An Encoding Algorithm of Triply Extended Reed-Solomon Codes With Asymptotically Optimal Complexities

In this paper, we devise a fast encoding algorithm for triply extended Reed-Solomon codes. The proposed approach requires approximately two XORs per bit, which improves the prior result of three XORs per bit established by certain maximum distance separable (MDS) array codes. We also prove that, for...

Full description

Saved in:
Bibliographic Details
Published inIEEE transactions on communications Vol. 66; no. 8; pp. 3235 - 3244
Main Author Lin, Sian-Jheng
Format Journal Article
LanguageEnglish
Published New York IEEE 01.08.2018
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Algorithm design and analysis
algorithm design and anlaysis
Algorithms
Approximation algorithms
Coding
Complexity theory
Computer simulation
Decoding
Encoding
Generators
Lower bounds
parallel processing
Reed-Solomon codes
Scheduling
Scheduling algorithms
Online AccessGet full text
ISSN0090-6778
1558-0857
DOI10.1109/TCOMM.2017.2737441

Cover

Abstract In this paper, we devise a fast encoding algorithm for triply extended Reed-Solomon codes. The proposed approach requires approximately two XORs per bit, which improves the prior result of three XORs per bit established by certain maximum distance separable (MDS) array codes. We also prove that, for MDS codes with two and three parities, the scheduling algorithms require at least two XORs per bit. To the best of our knowledge, this is the first provable scheduling algorithm for the triple-parity MDS codes to approach the theoretical lower bounds. The implementation with SIMD instructions is provided. The simulations show that the proposed approach is competitive, as compared with other cutting edge implementations.
AbstractList In this paper, we devise a fast encoding algorithm for triply extended Reed-Solomon codes. The proposed approach requires approximately two XORs per bit, which improves the prior result of three XORs per bit established by certain maximum distance separable (MDS) array codes. We also prove that, for MDS codes with two and three parities, the scheduling algorithms require at least two XORs per bit. To the best of our knowledge, this is the first provable scheduling algorithm for the triple-parity MDS codes to approach the theoretical lower bounds. The implementation with SIMD instructions is provided. The simulations show that the proposed approach is competitive, as compared with other cutting edge implementations.
Author Sian-Jheng Lin
Author_xml – sequence: 1
  givenname: Sian-Jheng
  orcidid: 0000-0002-6309-2876
  surname: Lin
  fullname: Lin, Sian-Jheng
BookMark eNp9kctOAjEUQBuDiYD-gG6auB7sY4bpLAnBRwIhUYzLSZneYslMO7Ylgb93EOLChatuzrk393SAetZZQOiWkhGlpHhYTZeLxYgRmo9YzvM0pReoT7NMJERkeQ_1CSlIMs5zcYUGIWwJISnhvI_UxOKZrZwydoMn9cZ5Ez8b7DReedPWBzzbR7AKFH4FUMmbq13jLJ46BQF_dCyehEPTRhdNJeuOX7bRNLLuiKatYW-igXCNLrWsA9yc3yF6f5ytps_JfPn0Mp3Mk4oVWUzGUulUAghZMao0kEKsBRNUQLFWmog1l1JqypgaVyrjknHFlM5yrrRKlSB8iO5Pc1vvvnYQYrl1O2-7lSWjNKecFiTtKHGiKu9C8KDLykQZjbPRS1OXlJTHpuVP0_LYtDw37VT2R219d60__C_dnSQDAL-C6H4gY2P-DfudhqM
CODEN IECMBT
CitedBy_id crossref_primary_10_1109_TIT_2023_3300919
crossref_primary_10_1109_TIT_2024_3353111
crossref_primary_10_31857_S003384942309019X
crossref_primary_10_1109_TC_2023_3262922
crossref_primary_10_1134_S1064226919080138
crossref_primary_10_1134_S1064226922080137
crossref_primary_10_1109_TC_2019_2963827
crossref_primary_10_1109_TC_2021_3060701
crossref_primary_10_1109_TC_2024_3387069
crossref_primary_10_1134_S106422692309019X
Cites_doi 10.1007/s00200-011-0160-6
10.1145/50202.50214
10.1109/FOCS.2014.41
10.1109/DSN.2015.19
10.1109/TC.2007.70830
10.1109/18.782102
10.1109/18.179343
10.1109/PIMRC.2016.7794681
10.1109/ITW.2007.4313077
10.1109/18.746809
10.1145/1542275.1542326
10.1137/0108018
10.1145/2421648.2421655
10.1109/ISIT.2006.261569
10.1109/TIT.2016.2536720
10.1145/777412.777458
10.1109/TC.2005.150
10.1109/TSP.2012.2192435
10.1145/339331.339345
10.1145/2700308
10.1145/502059.502053
10.1109/12.364531
10.1109/ISIT.2006.261570
10.1109/18.746771
10.1109/TIT.2011.2159049
ContentType Journal Article
Copyright Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2018
Copyright_xml – notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2018
DBID 97E
RIA
RIE
AAYXX
CITATION
7SP
8FD
L7M
DOI 10.1109/TCOMM.2017.2737441
DatabaseName IEEE All-Society Periodicals Package (ASPP) 2005–Present
IEEE All-Society Periodicals Package (ASPP) 1998–Present
IEEE Electronic Library (IEL)
CrossRef
Electronics & Communications Abstracts
Technology Research Database
Advanced Technologies Database with Aerospace
DatabaseTitle CrossRef
Technology Research Database
Advanced Technologies Database with Aerospace
Electronics & Communications Abstracts
DatabaseTitleList Technology Research Database
Database_xml – sequence: 1
  dbid: RIE
  name: IEEE Electronic Library (IEL)
  url: https://proxy.k.utb.cz/login?url=https://ieeexplore.ieee.org/
  sourceTypes: Publisher
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
EISSN 1558-0857
EndPage 3244
ExternalDocumentID 10_1109_TCOMM_2017_2737441
8004526
Genre orig-research
GrantInformation_xml – fundername: CAS Pioneer Hundred Talents Program
  grantid: KJ2100060007
– fundername: Fundamental Research Funds for the Central Universities
  grantid: WK2100000004
GroupedDBID -~X
.DC
0R~
29I
3EH
4.4
5GY
5VS
6IK
85S
97E
AAJGR
AARMG
AASAJ
AAWTH
ABAZT
ABFSI
ABQJQ
ABVLG
ACGFO
ACGFS
ACIWK
ACKIV
ACNCT
AENEX
AETIX
AGQYO
AGSQL
AHBIQ
AI.
AIBXA
AKJIK
AKQYR
ALLEH
ALMA_UNASSIGNED_HOLDINGS
ASUFR
ATWAV
BEFXN
BFFAM
BGNUA
BKEBE
BPEOZ
CS3
DU5
E.L
EBS
EJD
HZ~
H~9
IAAWW
IBMZZ
ICLAB
IES
IFIPE
IFJZH
IPLJI
JAVBF
LAI
M43
MS~
O9-
OCL
P2P
RIA
RIE
RNS
TAE
TN5
VH1
ZCA
ZCG
AAYXX
CITATION
7SP
8FD
L7M
RIG
ID FETCH-LOGICAL-c295t-6adf4aee8ac21dfe098b82818e9bdf08b3aaaf122d6cd53a23d2df573dfd4d803
IEDL.DBID RIE
ISSN 0090-6778
IngestDate Mon Jun 30 10:19:17 EDT 2025
Wed Oct 01 00:48:24 EDT 2025
Thu Apr 24 22:57:18 EDT 2025
Wed Aug 27 06:01:21 EDT 2025
IsPeerReviewed true
IsScholarly true
Issue 8
Language English
License https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c295t-6adf4aee8ac21dfe098b82818e9bdf08b3aaaf122d6cd53a23d2df573dfd4d803
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ORCID 0000-0002-6309-2876
PQID 2117131904
PQPubID 85472
PageCount 10
ParticipantIDs crossref_citationtrail_10_1109_TCOMM_2017_2737441
proquest_journals_2117131904
ieee_primary_8004526
crossref_primary_10_1109_TCOMM_2017_2737441
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate 2018-08-01
PublicationDateYYYYMMDD 2018-08-01
PublicationDate_xml – month: 08
  year: 2018
  text: 2018-08-01
  day: 01
PublicationDecade 2010
PublicationPlace New York
PublicationPlace_xml – name: New York
PublicationTitle IEEE transactions on communications
PublicationTitleAbbrev TCOMM
PublicationYear 2018
Publisher IEEE
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher_xml – name: IEEE
– name: The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
References ref35
ref13
ref34
ref36
ref14
ref31
plank (ref6) 0
farnum (ref9) 2016
ref32
ref10
desai (ref8) 2016
ref2
ref1
plank (ref25) 2011
ref38
ref16
ref19
ref18
bordewijk (ref37) 1956; 6
blömer (ref12) 1995
macwilliams (ref33) 1997
ref24
ref23
plank (ref39) 2013
ref26
corbett (ref17) 2004
ref20
plank (ref42) 2014
position (ref11) 2009
ref21
huang (ref4) 2012
ref28
(ref30) 2016
wang (ref22) 2012; 8
fedorenko (ref27) 2003
ref29
ref7
ref3
ref5
center (ref41) 2016
ref40
blaum (ref15) 2001
References_xml – ident: ref34
  doi: 10.1007/s00200-011-0160-6
– start-page: 15
  year: 2012
  ident: ref4
  article-title: Erasure coding in Windows Azure storage
  publication-title: Proc of USENIX Annual Technical Conf (USENIX)
– start-page: 1
  year: 2004
  ident: ref17
  article-title: Row-diagonal parity for double disk failure correction
  publication-title: Proc 3rd USENIX Symp File Storage Technol
– ident: ref10
  doi: 10.1145/50202.50214
– year: 2016
  ident: ref8
  publication-title: Erasure Code Support-Swift 2 9 1 dev229 Documentation
– ident: ref29
  doi: 10.1109/FOCS.2014.41
– ident: ref35
  doi: 10.1109/DSN.2015.19
– year: 2014
  ident: ref42
  article-title: Jerasure: A library in C facilitating erasure coding for storage applications-Version 2.0
– ident: ref21
  doi: 10.1109/TC.2007.70830
– year: 2016
  ident: ref30
  publication-title: Facebook's Realtime Distributed FS based on Apache Hadoop 0 20-append
– ident: ref36
  doi: 10.1109/18.782102
– volume: 6
  start-page: 1
  year: 1956
  ident: ref37
  article-title: Inter-reciprocity applied to electrical networks
  publication-title: Appl Sci Res sec A
– start-page: 503
  year: 2011
  ident: ref25
  article-title: XOR's, lower bounds and MDS codes for storage
  publication-title: Proc IEEE Inf Theory Workshop (ITW)
– year: 0
  ident: ref6
  article-title: Tutorial: Erasure coding for storage applications
– ident: ref24
  doi: 10.1109/18.179343
– ident: ref31
  doi: 10.1109/PIMRC.2016.7794681
– ident: ref26
  doi: 10.1109/ITW.2007.4313077
– ident: ref16
  doi: 10.1109/18.746809
– ident: ref20
  doi: 10.1145/1542275.1542326
– ident: ref7
  doi: 10.1137/0108018
– ident: ref23
  doi: 10.1145/2421648.2421655
– year: 1997
  ident: ref33
  publication-title: The Theory of Error-Correcting Codes
– ident: ref18
  doi: 10.1109/ISIT.2006.261569
– ident: ref5
  doi: 10.1109/TIT.2016.2536720
– ident: ref38
  doi: 10.1145/777412.777458
– ident: ref32
  doi: 10.1109/TC.2005.150
– ident: ref28
  doi: 10.1109/TSP.2012.2192435
– ident: ref1
  doi: 10.1145/339331.339345
– ident: ref40
  doi: 10.1145/2700308
– year: 2016
  ident: ref41
  publication-title: Intel(R) Intelligent Storage Acceleration Library
– volume: 8
  start-page: 1731
  year: 2012
  ident: ref22
  article-title: Triple-star: A coding scheme with optimal encoding complexity for tolerating triple disk failures in RAID
  publication-title: Int J Innov Comput Inf Control
– ident: ref2
  doi: 10.1145/502059.502053
– ident: ref14
  doi: 10.1109/12.364531
– year: 2016
  ident: ref9
  publication-title: Erasure Code-CEPH Documentation
– start-page: 1
  year: 2013
  ident: ref39
  article-title: Screaming fast Galois field arithmetic using Intel SIMD extensions
  publication-title: Proc 11th Conf File Storage Syst
– year: 1995
  ident: ref12
  article-title: An XOR-based erasure-resilient coding scheme
– ident: ref19
  doi: 10.1109/ISIT.2006.261570
– year: 2009
  ident: ref11
  publication-title: Common RAID Disk Data Format Specification Version 2 0
– start-page: 187
  year: 2001
  ident: ref15
  publication-title: The EVENODD Code and its Generalization
– ident: ref13
  doi: 10.1109/18.746771
– start-page: 108
  year: 2003
  ident: ref27
  article-title: On computing the fast Fourier transform over finite fields
  publication-title: Proc V Int Workshop Algebr Combin Coding Theory
– ident: ref3
  doi: 10.1109/TIT.2011.2159049
SSID ssj0004033
Score 2.342976
Snippet In this paper, we devise a fast encoding algorithm for triply extended Reed-Solomon codes. The proposed approach requires approximately two XORs per bit, which...
SourceID proquest
crossref
ieee
SourceType Aggregation Database
Enrichment Source
Index Database
Publisher
StartPage 3235
SubjectTerms Algorithm design and analysis
algorithm design and anlaysis
Algorithms
Approximation algorithms
Coding
Complexity theory
Computer simulation
Decoding
Encoding
Generators
Lower bounds
parallel processing
Reed-Solomon codes
Scheduling
Scheduling algorithms
Title An Encoding Algorithm of Triply Extended Reed-Solomon Codes With Asymptotically Optimal Complexities
URI https://ieeexplore.ieee.org/document/8004526
https://www.proquest.com/docview/2117131904
Volume 66
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVIEE
  databaseName: IEEE Electronic Library (IEL)
  customDbUrl:
  eissn: 1558-0857
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0004033
  issn: 0090-6778
  databaseCode: RIE
  dateStart: 19720101
  isFulltext: true
  titleUrlDefault: https://ieeexplore.ieee.org/
  providerName: IEEE
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV07b9swED4kmZKhbR5F3aYBh2ytHIqkKGo0DAdBATdA6qDZhOOrLWpLQSwP6a8vScvuE0U3DUeJwHe8B3X3HcB55Qr0ZVVmmFPMBKcuU8gxC64SmdWMc4yNwtP38upWvLsr7nbg7bYXxjmXis_cMD6mf_m2Nat4VXahEgG43IXdUsl1r9aPHkjKe8bJWM5eqk2DDK0uZuPr6TRWcZXD4KxLIfJfnFCaqvKHKU7-5fIpTDc7W5eVfB2uOj00334jbfzfrT-DJ32gSUZrzTiEHdccwcFP9IPHYEcNmTSmje6LjOaf2ocv3ecFaT2ZBVMyfyST_oac3AQfl30IdjIoLRm31i3JxyBLRsvHxX3XpvvwIH8d7M8ifDQamUi0GclaT-D2cjIbX2X91IXMsKroMonWC3ROoWG59Y5WSqvIGeUqbT1VmiOizxmz0tiCI-OWWV-U3HorrKL8Oew1beNeANFCGiORcu0KwRAr5rhFHl4mtReeDSDfwFCbnpI8TsaY1yk1oVWdoKsjdHUP3QDebNfcrwk5_il9HLHYSvYwDOB0g3bdn9llHVLhkLGHAEm8_PuqV7DPYvNDHAcjT2Gve1i51yEk6fRZ0sXvHrnexw
linkProvider IEEE
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV3Pb9MwFH4a4wA7MGCglQ3wgRukc2wncY5V1anAsknQid2i59geiDaZ1vQw_npsJy0wJsQth-fY0vfyfjjvfQ_gTW4StFmeRRhTjASnJpLIMXKuEplWjHP0jcLFaTo9Fx8ukosteLfphTHGhOIzM_SP4V--bqqVvyo7koEAPL0H9xMhRNJ1a_3qgqS855z0Be2ZXLfI0PxoNj4rCl_HlQ2du86EiP9wQ2Guyl_GOHiY410o1mfrCku-D1etGlY_btE2_u_hH8OjPtQko043nsCWqZ_Czm8EhHugRzWZ1FXjHRgZzS-b62_t1wVpLJk5YzK_IZP-jpx8cl4u-uwspVNbMm60WZIvTpaMljeLq7YJN-JO_sxZoIXb1JsZT7Xp6VqfwfnxZDaeRv3chahiedJGKWor0BiJFYu1NTSXSnrWKJMrbalUHBFtzJhOK51wZFwzbZOMa6uFlpQ_h-26qc0-ECXSqkqRcmUSwRBzZrhG7l6WKissG0C8hqGselJyPxtjXobkhOZlgK700JU9dAN4u1lz1VFy_FN6z2OxkexhGMDhGu2y_2qXpUuGXc7uQiTx4u5Vr-HBdFaclCfvTz8ewEO3j-yKAQ9hu71emZcuQGnVq6CXPwHvN-IZ
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=An+Encoding+Algorithm+of+Triply+Extended+Reed%E2%80%93Solomon+Codes+With+Asymptotically+Optimal+Complexities&rft.jtitle=IEEE+transactions+on+communications&rft.au=Lin%2C+Sian-Jheng&rft.date=2018-08-01&rft.issn=0090-6778&rft.eissn=1558-0857&rft.volume=66&rft.issue=8&rft.spage=3235&rft.epage=3244&rft_id=info:doi/10.1109%2FTCOMM.2017.2737441&rft.externalDBID=n%2Fa&rft.externalDocID=10_1109_TCOMM_2017_2737441
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0090-6778&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0090-6778&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0090-6778&client=summon