Improved Expression for Rank Distribution of Sparse Random Linear Network Coding
Characterization of the rank distribution of a sparse random matrix over a finite field can be decomposed into two subproblems. The first subproblem is the characterization of the probability <inline-formula> <tex-math notation="LaTeX">p(i,n) </tex-math></inline-formul...
Uloženo v:
| Vydáno v: | IEEE communications letters Ročník 25; číslo 5; s. 1472 - 1476 |
|---|---|
| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
New York
IEEE
01.05.2021
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 | Characterization of the rank distribution of a sparse random matrix over a finite field can be decomposed into two subproblems. The first subproblem is the characterization of the probability <inline-formula> <tex-math notation="LaTeX">p(i,n) </tex-math></inline-formula> that an <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula>-dimensional vector is linearly dependent of other <inline-formula> <tex-math notation="LaTeX">i </tex-math></inline-formula> linearly independent <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula>-dimensional vectors. The second subproblem is the characterization of the rank distribution of a sparse random matrix as a function of <inline-formula> <tex-math notation="LaTeX">p(i,n) </tex-math></inline-formula>. In this letter, we focus on the second subproblem and present an exact solution to it. The derivation is based on an absorbing Markov chain and the eigen decomposition of the transition matrix. Compared with the state-of-the-art expressions, the derived expression is closed-form and of lower complexity. As a necessity for the exactness of the derived expression, we prove that the derived expression is equivalent to the state-of-the-art expressions. |
|---|---|
| AbstractList | Characterization of the rank distribution of a sparse random matrix over a finite field can be decomposed into two subproblems. The first subproblem is the characterization of the probability <inline-formula> <tex-math notation="LaTeX">p(i,n) </tex-math></inline-formula> that an <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula>-dimensional vector is linearly dependent of other <inline-formula> <tex-math notation="LaTeX">i </tex-math></inline-formula> linearly independent <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula>-dimensional vectors. The second subproblem is the characterization of the rank distribution of a sparse random matrix as a function of <inline-formula> <tex-math notation="LaTeX">p(i,n) </tex-math></inline-formula>. In this letter, we focus on the second subproblem and present an exact solution to it. The derivation is based on an absorbing Markov chain and the eigen decomposition of the transition matrix. Compared with the state-of-the-art expressions, the derived expression is closed-form and of lower complexity. As a necessity for the exactness of the derived expression, we prove that the derived expression is equivalent to the state-of-the-art expressions. Characterization of the rank distribution of a sparse random matrix over a finite field can be decomposed into two subproblems. The first subproblem is the characterization of the probability [Formula Omitted] that an [Formula Omitted]-dimensional vector is linearly dependent of other [Formula Omitted] linearly independent [Formula Omitted]-dimensional vectors. The second subproblem is the characterization of the rank distribution of a sparse random matrix as a function of [Formula Omitted]. In this letter, we focus on the second subproblem and present an exact solution to it. The derivation is based on an absorbing Markov chain and the eigen decomposition of the transition matrix. Compared with the state-of-the-art expressions, the derived expression is closed-form and of lower complexity. As a necessity for the exactness of the derived expression, we prove that the derived expression is equivalent to the state-of-the-art expressions. |
| 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 | eNp9kMlOwzAQhi1UJNrCC8AlEucUL4kdH1EoUCmliOUcOckYuUtc7JTl7XEo4sCBy8xo5v9nRt8IDVrbAkKnBE8IwfKiyBfz-YRiiicMJyRL0gM0JGmaxTSEQahxJmMhZHaERt4vMcYZTckQ3c82W2ffoImmH1sH3hvbRtq66EG1q-jK-M6Zatf1Xaujx61yHvpZYzdRYVpQLrqD7t26VZTbxrQvx-hQq7WHk588Rs_X06f8Ni4WN7P8sohrKtMuppVOdaIYrpmkwESdVaLGogFGMeNSJELzJuOaSY5TULoSlAMNPc6xpJKwMTrf7w3vv-7Ad-XS7lwbTpY0pUHBJRdBRfeq2lnvHehy68xGuc-S4LInV36TK3ty5Q-5YMr-mGrTqZ5B55RZ_28921sNAPzeklTwhAr2BVgdfTQ |
| CODEN | ICLEF6 |
| CitedBy_id | crossref_primary_10_1109_LCOMM_2022_3181722 crossref_primary_10_1186_s13638_022_02132_4 crossref_primary_10_1007_s11277_021_08497_x crossref_primary_10_1109_LWC_2022_3147601 |
| Cites_doi | 10.1109/TCOMM.2017.2657621 10.1109/LCOMM.2019.2896626 10.1109/LCOMM.2017.2704110 10.1109/ISNETCOD.2011.5978939 10.1002/1098-2418(200010/12)17:3/4<197::AID-RSA2>3.0.CO;2-K 10.1109/ACCESS.2019.2907005 10.1017/CBO9780511987045 10.1093/oso/9780198534891.001.0001 10.1109/LCOMM.2010.110310.101480 10.1109/LCOMM.2020.2965928 |
| ContentType | Journal Article |
| Copyright | Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2021 |
| Copyright_xml | – notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2021 |
| DBID | 97E RIA RIE AAYXX CITATION 7SP 8FD L7M |
| DOI | 10.1109/LCOMM.2020.3041845 |
| DatabaseName | IEEE Xplore (IEEE) 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/IET Electronic Library url: https://ieeexplore.ieee.org/ sourceTypes: Publisher |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering |
| EISSN | 1558-2558 |
| EndPage | 1476 |
| ExternalDocumentID | 10_1109_LCOMM_2020_3041845 9276427 |
| 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-c295t-2bf5f4a30c392e37c8b7c07de320369747f6d86f39605eafb726e2f6d66092913 |
| IEDL.DBID | RIE |
| ISICitedReferencesCount | 4 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000648333800017&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 10:20:25 EDT 2025 Sat Nov 29 03:56:05 EST 2025 Tue Nov 18 21:29:46 EST 2025 Wed Aug 27 02:30:05 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 5 |
| 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-c295t-2bf5f4a30c392e37c8b7c07de320369747f6d86f39605eafb726e2f6d66092913 |
| 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 | 2522916967 |
| PQPubID | 85419 |
| PageCount | 5 |
| ParticipantIDs | proquest_journals_2522916967 ieee_primary_9276427 crossref_primary_10_1109_LCOMM_2020_3041845 crossref_citationtrail_10_1109_LCOMM_2020_3041845 |
| PublicationCentury | 2000 |
| PublicationDate | 2021-05-01 |
| PublicationDateYYYYMMDD | 2021-05-01 |
| PublicationDate_xml | – month: 05 year: 2021 text: 2021-05-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York |
| PublicationTitle | IEEE communications letters |
| PublicationTitleAbbrev | COML |
| PublicationYear | 2021 |
| 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 | ref8 ref7 ref9 ref4 ref3 ref6 ref5 ref2 ref1 macdonald (ref10) 1995 |
| References_xml | – ident: ref5 doi: 10.1109/TCOMM.2017.2657621 – ident: ref6 doi: 10.1109/LCOMM.2019.2896626 – ident: ref1 doi: 10.1109/LCOMM.2017.2704110 – ident: ref4 doi: 10.1109/ISNETCOD.2011.5978939 – ident: ref3 doi: 10.1002/1098-2418(200010/12)17:3/4<197::AID-RSA2>3.0.CO;2-K – ident: ref7 doi: 10.1109/ACCESS.2019.2907005 – ident: ref9 doi: 10.1017/CBO9780511987045 – year: 1995 ident: ref10 publication-title: Symmetric Functions and Hall Polynomials doi: 10.1093/oso/9780198534891.001.0001 – ident: ref8 doi: 10.1109/LCOMM.2010.110310.101480 – ident: ref2 doi: 10.1109/LCOMM.2020.2965928 |
| SSID | ssj0008251 |
| Score | 2.3551083 |
| Snippet | Characterization of the rank distribution of a sparse random matrix over a finite field can be decomposed into two subproblems. The first subproblem is the... |
| SourceID | proquest crossref ieee |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 1472 |
| SubjectTerms | Decoding Decomposition Eigenvalues and eigenfunctions Exact solutions Fields (mathematics) Markov chains Markov processes Matrices (mathematics) Matrix decomposition Network coding rank distribution Receivers Sparse matrices Sparse random linear network coding |
| Title | Improved Expression for Rank Distribution of Sparse Random Linear Network Coding |
| URI | https://ieeexplore.ieee.org/document/9276427 https://www.proquest.com/docview/2522916967 |
| Volume | 25 |
| WOSCitedRecordID | wos000648333800017&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: 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/eLvHCXMwlV1LS8QwEB5c8aAH3-L6IgdvWrebPtIcZd3Fg66LD_BW2mQCorbL7ir-fCdptyiK4K00SSkzSeb7knkAHJON19SmPTQCvTATgSe50J5MwogAtJS5clVLrsRwmDw-ytECnDaxMIjonM_wzD66u3xdqjd7VNahrxBcFi1oCRFXsVrNrmtDMCtnekmIUSbzABlfdq56N9fXRAU5MVQ_JEoTfTNCrqrKj63Y2ZfB2v_-bB1WaxzJzivFb8ACFpuw8iW74BaMqgMD1Kz_Ubu7FowwKrvNimd2YTPm1sWuWGnY3ZgoLto2Xb4yoqi0BNiwchJnvdKauG14GPTve5deXUDBU1xGM4_nJjJhFviKUBAGQiW5UL7QGNjrR8skTKyT2AREYyLMTC54jJzexbFPsKkb7MBiURa4C4yHSDTa6NhEQRgJPyPkqLTCUGueRJnfhu5coqmqs4vbIhcvqWMZvkydFlKrhbTWQhtOmjHjKrfGn723rNybnrXI23AwV1xaL79pyglVEu6Vsdj7fdQ-LHPrnOI8Fw9gcTZ5w0NYUu-zp-nkyM2sT62cyiw |
| linkProvider | IEEE |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3db9MwED-VDgl42AcD0X3hh71BmOfYcfw4dZ060XYVFGlvUWqfJQQkVdch_nzOTlqBQJP2FsV2FN3Zvt_Pvg-AU7Lxjtpcgl5jIkudJkZol5hcKgLQxsxtrFoy0pNJfntrph14v4mFQcTofIYfwmO8y3e1vQ9HZWf0FYLL-glsKSkFb6K1NvtuCMJs3OkNYUaTr0NkuDkb9W_GYyKDgjgql0Rq1F9mKNZV-Wczjhbmaudx_7YL2y2SZBeN6vegg9VLePFHfsF9mDZHBujY4Ffr8FoxQqnsU1l9Y5chZ25b7orVnn1eEMnF0ObqH4xIKi0CNmncxFm_DkbuFXy5Gsz6w6QtoZBYYdQqEXOvvCxTbgkHYaptPteWa4dpuIAMXMJnLs98SkRGYennWmQo6F2WcQJO5-lr6FZ1hW-ACYlEpL3LvEql0rwk7GidRemcyFXJe3C-lmhh2_zioczF9yLyDG6KqIUiaKFotdCDd5sxiya7xoO994PcNz1bkffgaK24ol2Ad4UgXEnI12T64P-j3sKz4Ww8KkbXk4-H8FwEV5Xox3gE3dXyHo_hqf25-nq3PImz7Dddpc1z |
| 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=Improved+Expression+for+Rank+Distribution+of+Sparse+Random+Linear+Network+Coding&rft.jtitle=IEEE+communications+letters&rft.au=Chen%2C+Wenlin&rft.au=Lu%2C+Fang&rft.au=Dong%2C+Yan&rft.date=2021-05-01&rft.pub=IEEE&rft.issn=1089-7798&rft.volume=25&rft.issue=5&rft.spage=1472&rft.epage=1476&rft_id=info:doi/10.1109%2FLCOMM.2020.3041845&rft.externalDocID=9276427 |
| 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 |