New array codes for multiple phased burst correction

Blaum, M.; Roth, Ron M.

doi:10.1109/18.179343

Cited by 149 publications

(181 citation statements)

References 15 publications

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“…Notably, this algorithm does not require finite field operations. This extends the algorithms of [3], applicable only for the case of a single symbol error.…”

Section: Decoding and Information Updatesmentioning

confidence: 98%

MDS array codes with independent parity symbols

Blaum

Bruck

Vardy

1996

IEEE Trans. Inform. Theory

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205

113

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-A n e w family of MDS a r r a y codes is presented. T h e code a r r a y s contain p information c o l u m n s a n d r i n d e p e n d e n t p a r i t y columns, w h e r e p is a prime. We give necessary a n d sufficient conditions for our codes to be MDS, a n d t h e n prove t h a t if p belongs to a certain class of p r i m e s t h e s e conditions a r e satisfied u p to r 5 8. We also develop efficient decodi n g procedures for t h e case of t w o a n d t h r e e c o l u m n errors, a n d a n y n u m b e r of c o l u m n erasures. Finally, we present u p p e r a n d lower b o u n d s o n t h e average n u m b e r of p a r i t y b i t s which have to be u p d a t e d in a n MDS code over GF(2"), following a n u p d a t e i n a single information bit. We show t h a t t h e u p p e r b o u n d o b t a i n e d f r o m o u r codes is close to t h e lower b o u n d a n d does n o t depend o n t h e size of t h e code symbols.

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“…Notably, this algorithm does not require finite field operations. This extends the algorithms of [3], applicable only for the case of a single symbol error.…”

Section: Decoding and Information Updatesmentioning

confidence: 98%

MDS array codes with independent parity symbols

Blaum

Bruck

Vardy

1996

IEEE Trans. Inform. Theory

Self Cite

205

113

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“…Let us point out that the construction of this type of codes is valid also over the ring of polynomials modulo M p (x) = 1 + x + · · · + x p−1 , p a prime number, as done with the Blaum-Roth (BR) codes [4]. In that case, O(α) = p, where…”

Section: Pmds and Sdmentioning

confidence: 99%

“…Utilizing the ring modulo M p (x) allows for XOR operations at the encoding and the decoding without look-up tables in a finite field, which is advantageous in erasure decoding [4]. It is well known that M p (x) is irreducible if and only if 2 is primitive in GF(p) [9].…”

Section: Pmds and Sdmentioning

confidence: 99%

“…The figure depicts five failure scenarios in a 4 × 5 array, encoded with a (1; 2) code, where erased elements are shaded in gray. The left scenario may be tolerated by both PMDS and SD codes, since each row is an [5,4,2] MDS code. The second two scenarios are also tolerated by both PMDS and SD codes, because four erasures are co-located in the same column.…”

Section: Introductionmentioning

confidence: 99%

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Partial MDS (PMDS) and Sector-Disk (SD) codes that tolerate the erasure of two random sectors

Blaum

Plank

Schwartz

et al. 2014

2014 IEEE International Symposium on Information Theory

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Abstract-Partial MDS (PMDS) codes are erasure codes combining local (row) correction with global additional correction of entries, while Sector-Disk (SD) codes are erasure codes that address the mixed failure mode of current RAID systems. It has been an open problem to construct general codes that have the PMDS and the SD properties, and previous work has relied on Monte-Carlo searches. In this paper, we present a general construction that addresses the case of any number of failed disks and in addition, two erased sectors. The construction requires a modest field size. This result generalizes previous constructions extending RAID 5 and RAID 6.

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“…I t is shown that for our codes q(C) does not depend on the size of the code symbols. In contrast, we also show that for Reed-Solomon codes, as well as for the MDS codes of Blaum and Roth [3], q(C) increases linearly with the symbol size.…”

Section: Decoding and Information Updatesmentioning

confidence: 61%