A Homomorphism Transform Based Analysis of Sparse Random Linear Network Coding Over Erasure Channels

In this letter, we provide a method for deriving the first exact expression for the decoding success probability of sparse random linear network coding over erasure channels. The key idea of the proposed method is to transform the characterization of the full rank probability of a sparse random matr...

Full description

Saved in:
Bibliographic Details
Published in:IEEE communications letters Vol. 26; no. 9; pp. 2009 - 2013
Main Authors: Chen, Wenlin, Lu, Fang, Dong, Yan
Format: Journal Article
Language:English
Published: New York IEEE 01.09.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Additives
Channels
Coding
Decoding
Encoding
Fields (mathematics)
full rank probability
Homomorphisms
Receivers
Reliability
Sparse matrices
Sparse random linear network coding
Transforms
ISSN:1089-7798, 1558-2558
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract In this letter, we provide a method for deriving the first exact expression for the decoding success probability of sparse random linear network coding over erasure channels. The key idea of the proposed method is to transform the characterization of the full rank probability of a sparse random matrix into the characterization of the homomorphism transform of the sparse distribution and to obtain a closed-form exact expression for the homomorphism transform of the sparse distribution. The former is solved by employing Möbius inversion theorem and the property of the homomorphism transform, and the latter is solved by employing the feature of the sparse distribution and the property of the nontrivial character of a finite field.
AbstractList In this letter, we provide a method for deriving the first exact expression for the decoding success probability of sparse random linear network coding over erasure channels. The key idea of the proposed method is to transform the characterization of the full rank probability of a sparse random matrix into the characterization of the homomorphism transform of the sparse distribution and to obtain a closed-form exact expression for the homomorphism transform of the sparse distribution. The former is solved by employing Möbius inversion theorem and the property of the homomorphism transform, and the latter is solved by employing the feature of the sparse distribution and the property of the nontrivial character of a finite field.
Author Chen, Wenlin
Dong, Yan
Lu, Fang
Author_xml – sequence: 1
  givenname: Wenlin
  orcidid: 0000-0001-5766-4551
  surname: Chen
  fullname: Chen, Wenlin
  email: wenlinchen@hust.edu.cn
  organization: School of Electronic Information and Communications, Huazhong University of Science and Technology, Wuhan, China
– sequence: 2
  givenname: Fang
  orcidid: 0000-0002-9491-4895
  surname: Lu
  fullname: Lu, Fang
  email: lufang@hust.edu.cn
  organization: School of Electronic Information and Communications, Huazhong University of Science and Technology, Wuhan, China
– sequence: 3
  givenname: Yan
  orcidid: 0000-0002-9512-6903
  surname: Dong
  fullname: Dong, Yan
  email: dongyan@hust.edu.cn
  organization: School of Electronic Information and Communications, Huazhong University of Science and Technology, Wuhan, China
BookMark eNo9kFFLwzAUhYNMcE7_gL4EfO5M0qZNHmeZTugc6HwOaXPrOtekJpuyf2_nhly45z6cc-F8l2hgnQWEbigZU0rkfZEv5vMxI4yNYypoxtgZGlLORcT6NehvImSUZVJcoMsQ1oQQwTgdIjPBM9f247tVE1q89NqG2vkWP-gABk-s3uxDE7Cr8VunfQD8qq1xLS4aC9rjF9j-OP-Jc2ca-4EX3-Dx1Ouw84DzlbYWNuEKndd6E-D6pCP0_jhd5rOoWDw955MiqliSbiOotM5YVZc81qIXSrSUxoAoK1qC1HVsSJ3yUqQkTkXNYwGcJaJKMsooFSYeobvj3867rx2ErVq7ne8bBMV6D-FJJtLexY6uyrsQPNSq802r_V5Rog401R9NdaCpTjT70O0x1ADAf0BmksWExb_YfXNV
CODEN ICLEF6
Cites_doi 10.1109/TIT.2008.926449
10.1017/CBO9780511987045
10.1109/LCOMM.2020.2965928
10.1109/TVT.2018.2790436
10.1109/LCOMM.2020.3041845
10.1109/LCOMM.2019.2896626
10.1090/gsm/180
10.1016/s0924-6509(08)x7030-8
10.1109/TCOMM.2017.2657621
10.1016/0012-365X(90)90322-9
ContentType Journal Article
Copyright Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2022
Copyright_xml – notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2022
DBID 97E
RIA
RIE
AAYXX
CITATION
7SP
8FD
L7M
DOI 10.1109/LCOMM.2022.3181722
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://ieeexplore.ieee.org/
  sourceTypes: Publisher
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
EISSN 1558-2558
EndPage 2013
ExternalDocumentID 10_1109_LCOMM_2022_3181722
9792302
Genre orig-research
GrantInformation_xml – fundername: National Nature Science Foundation of China
  grantid: 91538203
  funderid: 10.13039/501100001809
GroupedDBID -~X
0R~
29I
4.4
5GY
5VS
6IK
97E
AAJGR
AARMG
AASAJ
AAWTH
ABAZT
ABQJQ
ABVLG
ACGFO
ACIWK
AENEX
AETIX
AGQYO
AGSQL
AHBIQ
AI.
AIBXA
AKJIK
AKQYR
ALLEH
ALMA_UNASSIGNED_HOLDINGS
ATWAV
AZLTO
BEFXN
BFFAM
BGNUA
BKEBE
BPEOZ
CS3
DU5
EBS
EJD
HZ~
H~9
IES
IFIPE
IFJZH
IPLJI
JAVBF
LAI
M43
O9-
OCL
P2P
RIA
RIE
RNS
TN5
VH1
AAYXX
CITATION
7SP
8FD
L7M
ID FETCH-LOGICAL-c246t-ecaa72cfb53a8cfb10a99dde8bc1be9af3d0f65b860368f538e5248c4712118d3
IEDL.DBID RIE
ISICitedReferencesCount 0
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000852215600011&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 1089-7798
IngestDate Mon Jun 30 10:14:31 EDT 2025
Sat Nov 29 03:56:09 EST 2025
Wed Aug 27 02:14:25 EDT 2025
IsPeerReviewed true
IsScholarly true
Issue 9
Language English
License https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html
https://doi.org/10.15223/policy-029
https://doi.org/10.15223/policy-037
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c246t-ecaa72cfb53a8cfb10a99dde8bc1be9af3d0f65b860368f538e5248c4712118d3
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ORCID 0000-0002-9512-6903
0000-0001-5766-4551
0000-0002-9491-4895
PQID 2712054786
PQPubID 85419
PageCount 5
ParticipantIDs crossref_primary_10_1109_LCOMM_2022_3181722
ieee_primary_9792302
proquest_journals_2712054786
PublicationCentury 2000
PublicationDate 2022-09-01
PublicationDateYYYYMMDD 2022-09-01
PublicationDate_xml – month: 09
  year: 2022
  text: 2022-09-01
  day: 01
PublicationDecade 2020
PublicationPlace New York
PublicationPlace_xml – name: New York
PublicationTitle IEEE communications letters
PublicationTitleAbbrev LCOMM
PublicationYear 2022
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 ref7
ref12
ref4
ref3
Cameron (ref8) 2014
ref6
ref11
ref5
ref10
Rice (ref9) 1977
ref2
ref1
References_xml – ident: ref6
  doi: 10.1109/TIT.2008.926449
– ident: ref12
  doi: 10.1017/CBO9780511987045
– ident: ref5
  doi: 10.1109/LCOMM.2020.2965928
– ident: ref2
  doi: 10.1109/TVT.2018.2790436
– volume-title: Notes on Weight Distribution of Codes
  year: 1977
  ident: ref9
– ident: ref4
  doi: 10.1109/LCOMM.2020.3041845
– ident: ref3
  doi: 10.1109/LCOMM.2019.2896626
– ident: ref7
  doi: 10.1090/gsm/180
– ident: ref11
  doi: 10.1016/s0924-6509(08)x7030-8
– ident: ref1
  doi: 10.1109/TCOMM.2017.2657621
– year: 2014
  ident: ref8
  article-title: Lecture notes on advanced combinatorics: Error-correcting codes
– ident: ref10
  doi: 10.1016/0012-365X(90)90322-9
SSID ssj0008251
Score 2.3736656
Snippet In this letter, we provide a method for deriving the first exact expression for the decoding success probability of sparse random linear network coding over...
SourceID proquest
crossref
ieee
SourceType Aggregation Database
Index Database
Publisher
StartPage 2009
SubjectTerms Additives
Channels
Coding
Decoding
Encoding
Fields (mathematics)
full rank probability
Homomorphisms
Receivers
Reliability
Sparse matrices
Sparse random linear network coding
Transforms
Title A Homomorphism Transform Based Analysis of Sparse Random Linear Network Coding Over Erasure Channels
URI https://ieeexplore.ieee.org/document/9792302
https://www.proquest.com/docview/2712054786
Volume 26
WOSCitedRecordID wos000852215600011&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 Electronic Library (IEL)
  customDbUrl:
  eissn: 1558-2558
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0008251
  issn: 1089-7798
  databaseCode: RIE
  dateStart: 19970101
  isFulltext: true
  titleUrlDefault: https://ieeexplore.ieee.org/
  providerName: IEEE
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV07T8MwED6VigEGXgVRXvLABqFpHo49QtWqA20RFKlb5PghMTSp-uD3c3aSCgQLypAMSWTd2ffdZ98D4BbtXazQ9noypqEXaWY8EYmuZxTSOBqKmGnfNZtIxmM2m_GXBtxvc2G01i74TD_YR3eWrwq5sVtlHW6L3dnKkTtJQstcra3VtSmYZTA9R4-RszpBxued595kNEIqGATIUBkidvADhFxXlV-m2OHL4PB_IzuCg8qPJI-l4o-hofMT2P9WXbAF6pEMizleKMqP1ZxMax-VPCF0KVLXIyGFIW8LJLiavIpcFXOCBBUXABmXIeKkV1iAIxOc9aS_dHuKxGYl5Iirp_A-6E97Q69qquDJIKJrT0shkkCaLA4Fw1vXF5yjjWOZ7GaaCxMq39A4YxSxjRm0hzoOIiZRqcgVmQrPoJkXuT4HkmVUi0TykCr0YpDrRtxXSPdMxg36XaYNd7WU00VZOyN1nMPnqdNJanWSVjppQ8vKdftmJdI2XNWKSavltUoDHIxvK5HRi7-_uoQ9--8yGOwKmuvlRl_Drvxcf6yWN27mfAHKAsJm
linkProvider IEEE
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV07T8MwED4hQAIG3ohCAQ9sEOrmVXuEqlURbUBQJLbI8UPq0AS1hd_P2UkqECwoQzIkinVn33effQ-AS7R3kULb68koDrxQM-OJULQ9o5DGxYGImKau2UQnSdjbG39agetlLozW2gWf6Rv76M7yVSE_7FZZi9tid7Zy5FoUhj4ts7WWdtcmYZbh9Bx9Rs7qFBnKW8Pu42iEZND3kaMyxGz_Bwy5viq_jLFDmP7O_8a2C9uVJ0luS9XvwYrO92HrW33BA1C3ZFBM8UJhTuZTMq69VHKH4KVIXZGEFIa8vCPF1eRZ5KqYEqSouARIUgaJk25hIY484rwnvZnbVSQ2LyFHZD2E135v3B14VVsFT_phvPC0FKLjS5NFgWB4a1PBOVo5lsl2prkwgaImjjIWI7oxgxZRR37IJKoV2SJTwRGs5kWuj4FkWaxFR_IgVujHINsNOVVI-EzGDXpepgFXtZTT97J6RupYB-Wp00lqdZJWOmnAgZXr8s1KpA1o1opJqwU2T30cDLW1yOKTv7-6gI3BeDRMh_fJwyls2v-UoWFNWF3MPvQZrMvPxWQ-O3ez6AsRvcWt
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=A+Homomorphism+Transform+Based+Analysis+of+Sparse+Random+Linear+Network+Coding+Over+Erasure+Channels&rft.jtitle=IEEE+communications+letters&rft.au=Chen%2C+Wenlin&rft.au=Lu%2C+Fang&rft.au=Dong%2C+Yan&rft.date=2022-09-01&rft.pub=IEEE&rft.issn=1089-7798&rft.volume=26&rft.issue=9&rft.spage=2009&rft.epage=2013&rft_id=info:doi/10.1109%2FLCOMM.2022.3181722&rft.externalDocID=9792302
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1089-7798&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1089-7798&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1089-7798&client=summon