Construction of Partial MDS and Sector-Disk Codes with Two Global Parity Symbols

Mario Blaum; James S. Plank; Moshe Schwartz; Eitan Yaakobi

doi:10.1109/TIT.2016.2536720

Construction of Partial MDS and Sector-Disk Codes with Two Global Parity Symbols

Mario Blaum, James S. Plank, Moshe Schwartz, Eitan Yaakobi

Department of Electrical & Computer Engineering

Research output: Contribution to journal › Article › peer-review

46 Scopus citations

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 redundant arrays of independent disk (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.

Original language	English
Article number	7422796
Pages (from-to)	2673-2681
Number of pages	9
Journal	IEEE Transactions on Information Theory
Volume	62
Issue number	5
DOIs	https://doi.org/10.1109/TIT.2016.2536720
State	Published - 1 May 2016

Keywords

Partial MDS codes
locally recoverable codes
maximally recoverable codes
sector-disk codes

ASJC Scopus subject areas

Information Systems
Computer Science Applications
Library and Information Sciences

Access to Document

10.1109/TIT.2016.2536720

Cite this

@article{aa02fcbc79404c038acedab7678c5283,

title = "Construction of Partial MDS and Sector-Disk Codes with Two Global Parity Symbols",

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 redundant arrays of independent disk (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.",

keywords = "Partial MDS codes, locally recoverable codes, maximally recoverable codes, sector-disk codes",

author = "Mario Blaum and Plank, {James S.} and Moshe Schwartz and Eitan Yaakobi",

note = "Funding Information: This work was supported in part by the National Science Foundation under Grant CSR-1016636 and in part by the IBM Faculty Award. Publisher Copyright: {\textcopyright} 2016 IEEE.",

year = "2016",

month = may,

day = "1",

doi = "10.1109/TIT.2016.2536720",

language = "English",

volume = "62",

pages = "2673--2681",

journal = "IEEE Transactions on Information Theory",

issn = "0018-9448",

publisher = "Institute of Electrical and Electronics Engineers",

number = "5",

}

TY - JOUR

T1 - Construction of Partial MDS and Sector-Disk Codes with Two Global Parity Symbols

AU - Blaum, Mario

AU - Plank, James S.

AU - Schwartz, Moshe

AU - Yaakobi, Eitan

PY - 2016/5/1

Y1 - 2016/5/1

N2 - 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 redundant arrays of independent disk (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.

AB - 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 redundant arrays of independent disk (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.

KW - Partial MDS codes

KW - locally recoverable codes

KW - maximally recoverable codes

KW - sector-disk codes

UR - http://www.scopus.com/inward/record.url?scp=84964869981&partnerID=8YFLogxK

U2 - 10.1109/TIT.2016.2536720

DO - 10.1109/TIT.2016.2536720

M3 - Article

AN - SCOPUS:84964869981

SN - 0018-9448

VL - 62

SP - 2673

EP - 2681

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 5

M1 - 7422796

ER -

Construction of Partial MDS and Sector-Disk Codes with Two Global Parity Symbols

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this