Network Coding Capacity Regions via Entropy Functions
In this paper, we use entropy functions to characterize the set of rate-capacity tuples achievable with either zero decoding error, or vanishing decoding error, for general network coding problems for acyclic networks. We show that when sources are colocated, the outer bound is tight and the sets of...
Saved in:
| Published in | IEEE transactions on information theory Vol. 60; no. 9; pp. 5347 - 5374 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York, NY
IEEE
01.09.2014
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0018-9448 1557-9654 |
| DOI | 10.1109/TIT.2014.2334291 |
Cover
Loading…
| Abstract | In this paper, we use entropy functions to characterize the set of rate-capacity tuples achievable with either zero decoding error, or vanishing decoding error, for general network coding problems for acyclic networks. We show that when sources are colocated, the outer bound is tight and the sets of zero-error achievable and vanishing-error achievable rate-capacity tuples are the same. Then, we extend this paper to networks subject to linear encoding constraints, routing constraints (where some or all nodes can only perform routing), and secrecy constraints. Finally, we show that even for apparently simple networks, design of optimal codes may be difficult. In particular, we prove that for the incremental multicast problem and for the single-source secure network coding problem, characterization of the achievable set can be very hard and linear network codes may not be optimal. |
|---|---|
| AbstractList | In this paper, we use entropy functions to characterize the set of rate-capacity tuples achievable with either zero decoding error, or vanishing decoding error, for general network coding problems for acyclic networks. We show that when sources are colocated, the outer bound is tight and the sets of zero-error achievable and vanishing-error achievable rate-capacity tuples are the same. Then, we extend this paper to networks subject to linear encoding constraints, routing constraints (where some or all nodes can only perform routing), and secrecy constraints. Finally, we show that even for apparently simple networks, design of optimal codes may be difficult. In particular, we prove that for the incremental multicast problem and for the single-source secure network coding problem, characterization of the achievable set can be very hard and linear network codes may not be optimal. |
| Author | Chan, Terence H. Grant, Alex |
| Author_xml | – sequence: 1 givenname: Terence H. surname: Chan fullname: Chan, Terence H. email: terence.chan@unisa.edu.au organization: Inst. for Telecommun. Res., Univ. of South Australia, Adelaide, SA, Australia – sequence: 2 givenname: Alex surname: Grant fullname: Grant, Alex email: alex.grant@unisa.edu.au organization: Inst. for Telecommun. Res., Univ. of South Australia, Adelaide, SA, Australia |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=28807048$$DView record in Pascal Francis |
| BookMark | eNp9kM1Lw0AQxRdRsK3eBS8B8Zg6-5XNHiW0WigKUs_LJtmUrTUbd1Ol_70bWj148DTM8HtveG-MTlvXGoSuMEwxBnm3WqymBDCbEkoZkfgEjTDnIpUZZ6doBIDzVDKWn6NxCJu4Mo7JCPEn0385_5YUrrbtOil0pyvb75MXs7auDcmn1cms7b3r9sl811b9cL1AZ43eBnN5nBP0Op-tisd0-fywKO6XaUUJ7lMhgUgtRUk41JqJrAFKjKh5KUlTMg4yaxpccSnreC8xr0qoDRCtjaw1xnSCbg6-nXcfOxN6tXE738aXKobjlHIqIFK3R0qHSm8br9vKBtV5-679XpE8BwEsj1x24CrvQvCmUTGpHgL1XtutwqCGKlWsUg1VqmOVUQh_hD_e_0iuDxJrjPnFs5wJApx-AyWFfts |
| CODEN | IETTAW |
| CitedBy_id | crossref_primary_10_1109_TIT_2019_2900669 crossref_primary_10_1109_TIT_2018_2889687 crossref_primary_10_1016_j_comnet_2024_110221 crossref_primary_10_1016_j_comnet_2018_03_013 crossref_primary_10_1109_TIT_2016_2628819 crossref_primary_10_1109_TCOMM_2018_2870831 crossref_primary_10_1109_TIT_2018_2866244 crossref_primary_10_1109_TIT_2018_2820686 crossref_primary_10_1109_TIT_2016_2539280 crossref_primary_10_1109_TIT_2019_2949803 |
| Cites_doi | 10.1007/978-1-4419-8608-5 10.1109/ITA.2011.5743582 10.1109/TIT.2002.807285 10.1109/TIT.2010.2090197 10.1109/TIT.2008.928963 10.1109/Allerton.2011.6120342 10.1007/s10922-005-9019-0 10.1109/ALLERTON.2010.5706933 10.1109/18.850663 10.1109/18.681320 10.1145/359168.359176 10.1109/TIT.2003.820015 10.1109/ISIT.2009.5205943 10.1109/18.641556 10.1109/ISIT.2007.4557284 10.1109/TIT.2012.2201340 10.1109/TIT.2006.874531 10.1109/TIT.2002.1013138 10.1109/ISIT.2007.4557201 10.1002/0471200611 10.3390/e13020379 |
| ContentType | Journal Article |
| Copyright | 2015 INIST-CNRS Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Sep 2014 |
| Copyright_xml | – notice: 2015 INIST-CNRS – notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Sep 2014 |
| DBID | 97E RIA RIE AAYXX CITATION IQODW 7SC 7SP 8FD JQ2 L7M L~C L~D |
| DOI | 10.1109/TIT.2014.2334291 |
| DatabaseName | IEEE All-Society Periodicals Package (ASPP) 2005–Present IEEE All-Society Periodicals Package (ASPP) 1998–Present IEEE Electronic Library (IEL) CrossRef Pascal-Francis 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 Electronic Library (IEL) url: https://proxy.k.utb.cz/login?url=https://ieeexplore.ieee.org/ sourceTypes: Publisher |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Computer Science Applied Sciences |
| EISSN | 1557-9654 |
| EndPage | 5374 |
| ExternalDocumentID | 3410494311 28807048 10_1109_TIT_2014_2334291 6847205 |
| Genre | orig-research |
| GrantInformation_xml | – fundername: Australian Government through the Australian Research Council grantid: DP1094571 |
| 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 AAYOK AAYXX CITATION RIG IQODW 7SC 7SP 8FD JQ2 L7M L~C L~D |
| ID | FETCH-LOGICAL-c321t-79029a97b250da476f032e7d5b92fb45096ff1c599d32eb15cb0de02aae9da113 |
| IEDL.DBID | RIE |
| ISSN | 0018-9448 |
| IngestDate | Sun Jun 29 12:52:07 EDT 2025 Wed Apr 02 07:25:25 EDT 2025 Tue Jul 01 02:34:35 EDT 2025 Thu Apr 24 23:11:23 EDT 2025 Tue Aug 26 16:46:28 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 9 |
| Keywords | Network coding achievable rate regions linearity constraint incremental multicast Packet switching Source coding Error rate Routing Entropy Decoding Data broadcast Information dissemination Multicast Linear code Linear coding Linearity Optimal code Secrecy |
| Language | English |
| License | https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html CC BY 4.0 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c321t-79029a97b250da476f032e7d5b92fb45096ff1c599d32eb15cb0de02aae9da113 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| PQID | 1555335370 |
| PQPubID | 36024 |
| PageCount | 28 |
| ParticipantIDs | pascalfrancis_primary_28807048 crossref_citationtrail_10_1109_TIT_2014_2334291 ieee_primary_6847205 crossref_primary_10_1109_TIT_2014_2334291 proquest_journals_1555335370 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2014-09-01 |
| PublicationDateYYYYMMDD | 2014-09-01 |
| PublicationDate_xml | – month: 09 year: 2014 text: 2014-09-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationPlace | New York, NY |
| PublicationPlace_xml | – name: New York, NY – name: New York |
| PublicationTitle | IEEE transactions on information theory |
| PublicationTitleAbbrev | TIT |
| PublicationYear | 2014 |
| Publisher | IEEE Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher_xml | – name: IEEE – name: Institute of Electrical and Electronics Engineers – name: The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| References | ref13 ref12 ref15 ref14 ref11 ref10 yeung (ref2) 2002 ref1 ref17 ref16 kschischang (ref20) 2011 oxley (ref18) 1992 ref24 ref23 cai (ref9) 2002 ref25 ref22 ref21 wu (ref19) 2004 ref8 ref7 ref4 ref3 ref6 ref5 |
| References_xml | – year: 2002 ident: ref2 publication-title: A First Course in Information Theory doi: 10.1007/978-1-4419-8608-5 – ident: ref6 doi: 10.1109/ITA.2011.5743582 – ident: ref8 doi: 10.1109/TIT.2002.807285 – ident: ref24 doi: 10.1109/TIT.2010.2090197 – ident: ref4 doi: 10.1109/TIT.2008.928963 – ident: ref7 doi: 10.1109/Allerton.2011.6120342 – ident: ref11 doi: 10.1007/s10922-005-9019-0 – year: 2004 ident: ref19 article-title: A comparison of network coding and tree packing publication-title: Proc IEEE Int Symp Inf Theory – ident: ref5 doi: 10.1109/ALLERTON.2010.5706933 – ident: ref21 doi: 10.1109/18.850663 – ident: ref15 doi: 10.1109/18.681320 – ident: ref22 doi: 10.1145/359168.359176 – ident: ref16 doi: 10.1109/TIT.2003.820015 – ident: ref12 doi: 10.1109/ISIT.2009.5205943 – ident: ref13 doi: 10.1109/18.641556 – year: 2011 ident: ref20 article-title: An introduction to network coding publication-title: Network Coding Fundamentals and Applications – ident: ref25 doi: 10.1109/ISIT.2007.4557284 – ident: ref1 doi: 10.1109/TIT.2012.2201340 – ident: ref10 doi: 10.1109/TIT.2006.874531 – ident: ref17 doi: 10.1109/TIT.2002.1013138 – year: 2002 ident: ref9 article-title: Secure network coding publication-title: Proc IEEE Int Symp Inf Theory – year: 1992 ident: ref18 publication-title: Matroid Theory – ident: ref3 doi: 10.1109/ISIT.2007.4557201 – ident: ref23 doi: 10.1002/0471200611 – ident: ref14 doi: 10.3390/e13020379 |
| SSID | ssj0014512 |
| Score | 2.2834275 |
| Snippet | In this paper, we use entropy functions to characterize the set of rate-capacity tuples achievable with either zero decoding error, or vanishing decoding... |
| SourceID | proquest pascalfrancis crossref ieee |
| SourceType | Aggregation Database Index Database Enrichment Source Publisher |
| StartPage | 5347 |
| SubjectTerms | Applied sciences Coding, codes Decoding Encoding Entropy Error correction & detection Error probability Exact sciences and technology Indexes Information theory Information, signal and communications theory Linear codes Network coding Random variables Routing Secret Signal and communications theory Systems, networks and services of telecommunications Telecommunications Telecommunications and information theory Transmission and modulation (techniques and equipments) |
| Title | Network Coding Capacity Regions via Entropy Functions |
| URI | https://ieeexplore.ieee.org/document/6847205 https://www.proquest.com/docview/1555335370 |
| Volume | 60 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV1JSwMxFH5UT3pwF-tScvAiOO0kM5lMjlJaVGgPUsHbkG1AlFZsK-iv92U2rIp4G2Yy23t5S5Iv3wM450wqzYUJhNUiiK0TgUpjFuRGM0mt5Mr5qYHROLm-j28f-EMLLpu9MM65Anzmuv6wWMu3M7P0U2W9BF0p84SlazhwK_dqNSsGMaclMzhFA8YxR70kGcre5GbiMVxxl0URul-6EoKKmioeEanmKJS8rGbxwzEX0Wa4DaP6O0uQyVN3udBd8_GNwvG_P7IDW1XaSa7KfrILLTfdg-26pAOpLHwPNr_wE-4DH5cgcdKf-RBH-hhZDabt5M55GPOcvD0qMvBY95d3MsQIWXTiA7gfDib966CqsxCYiNFFIGSIGpNCYzpkVSySPIyYE5ZryXIde4KYPKeGS2nxvKbc6NC6kCnlpFWURoewPp1N3REQTOBcFKa-zgKNLVfSk63SJE2TFC3dyjb0atFnpiIh97UwnrNiMBLKDJWVeWVllbLacNHc8VIScPzRdt_LumlXibkNnRXtNtcZOi-BLqwNp7W6s8qE5xkmWpgK80iEx78_9gQ28OVJCUg7hfXF69KdYYay0J2ia34CyAXf-A |
| linkProvider | IEEE |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV3NT9swFH-q4MB2oKMwka1jPnBBIm3sxHF8RFWrMtoepiJxi_wVCYFaRNtJ21-_53xpbBPiFiVO5Lzn92H7598DOOdMKs2FCYXVIkysE6HKEhYWRjNJreTK-aWB-SKd3ibf7vhdBy7bszDOuRJ85gb-stzLt2uz80tlwxRdKfOEpfsY9zmtTmu1ewYJpxU3OEUTxllHsykZyeHyeulRXMmAxTE6YPoiCJVVVTwmUm1QLEVVz-If11zGm0kX5k1PK5jJw2C31QPz6y8Sx7f-ygc4rBNPclWNlCPouFUPuk1RB1LbeA_e_8FQeAx8UcHEyWjtgxwZYWw1mLiT784DmTfkx70iY492f_pJJhgjy2F8AreT8XI0DetKC6GJGd2GQkaoMyk0JkRWJSItopg5YbmWrNCJp4gpCmq4lBbva8qNjqyLmFJOWkVp_BH2VuuVOwWCKZyLo8xXWqCJ5Up6ulWaZlmaoa1bGcCwEX1uahpyXw3jMS-nI5HMUVm5V1ZeKyuAi_aNp4qC45W2x17WbbtazAGcvdBu-5yh-xLoxALoN-rOayPe5JhqYTLMYxF9-v9nv8LBdDmf5bPrxc1neOc7UsHP-rC3fd65L5ivbPVZOUx_A6Ju40U |
| 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=Network+Coding+Capacity+Regions+via+Entropy+Functions&rft.jtitle=IEEE+transactions+on+information+theory&rft.au=Chan%2C+Terence+H.&rft.au=Grant%2C+Alex&rft.date=2014-09-01&rft.pub=IEEE&rft.issn=0018-9448&rft.volume=60&rft.issue=9&rft.spage=5347&rft.epage=5374&rft_id=info:doi/10.1109%2FTIT.2014.2334291&rft.externalDocID=6847205 |
| 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 |