Correcting Grain-Errors in Magnetic Media

This paper studies new bounds and code constructions that are applicable to the combinatorial granular channel model previously introduced by Sharov and Roth. We derive new bounds on the maximum cardinality of a grain-error-correcting code and propose constructions of codes that correct grain-errors...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on information theory Vol. 61; no. 5; pp. 2256 - 2272
Main Authors: Gabrys, Ryan, Yaakobi, Eitan, Dolecek, Lara
Format: Journal Article
Language:English
Published: New York IEEE 01.05.2015
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Additives
Channel models
Context
Error correction & detection
Information theory
Magnetic recording
Mathematical models
Media
Upper bound
Vectors
Algebraic-coding theory
coding for storage
group codes
granular media
ISSN:0018-9448, 1557-9654
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract This paper studies new bounds and code constructions that are applicable to the combinatorial granular channel model previously introduced by Sharov and Roth. We derive new bounds on the maximum cardinality of a grain-error-correcting code and propose constructions of codes that correct grain-errors. We demonstrate that a permutation of the classical group codes (e.g., Constantin-Rao codes) can correct a single grain-error. In many cases of interest, our results improve upon the currently best known bounds and constructions. Some of the approaches adopted in the context of grain-errors may have application to related channel models.
AbstractList This paper studies new bounds and code constructions that are applicable to the combinatorial granular channel model previously introduced by Sharov and Roth. We derive new bounds on the maximum cardinality of a grain-error-correcting code and propose constructions of codes that correct grain-errors. We demonstrate that a permutation of the classical group codes (e.g., Constantin-Rao codes) can correct a single grain-error. In many cases of interest, our results improve upon the currently best known bounds and constructions. Some of the approaches adopted in the context of grain-errors may have application to related channel models.
Author Gabrys, Ryan
Yaakobi, Eitan
Dolecek, Lara
Author_xml – sequence: 1
  givenname: Ryan
  surname: Gabrys
  fullname: Gabrys, Ryan
  email: rgabrys@ucla.edu
  organization: Univ. of California at Los Angeles, Los Angeles, CA, USA
– sequence: 2
  givenname: Eitan
  surname: Yaakobi
  fullname: Yaakobi, Eitan
  email: yaakobi@cs.technion.ac.il
  organization: California Inst. of Technol., Pasadena, CA, USA
– sequence: 3
  givenname: Lara
  surname: Dolecek
  fullname: Dolecek, Lara
  email: dolecek@ee.ucla.edu
  organization: Univ. of California at Los Angeles, Los Angeles, CA, USA
BookMark eNp9kM1LAzEQxYNUsK3eBS8LnjxsnWw-NjlKqbXQ4qWeQ5rNlpSa1CQ9-N-b0uLBg6dh4P3mvXkjNPDBW4TuMUwwBvm8XqwnDWA2aShIweEKDTFjbS05owM0BMCilpSKGzRKaVdWynAzRE_TEKM12fltNY_a-XoWY4ipcr5a6a232ZlqZTunb9F1r_fJ3l3mGH28ztbTt3r5Pl9MX5a1aSTONSVCyNZgYixoJoXuZdcTY5hk2pCGmQ73XAOxsKGMbzYgJDGMnvLI1rKOjNHj-e4hhq-jTVntwjH6YqkwbznlXAAuKjirTAwpRdurQ3SfOn4rDOpUiCqFqFMh6lJIQfgfxLissws-l8f3_4EPZ9BZa399WmC05CY_y-ts-Q
CODEN IETTAW
CitedBy_id crossref_primary_10_1109_TCOMM_2017_2662003
crossref_primary_10_1109_TIT_2023_3319088
crossref_primary_10_1109_TIT_2015_2445758
crossref_primary_10_1109_TIT_2017_2738634
crossref_primary_10_1109_TIT_2017_2762676
Cites_doi 10.1109/TIT.2011.2158514
10.1109/TIT.2014.2301811
10.1109/ISIT.2012.6284242
10.1109/ISIT.2012.6284659
10.1017/CBO9780511808968
10.1109/FTCS.1990.89375
10.1016/S0019-9958(79)90329-2
10.1109/20.560144
10.1109/TIT.2013.2257917
10.1109/ISIT.2013.6620314
10.1017/CBO9780511804441
10.1109/TMAG.2008.2010676
10.1016/S0019-9958(80)90082-0
10.1109/TIT.2014.2329008
10.1109/TMAG.2010.2080667
ContentType Journal Article
Copyright Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) May 2015
Copyright_xml – notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) May 2015
DBID 97E
RIA
RIE
AAYXX
CITATION
7SC
7SP
8FD
JQ2
L7M
L~C
L~D
DOI 10.1109/TIT.2015.2409860
DatabaseName IEEE All-Society Periodicals Package (ASPP) 2005–Present
IEEE All-Society Periodicals Package (ASPP) 1998–Present
IEEE/IET Electronic Library
CrossRef
Computer and Information Systems Abstracts
Electronics & Communications Abstracts
Technology Research Database
ProQuest Computer Science Collection
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts – Academic
Computer and Information Systems Abstracts Professional
DatabaseTitle CrossRef
Technology Research Database
Computer and Information Systems Abstracts – Academic
Electronics & Communications Abstracts
ProQuest Computer Science Collection
Computer and Information Systems Abstracts
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts Professional
DatabaseTitleList Technology Research Database
Database_xml – sequence: 1
  dbid: RIE
  name: IEEE/IET Electronic Library
  url: https://ieeexplore.ieee.org/
  sourceTypes: Publisher
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
Computer Science
EISSN 1557-9654
EndPage 2272
ExternalDocumentID 3669037261
10_1109_TIT_2015_2409860
7054540
Genre orig-research
Feature
GrantInformation_xml – fundername: ISEF Foundation
  funderid: 10.13039/100007255
– fundername: SMART Scholarship
– fundername: Division of Computing and Communication Foundations through the NSF
  grantid: CCF-1029030; CCF-1150212
  funderid: 10.13039/100000143
GroupedDBID -~X
.DC
0R~
29I
3EH
4.4
5GY
5VS
6IK
97E
AAJGR
AARMG
AASAJ
AAWTH
ABAZT
ABFSI
ABQJQ
ABVLG
ACGFO
ACGFS
ACGOD
ACIWK
AENEX
AETEA
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
F5P
HZ~
H~9
IAAWW
IBMZZ
ICLAB
IDIHD
IFIPE
IFJZH
IPLJI
JAVBF
LAI
M43
MS~
O9-
OCL
P2P
PQQKQ
RIA
RIE
RNS
RXW
TAE
TN5
VH1
VJK
AAYXX
CITATION
7SC
7SP
8FD
JQ2
L7M
L~C
L~D
ID FETCH-LOGICAL-c291t-438897c13ce0a598af9df3cc595ac325cd1f6a03e0b456bb0893c54014597e5d3
IEDL.DBID RIE
ISICitedReferencesCount 6
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000353515700004&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0018-9448
IngestDate Sun Sep 07 03:21:02 EDT 2025
Sat Nov 29 03:31:34 EST 2025
Tue Nov 18 22:26:23 EST 2025
Tue Aug 26 16:50:03 EDT 2025
IsPeerReviewed true
IsScholarly true
Issue 5
Keywords Algebraic-coding theory
coding for storage
group codes
granular media
Language English
License https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c291t-438897c13ce0a598af9df3cc595ac325cd1f6a03e0b456bb0893c54014597e5d3
Notes SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
PQID 1676466801
PQPubID 36024
PageCount 17
ParticipantIDs proquest_journals_1676466801
crossref_citationtrail_10_1109_TIT_2015_2409860
crossref_primary_10_1109_TIT_2015_2409860
ieee_primary_7054540
PublicationCentury 2000
PublicationDate 2015-May
2015-5-00
20150501
PublicationDateYYYYMMDD 2015-05-01
PublicationDate_xml – month: 05
  year: 2015
  text: 2015-May
PublicationDecade 2010
PublicationPlace New York
PublicationPlace_xml – name: New York
PublicationTitle IEEE transactions on information theory
PublicationTitleAbbrev TIT
PublicationYear 2015
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 ref13
ref12
ref15
ref11
ref10
ref2
ref1
rotman (ref14) 1994
ref19
west (ref17) 2001; 2
ref18
ref8
gould (ref5) 2014
ref7
ref9
ref4
ref3
ref6
(ref16) 2011
References_xml – ident: ref10
  doi: 10.1109/TIT.2011.2158514
– year: 2014
  ident: ref5
  publication-title: Tables of Combinatorial Identities
– year: 2011
  ident: ref16
  publication-title: MAGMA computational algebra system
– ident: ref15
  doi: 10.1109/TIT.2014.2301811
– ident: ref3
  doi: 10.1109/ISIT.2012.6284242
– ident: ref6
  doi: 10.1109/ISIT.2012.6284659
– ident: ref13
  doi: 10.1017/CBO9780511808968
– volume: 2
  year: 2001
  ident: ref17
  publication-title: Introduction to Graph Theory
– ident: ref12
  doi: 10.1109/FTCS.1990.89375
– ident: ref2
  doi: 10.1016/S0019-9958(79)90329-2
– ident: ref18
  doi: 10.1109/20.560144
– year: 1994
  ident: ref14
  publication-title: An Introduction to the Theory of Groups
– ident: ref9
  doi: 10.1109/TIT.2013.2257917
– ident: ref4
  doi: 10.1109/ISIT.2013.6620314
– ident: ref1
  doi: 10.1017/CBO9780511804441
– ident: ref19
  doi: 10.1109/TMAG.2008.2010676
– ident: ref11
  doi: 10.1016/S0019-9958(80)90082-0
– ident: ref8
  doi: 10.1109/TIT.2014.2329008
– ident: ref7
  doi: 10.1109/TMAG.2010.2080667
SSID ssj0014512
Score 2.190345
Snippet This paper studies new bounds and code constructions that are applicable to the combinatorial granular channel model previously introduced by Sharov and Roth....
SourceID proquest
crossref
ieee
SourceType Aggregation Database
Enrichment Source
Index Database
Publisher
StartPage 2256
SubjectTerms Additives
Channel models
Context
Error correction & detection
Information theory
Magnetic recording
Mathematical models
Media
Upper bound
Vectors
Title Correcting Grain-Errors in Magnetic Media
URI https://ieeexplore.ieee.org/document/7054540
https://www.proquest.com/docview/1676466801
Volume 61
WOSCitedRecordID wos000353515700004&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVIEE
  databaseName: IEEE/IET Electronic Library
  customDbUrl:
  eissn: 1557-9654
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0014512
  issn: 0018-9448
  databaseCode: RIE
  dateStart: 19630101
  isFulltext: true
  titleUrlDefault: https://ieeexplore.ieee.org/
  providerName: IEEE
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3PS8MwFH7M4UEPTjfF6ZQevAzMljZNkxxlbCro8DBlt5KlqQykk27z7zdJfygogrcekhK-5PW91_fyfQBXocZaRwSjRAmMwoQRxDVPkTFKnQQL49QcffHLA5tO-XwunhpwXd-F0Vq75jM9sI-ulp-s1Nb-KhsyE1-YCGMHdhhjxV2tumIQUr9gBveNAZucoypJYjGc3c9sDxcdGO8luCOj_HJBTlPlx4fYeZdJ63_rOoSDMor0boptP4KGztrQqhQavNJg27D_jW6wA_2RleJQttHZu7XSEGic56t87S0z71G-ZvY-o2crN_IYnifj2egOlVIJSAXC36CQcC6Y8onSWFLBZSqSlChFBZWKBFQlfhpJTDRemIhpscAmTFFmyQY2wTRNyAk0s1WmT8Gj0iatqeWxs0W-UPCUiUjTQJrkR3LShWGFXqxKHnErZ_EWu3wCi9jgHVu84xLvLvTrGe8Fh8YfYzsW33pcCW0XetUGxaWRrWM_YlEYRcbHnv0-6xz27LuL_sQeNDf5Vl_ArvrYLNf5pTs_n9w4vr4
linkProvider IEEE
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3PT8IwFH5BNFEPoqARRd3BC4mDbl239mgICBGIh2m4LV3XGRIzzAD_ftv90kRj4m2HNmu-9u29t_f6fQC3jkRSuhiZkWDIdCIPm1TS2FRGKSM7VE4toy9-mXrzOV0s2FMN7qq7MFLKrPlM9vRjVsuPVmKrf5X1PRVfqAhjB3aJ49hWflurqhk4xMq5wS1lwirrKIuSiPX9ia-7uEhP-S9GMzrKLyeUqar8-BRn_mXU-N_KjuGoiCON-3zjT6AmkyY0So0GozDZJhx-IxxsQXegxTiEbnU2HrQ4hDlM01W6NpaJMeOvib7RaOjaDT-F59HQH4zNQizBFDazNqaDKWWesLCQiBNGecyiGAtBGOEC20REVuxyhCUKVcwUhkgFKkItWcHGPEkifAb1ZJXIczAI12lrrJnsdJnPYTT2mCuJzVX6wyluQ79ELxAFk7gWtHgLsowCsUDhHWi8gwLvNnSrGe85i8YfY1sa32pcAW0bOuUGBYWZrQPL9VzHdZWXvfh91g3sj_3ZNJhO5o-XcKDfk3crdqC-SbfyCvbEx2a5Tq-zs_QJ-LLCBQ
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=Correcting+Grain-Errors+in+Magnetic+Media&rft.jtitle=IEEE+transactions+on+information+theory&rft.au=Gabrys%2C+R&rft.au=Yaakobi%2C+E&rft.au=Dolecek%2C+L&rft.date=2015-05-01&rft.pub=The+Institute+of+Electrical+and+Electronics+Engineers%2C+Inc.+%28IEEE%29&rft.issn=0018-9448&rft.eissn=1557-9654&rft.volume=61&rft.issue=5&rft.spage=2256&rft_id=info:doi/10.1109%2FTIT.2015.2409860&rft.externalDBID=NO_FULL_TEXT&rft.externalDocID=3669037261
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0018-9448&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0018-9448&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0018-9448&client=summon