms
Maximum Distance Separable
Related Publications
(11)
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Lowdensity MDS codes and factors of complete graphs
Lowdensity MDS codes and factors of complete graphs,10.1109/18.782102,IEEE Transactions on Information Theory,Lihao Xu,Vasken Bohossian,Jehoshua Bruc
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Lowdensity MDS codes and factors of complete graphs
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Citations: 65
)
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Lihao Xu
,
Vasken Bohossian
,
Jehoshua Bruck
,
David G. Wagner
We present a class of array code of size , where or , called BCode. The distances of the BCode and its dual are and , respectively. The BCode and its dual are optimal in the sense that i) they are maximumdistance separable (MDS), ii) they have an optimal encoding property, i.e., the number of the parity bits that are affected by change of a single information bit is minimal, and iii) they have optimal length. Using a new graph description of the codes, we prove an
equivalence relation
between the construction of the BCode (or its dual) and a combinatorial problem known as perfect one factorization of complete graphs, thus obtaining constructions of two families of the BCode and its dual, one of which is new. Efficient decoding algorithms are also given, both for erasure correcting and for error correcting. The existence of perfect one factorizations for every
complete graph
with an even number of nodes is a 35 years long conjecture in graph theory. The construction of BCodes of arbitrary odd length will provide an affirmative answer to the conjecture.
Journal:
IEEE Transactions on Information Theory  TIT
, vol. 45, no. 6, pp. 18171836, 1999
DOI:
10.1109/18.782102
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Citation Context
(47)
...Examples of MDS array codes are EVENODD [1], [2], Bcode [
3
], Xcode [4], RDP [5], and STARcode [6]...
...and the corresponding permutation of v is [2,
3
, 0, 1]. In addition, we define Xv as the set of integers x in [0, 2 m − 1] such that the inner product between their binary representation and v satisfies x · v = 0, e.g., X (1,0) = {0, 1}. The construction of the two parity columns is as follows: The first parity column is simply the row sums...
...and the permutation f l v is [2, 0, 1, 5,
3
, 4, 8, 6, 7]. For x ∈ [0, r m − 1], we define the zigzag set Zx in parity node l as the elements ai,j such that their coordinates satisfy f l vj (i) = x...
Itzhak Tamo
,
et al.
MDS Array Codes with Optimal Rebuilding
...Xu, et al. [
12
] found the equivalence between the con...
Chao Jin
,
et al.
Extending and analysis of XCode
...RAID6 Code ED2 Code MDS Bcode [
20
] YES YES Xcode [8] YES YES BCP code [21] YES YES ZZS code [22] YES YES WEAVER codes [11] YES NO LSI code [23] YES NO EVENODD [9] NO YES RDP [10] NO YES...
Jianqiang Luo
,
et al.
SCAN: An Efficient Decoding Algorithm for RAID6 Codes
...Given a data item to be encoded with an erasure code (n,k), the algorithm produces n � k fragments; m fragments are necessary and sufficient to recover the original data item, where k � m � n. When m ¼ k, the erasure code algorithm is said to be optimal [
19
]...
Andrea Bondavalli
,
et al.
The HIDENETS Holistic Approach for the Analysis of Large Critical Mobi...
...According to the structure and distribution of different parities, MDS codes can be categorized into horizontal codes [30], [5], [3], [8], [4], [28], [27] and vertical codes [6], [
41
], [42], [23]...
...3) Vertical Parity (VP): Vertical parity normally appears in vertical codes, such as in BCode [
41
] and PCode [23]...
...Researchers have presented many RAID6 implementations based on various erasure coding technologies, including ReedSolomon code [30], Cauchy ReedSolomon code [5], EVENODD code [3], RDP code [8], BlaumRoth code [4], Liberation code [28], Liber8tion code [27], Cyclic code [6], BCode [
41
], XCode [42], and PCode [23]...
Chentao Wu
,
et al.
HDP code: A HorizontalDiagonal Parity Code to Optimize I/O load balan...
References
(14)
XCode: MDS Array Codes with Optimal Encoding
(
Citations: 112
)
Lihao Xu
,
Jehoshua Bruck
Journal:
IEEE Transactions on Information Theory  TIT
, vol. 45, no. 1, pp. 272276, 1999
EVENODD: An Efficient Scheme for Tolerating Double Disk Failures in RAID Architectures
(
Citations: 197
)
Mario Blaum
,
Jim Brady
,
Jehoshua Bruck
,
Jai Menon
Journal:
IEEE Transactions on Computers  TC
, vol. 44, no. 2, pp. 192202, 1995
On Lowest Density MDS Codes
(
Citations: 48
)
Mario Blaum
,
Ron M. Roth
Journal:
IEEE Transactions on Information Theory  TIT
, vol. 45, no. 1, pp. 4659, 1999
A survey of array error control codes
(
Citations: 32
)
Patrick Guy Farrell
Journal:
European Transactions on Telecommunications  EUR TRANS TELECOMMUN
, vol. 3, no. 5, pp. 441454, 1992
Hamilton Graphs and Hamilton Circuits
(
Citations: 12
)
A. Kotzig
Published in 1963.
Sort by:
Citations
(65)
MDS Array Codes with Optimal Rebuilding
(
Citations: 3
)
Itzhak Tamo
,
Zhiying Wang
,
Jehoshua Bruck
Conference:
IEEE International Symposium on Information Theory  ISIT
, vol. abs/1103.3, pp. 12401244, 2011
Extending and analysis of XCode
(
Citations: 1
)
Chao Jin
,
Dan Feng
,
Jingning Liu
Journal:
Journal of Shanghai University (english Edition)
, vol. 15, no. 3, pp. 194200, 2011
SCAN: An Efficient Decoding Algorithm for RAID6 Codes
(
Citations: 1
)
Jianqiang Luo
,
Lihao Xu
Conference:
Network Computing and Applications  NCA
, 2011
The HIDENETS Holistic Approach for the Analysis of Large Critical Mobile Systems
Andrea Bondavalli
,
Ossama Hamouda
,
Mohamed Kaâniche
,
Paolo Lollini
,
István Majzik
,
HansPeter Schwefel
Journal:
IEEE Transactions on Mobile Computing  TMC
, vol. 10, no. 6, pp. 783796, 2011
HDP code: A HorizontalDiagonal Parity Code to Optimize I/O load balancing in RAID6
Chentao Wu
,
Xubin He
,
Guanying Wu
,
Shenggang Wan
,
Xiaohua Liu
,
Qiang Cao
,
Changsheng Xie
Conference:
Dependable Systems and Networks  DSN
, pp. 209220, 2011