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...
Uloženo v:
| Vydáno v: | IEEE communications letters Ročník 26; číslo 9; s. 2009 - 2013 |
|---|---|
| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
New York
IEEE
01.09.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Témata: | |
| ISSN: | 1089-7798, 1558-2558 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| 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 | 2.373755 |
| 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/eLvHCXMwlV07T8MwELZKxQADr4IoFOSBDQKpEyf2WKpWHfpAUFC3yK9IHZpUffD7OTtJBYIFZUiGJLLu7Pv82XefEboLVZCGoq08yWjqhcpQTwDueSqmoZBGxoWA6ccwHo_ZbMZfauhhVwtjjHHJZ-bRPrq9fJ2rrV0qe-JW7M4qR-7FcVTUau2iri3BLJLpOcwYOasKZHz-NOxORiOggoQAQ2WA2OQHCLlTVX6FYocv_eP_tewEHZXzSNwpHH-KaiY7Q4ff1AUbSHfwIF_ABaacrxd4Ws1R8TNAl8aVHgnOU_y2BIJr8KvIdL7AQFBhAOBxkSKOu7kFODyBXo97K7emiG1VQga4eo7e-71pd-CVhyp4ioTRxjNKiJioVNJAMLi1fcE5xDgmVVsaLtJA-2lEJYsA21gK8dBQEjIFIAZckengAtWzPDOXCFNBeaDsTqFkoZGas0jERkcUQDEVjDTRfWXlZFloZySOc_g8cT5JrE-S0idN1LB23b1ZmrSJWpVjknJ4rRMCjfGtEll09fdX1-jA_rtIBmuh-ma1NTdoX31u5uvVres5XzxDwic |
| linkProvider | IEEE |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV07T8MwED4hQAIGXgVRKOCBDQKpYyf2CFVREX0gKIgtsh1HYmiC2sLv55xHBYIFZUiGRLHu7Pv82XefAc6YCVKm2sbTgqceM5Z7CnHPMxFnSlsdlQKmL_1oOBSvr_JhCS4WtTDW2iL5zF66x2IvP8nNh1squ5JO7M4pR65wxqhfVmst4q4rwizT6SXOGaWoS2R8edXvjAYDJIOUIkcViNn0BwwV56r8CsYFwtxu_a9t27BZzSTJden6HViy2S5sfNMXbEByTXr5BC805ttsQsb1LJXcIHglpFYkIXlKnt6R4lryqLIknxCkqDgEyLBMEied3EEcGWG_J91psapIXF1Chsi6B8-33XGn51XHKniGsnDuWaNURE2qeaAE3tq-khKjnNCmra1UaZD4aci1CBHdRIoR0XLKhEEYQ7YokmAflrM8swdAuOIyMG6vUAtmdSJFqCKbhBxhMVWCNuG8tnL8XqpnxAXr8GVc-CR2PokrnzSh4ey6eLMyaRNatWPiaoDNYoqN8Z0WWXj491ensNYbD_px_254fwTr7j9lalgLlufTD3sMq-Zz_jabnhS96AuAk8Vu |
| 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 |