Information-Theoretically Secure Erasure Codes for Distributed Storage
Repair operations in erasure-coded distributed storage systems involve a lot of data movement. This can potentially expose data to malicious acts of passive eavesdroppers or active adversaries, putting security of the system at risk. This paper presents coding schemes and repair algorithms that ensu...
Uloženo v:
| Vydáno v: | IEEE transactions on information theory Ročník 64; číslo 3; s. 1621 - 1646 |
|---|---|
| Hlavní autoři: | , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
New York
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
01.03.2018
|
| Témata: | |
| ISSN: | 0018-9448, 1557-9654 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | Repair operations in erasure-coded distributed storage systems involve a lot of data movement. This can potentially expose data to malicious acts of passive eavesdroppers or active adversaries, putting security of the system at risk. This paper presents coding schemes and repair algorithms that ensure security of the data in the presence of passive eavesdroppers and active adversaries while maintaining high availability, reliability, and resource efficiency in the system. The proposed codes are optimal in that they meet previously proposed lower bounds on storage and network-bandwidth requirements for a wide range of system parameters. The results thus establish the secure storage capacity of such systems. The proposed codes are based on an optimal class of codes called product-matrix codes. The constructions presented for security from active adversaries provide an additional appealing feature of “on-demand security,” where the desired level of security can be chosen separately for each instance of repair, and the proposed algorithms remain optimal simultaneously for all possible security levels. This paper also provides necessary and sufficient conditions governing the transformation of any (non-secure) code into one providing on-demand security. |
|---|---|
| AbstractList | Repair operations in erasure-coded distributed storage systems involve a lot of data movement. This can potentially expose data to malicious acts of passive eavesdroppers or active adversaries, putting security of the system at risk. This paper presents coding schemes and repair algorithms that ensure security of the data in the presence of passive eavesdroppers and active adversaries while maintaining high availability, reliability, and resource efficiency in the system. The proposed codes are optimal in that they meet previously proposed lower bounds on storage and network-bandwidth requirements for a wide range of system parameters. The results thus establish the secure storage capacity of such systems. The proposed codes are based on an optimal class of codes called product-matrix codes. The constructions presented for security from active adversaries provide an additional appealing feature of “on-demand security,” where the desired level of security can be chosen separately for each instance of repair, and the proposed algorithms remain optimal simultaneously for all possible security levels. This paper also provides necessary and sufficient conditions governing the transformation of any (non-secure) code into one providing on-demand security. |
| Author | Ramchandran, Kannan Shah, Nihar B. Rashmi, K. V. Kumar, P. Vijay |
| Author_xml | – sequence: 1 givenname: K. V. orcidid: 0000-0002-2227-7460 surname: Rashmi fullname: Rashmi, K. V. – sequence: 2 givenname: Nihar B. orcidid: 0000-0001-5158-9677 surname: Shah fullname: Shah, Nihar B. – sequence: 3 givenname: Kannan surname: Ramchandran fullname: Ramchandran, Kannan – sequence: 4 givenname: P. Vijay orcidid: 0000-0003-0990-2847 surname: Kumar fullname: Kumar, P. Vijay |
| BookMark | eNp1kD1PwzAQhi1UJNrCzhiJOeXOcZxkRKWFSpUYGmbL8QekSuNiO0P_PSllQmJ6ddL73OmeGZn0rjeE3CMsEKF6rDf1ggIWC1rwCgGvyBTzvEgrnrMJmQJgmVaMlTdkFsJ-HFmOdErWm946f5CxdX1afxrnTWyV7LpTsjNq8CZZeRnOuXTahGQsJ89tiL5thmh0sovOyw9zS66t7IK5-805eV-v6uVrun172SyftqmiBcZUaWsypstKM8hYiSg5mkyZRirQCqCwleWNZgVryoxqaJpClRZLakcGcpPNycNl79G7r8GEKPZu8P14UlAATlnFeTa2-KWlvAvBGytUG39ejF62nUAQZ2didCbOzsSvsxGEP-DRtwfpT_8j37T7cMs |
| CitedBy_id | crossref_primary_10_1109_TIT_2018_2871451 crossref_primary_10_1016_j_cose_2025_104671 crossref_primary_10_1109_TIT_2018_2878223 crossref_primary_10_1109_TCOMM_2021_3057112 crossref_primary_10_1016_j_displa_2025_103184 crossref_primary_10_1109_TCC_2022_3149963 crossref_primary_10_1109_TIFS_2021_3128822 crossref_primary_10_1109_JIOT_2023_3252040 crossref_primary_10_1109_JIOT_2024_3476312 crossref_primary_10_1007_s11432_018_9482_6 crossref_primary_10_3390_electronics13214216 crossref_primary_10_1109_TIT_2024_3506990 crossref_primary_10_1109_TIFS_2022_3140924 crossref_primary_10_3390_electronics12112423 |
| Cites_doi | 10.1109/TIT.2013.2241819 10.1109/P2P.2011.6038668 10.1109/TIT.2011.2178588 10.1109/TIT.2010.2054295 10.1109/TIT.2010.2090197 10.1109/TIT.2011.2105003 10.1109/ALLERTON.2009.5394912 10.1109/ISIT.2011.6033733 10.1109/NetCod.2013.6570831 10.1109/GLOCOM.2011.6133754 10.1109/Allerton.2012.6483348 10.1109/ACSSC.2011.6190343 10.1109/ISIT.2013.6620356 10.1145/2740070.2626325 10.1109/Allerton.2013.6736597 10.1109/TIT.2011.2159049 10.1145/2390231.2390234 10.14778/2535573.2488339 10.1109/ALLERTON.2009.5394538 10.1109/TIT.2017.2715043 10.1109/LCOMM.2013.040213.130006 10.1109/ISIT.2012.6283046 10.1109/TIT.2012.2227110 10.1109/ISIT.2012.6283041 10.1109/ISIT.2015.7282577 10.1109/ISIT.2013.6620499 10.1109/ISIT.2015.7282817 10.1109/ISIT.2014.6875270 10.1109/TIT.2008.926449 10.1109/ITA.2016.7888191 10.1109/JSAC.2013.131210 10.1109/ISIT.2013.6620501 10.1109/ALLERTON.2014.7028489 10.1109/ITWKSPS.2010.5503165 10.1109/TIT.2011.2162191 10.1109/JSAC.2014.140518 10.1109/ISIT.2013.6620463 10.1145/2408776.2408794 10.1145/359168.359176 10.1109/ISIT.2011.6033730 10.1109/TPDS.2013.2297109 10.1109/ISIT.2010.5513354 10.1007/3-540-39757-4_5 10.1109/ISIT.2013.6620462 10.1109/TIT.2013.2288784 10.1109/NETCOD.2009.5191401 10.1109/ISIT.2012.6283044 10.1109/INFCOM.2012.6195641 10.1109/ACSSC.2015.7421189 10.1145/293347.293350 10.1145/1165389.945450 10.1109/TIT.2011.2173792 10.1109/INFCOM.2013.6567040 10.1109/INFCOM.2007.78 10.1109/ISIT.2014.6874954 10.1109/ISIT.2014.6875177 10.1109/TIT.2008.928291 10.1109/TNET.2013.2294254 10.1109/ISIT.2011.6033778 10.1109/ISIT.2017.8006603 |
| ContentType | Journal Article |
| Copyright | Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2018 |
| Copyright_xml | – notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2018 |
| DBID | AAYXX CITATION 7SC 7SP 8FD JQ2 L7M L~C L~D |
| DOI | 10.1109/TIT.2017.2769101 |
| DatabaseName | 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 |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Computer Science |
| EISSN | 1557-9654 |
| EndPage | 1646 |
| ExternalDocumentID | 10_1109_TIT_2017_2769101 |
| GroupedDBID | -~X .DC 0R~ 29I 3EH 4.4 5GY 5VS 6IK 97E AAJGR AASAJ AAWTH AAYXX 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 CITATION 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 7SC 7SP 8FD ABAZT JQ2 L7M L~C L~D |
| ID | FETCH-LOGICAL-c271t-cdfe34d89d4034811a61e3cebac0dc007f9f6bd474b832d0bb7c8f182fd8905e3 |
| ISICitedReferencesCount | 23 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000425665200014&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 Nov 09 07:15:08 EST 2025 Sat Nov 29 03:31:39 EST 2025 Tue Nov 18 20:59:37 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 3 |
| 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 | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c271t-cdfe34d89d4034811a61e3cebac0dc007f9f6bd474b832d0bb7c8f182fd8905e3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0003-0990-2847 0000-0001-5158-9677 0000-0002-2227-7460 |
| PQID | 2006249663 |
| PQPubID | 36024 |
| PageCount | 26 |
| ParticipantIDs | proquest_journals_2006249663 crossref_citationtrail_10_1109_TIT_2017_2769101 crossref_primary_10_1109_TIT_2017_2769101 |
| PublicationCentury | 2000 |
| PublicationDate | 2018-03-01 |
| PublicationDateYYYYMMDD | 2018-03-01 |
| PublicationDate_xml | – month: 03 year: 2018 text: 2018-03-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York |
| PublicationTitle | IEEE transactions on information theory |
| PublicationYear | 2018 |
| Publisher | The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher_xml | – name: The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| References | ref57 ref13 ref56 ref12 ref59 ref15 ref58 ref14 ref52 ref55 ref11 ref54 ref10 ford (ref3) 2010 ref17 ref16 lehman (ref36) 2004 goparaju (ref61) 2016 ref19 ref18 rashmi (ref51) 2016 rashmi (ref8) 2015 ananthanarayanan (ref53) 2012 ref46 ref45 ref48 (ref33) 2012 ref47 feldman (ref37) 2004 ref42 ref41 ref44 ref43 jiekak (ref30) 2012 rashmi (ref7) 2014 (ref31) 2011 ref49 ref9 li (ref24) 2013 ref5 ref81 ref40 rashmi (ref4) 2013 ref80 ref79 ref35 ref78 ref34 ref75 ref74 ref77 ref76 ref2 ref1 ref39 ref38 kurihara (ref25) 2013 bernstein (ref82) 2005 ref70 ref73 gerami (ref27) 2013 ref72 ref68 ref67 ref23 gastón (ref22) 2012 ref26 macwilliams (ref50) 1977 ref69 ref64 ref20 ref65 ref21 ref28 ref29 (ref6) 2017 ref60 ref62 huang (ref71) 2015 (ref32) 2012 tandon (ref66) 2013 sasidharan (ref63) 2013 |
| References_xml | – ident: ref15 doi: 10.1109/TIT.2013.2241819 – ident: ref74 doi: 10.1109/P2P.2011.6038668 – ident: ref14 doi: 10.1109/TIT.2011.2178588 – ident: ref34 doi: 10.1109/TIT.2010.2054295 – ident: ref44 doi: 10.1109/TIT.2010.2090197 – start-page: 17 year: 2012 ident: ref53 article-title: Why let resources idle? Aggressive cloning of jobs with dolly publication-title: Proc USENIX HotCloud – ident: ref20 doi: 10.1109/TIT.2011.2105003 – year: 2013 ident: ref24 publication-title: A framework of constructions of minimal storage regenerating codes with the optimal access/update property – ident: ref42 doi: 10.1109/ALLERTON.2009.5394912 – ident: ref59 doi: 10.1109/ISIT.2011.6033733 – ident: ref65 doi: 10.1109/NetCod.2013.6570831 – ident: ref1 doi: 10.1109/GLOCOM.2011.6133754 – ident: ref64 doi: 10.1109/Allerton.2012.6483348 – ident: ref17 doi: 10.1109/ACSSC.2011.6190343 – ident: ref77 doi: 10.1109/ISIT.2013.6620356 – year: 2012 ident: ref22 publication-title: Quasi-cyclic flexible regenerating codes – year: 2013 ident: ref25 publication-title: Generalization of Rashmi-Shah-Kumar minimum-storage-regenerating codes – start-page: 331 year: 2014 ident: ref7 article-title: A 'Hitchhiker's' guide to fast and efficient data reconstruction in erasure-coded data centers publication-title: Proc ACM Sigcomm doi: 10.1145/2740070.2626325 – ident: ref55 doi: 10.1109/Allerton.2013.6736597 – start-page: 142 year: 2004 ident: ref36 article-title: Complexity classification of network information flow problems publication-title: Proc 15th Annu ACM-SIAM Symp Discrete Algorithms – ident: ref12 doi: 10.1109/TIT.2011.2159049 – ident: ref52 doi: 10.1145/2390231.2390234 – ident: ref9 doi: 10.14778/2535573.2488339 – ident: ref10 doi: 10.1109/ALLERTON.2009.5394538 – ident: ref18 doi: 10.1109/TIT.2017.2715043 – ident: ref29 doi: 10.1109/LCOMM.2013.040213.130006 – ident: ref2 doi: 10.1109/ISIT.2012.6283046 – ident: ref16 doi: 10.1109/TIT.2012.2227110 – ident: ref19 doi: 10.1109/ISIT.2012.6283041 – ident: ref48 doi: 10.1109/ISIT.2015.7282577 – ident: ref21 doi: 10.1109/ISIT.2013.6620499 – ident: ref47 doi: 10.1109/ISIT.2015.7282817 – ident: ref46 doi: 10.1109/ISIT.2014.6875270 – ident: ref39 doi: 10.1109/TIT.2008.926449 – ident: ref62 doi: 10.1109/ITA.2016.7888191 – year: 2017 ident: ref6 publication-title: HDFS and Erasure Codes (HDFS-RAID) – ident: ref67 doi: 10.1109/JSAC.2013.131210 – ident: ref26 doi: 10.1109/ISIT.2013.6620501 – ident: ref69 doi: 10.1109/ALLERTON.2014.7028489 – year: 2005 ident: ref82 publication-title: Matrix Mathematics Theory Facts and Formulas With Application to Linear Systems Theory – ident: ref11 doi: 10.1109/ITWKSPS.2010.5503165 – year: 2012 ident: ref33 publication-title: Yahoo Confirms Apologizes for the Email Hack Says Still Fixing TechCrunch – ident: ref35 doi: 10.1109/TIT.2011.2162191 – ident: ref56 doi: 10.1109/JSAC.2014.140518 – year: 2012 ident: ref30 publication-title: CROSS-MBCR Exact Minimum Bandwidth Coordinated Regenerating Codes – ident: ref28 doi: 10.1109/ISIT.2013.6620463 – start-page: 1 year: 2004 ident: ref37 article-title: On the capacity of secure network coding publication-title: Proc 42nd Annu Allerton Conf Commun Control Comput – year: 2011 ident: ref31 publication-title: Citi Data Theft Points Up a Nagging Problem CNBC – ident: ref54 doi: 10.1145/2408776.2408794 – year: 2012 ident: ref32 publication-title: LinkedIn Hack is Latest Blow to Online Confidence USA Today – ident: ref80 doi: 10.1145/359168.359176 – ident: ref60 doi: 10.1109/ISIT.2011.6033730 – ident: ref23 doi: 10.1109/TPDS.2013.2297109 – ident: ref76 doi: 10.1109/ISIT.2010.5513354 – ident: ref81 doi: 10.1007/3-540-39757-4_5 – ident: ref45 doi: 10.1109/ISIT.2013.6620462 – year: 2015 ident: ref71 publication-title: On secrecy capacity of minimum storage regenerating codes – ident: ref49 doi: 10.1109/TIT.2013.2288784 – ident: ref41 doi: 10.1109/NETCOD.2009.5191401 – ident: ref57 doi: 10.1109/ISIT.2012.6283044 – start-page: 401 year: 2016 ident: ref51 article-title: EC-cache: Load-balanced, low-latency cluster caching with online erasure coding publication-title: Proc of USENIX Symp on Operating Systems Design and Implementation (OSDI) – ident: ref73 doi: 10.1109/INFCOM.2012.6195641 – ident: ref70 doi: 10.1109/ACSSC.2015.7421189 – ident: ref78 doi: 10.1145/293347.293350 – ident: ref5 doi: 10.1145/1165389.945450 – ident: ref13 doi: 10.1109/TIT.2011.2173792 – year: 2013 ident: ref63 publication-title: An Improved Outer Bound on the Storage-Repair-Bandwidth Tradeoff of Exact-Repair Regenerating Codes – ident: ref58 doi: 10.1109/INFCOM.2013.6567040 – ident: ref38 doi: 10.1109/INFCOM.2007.78 – ident: ref79 doi: 10.1109/ISIT.2014.6874954 – year: 2013 ident: ref27 publication-title: Optimized-cost Repair in Multi-hop Distributed Storage Systems with Network Coding – start-page: 61 year: 2010 ident: ref3 article-title: Availability in globally distributed storage systems publication-title: Proc USENIX Symp on Operating System Design and Implementation – ident: ref68 doi: 10.1109/ISIT.2014.6875177 – ident: ref40 doi: 10.1109/TIT.2008.928291 – ident: ref43 doi: 10.1109/TNET.2013.2294254 – start-page: 81 year: 2015 ident: ref8 article-title: Having your cake and eating it too: Jointly optimal erasure codes for I/O, storage, and network-bandwidth publication-title: Proc USENIX Conf File Storage Technol (FAST) – ident: ref75 doi: 10.1109/ISIT.2011.6033778 – start-page: 8 year: 2013 ident: ref4 article-title: A solution to the network challenges of data recovery in erasure-coded distributed storage systems: A study on the Facebook warehouse cluster publication-title: Proc USENIX HotStorage – ident: ref72 doi: 10.1109/ISIT.2017.8006603 – year: 2016 ident: ref61 publication-title: Minimum storage regenerating codes for all parameters – year: 1977 ident: ref50 publication-title: The Theory of Error-Correcting Codes Part I – year: 2013 ident: ref66 publication-title: Towards Optimal Secure Distributed Storage Systems with Exact Repair |
| SSID | ssj0014512 |
| Score | 2.4026668 |
| Snippet | Repair operations in erasure-coded distributed storage systems involve a lot of data movement. This can potentially expose data to malicious acts of passive... |
| SourceID | proquest crossref |
| SourceType | Aggregation Database Enrichment Source Index Database |
| StartPage | 1621 |
| SubjectTerms | Algorithms Codes Cybersecurity Eavesdropping Lower bounds Matrix codes Repair Storage capacity Storage systems |
| Title | Information-Theoretically Secure Erasure Codes for Distributed Storage |
| URI | https://www.proquest.com/docview/2006249663 |
| Volume | 64 |
| WOSCitedRecordID | wos000425665200014&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 (IEL) (UW System Shared) 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/eLvHCXMwtV1LTxRBEO6s4EEPiqgRRdIHL8bMMo_e7umjIRANhhAzEm6Tfk12yTKS3YXA3_GXWv2a2SVi4MBlMun01Dzqm6qu6nog9IkLLkAtNknJpUmIKFjCQc8kBaUyFxosZ5f1fvKDHR2Vp6f8eDD4E3Nhrqasbcvra37xqKyGMWC2TZ19ALs7ojAA58B0OALb4XgvxocEI3uDpOrTFKc33rduQPQ5tyCIAm1cNQZbgtM3vnKrTwDFaoCQNQhtL4nYWNztMEz62_hsyM43_1PMx-c-SGD45WTY-XDGYuyxNxY2waWffm6zj_XMu2IPRdv2iO0iwI-B1OQsRPwEL0VW9mFaUfLCGCe-qubQBGE7AmRQX0Q6SmNf0zygrlgSrRn1qdRBTdu6aP9WAa6CavW9snF7bJgzCiuirFd3cYv_lhbsYhOdVZTyGijUlkIdKDxB6zkb8dLnCHY7VWSU-Yr04f3iVnjKd28_w-rSZ1Xzu-VMtYFeBDsEf_X4eYUGpt1EL2OPDxxE_iZ6vlSw8jU6uBNc2IMLB3BhBy4Mk_ESuHAA1xv062C_2vuWhE4cicpZtkiUbkxBdMk1SW3mdiZoZgplpFCpVrDMbHhDpSaMSNAQOpWSqbIB07WBa9KRKd6itfZ3a94hzGlONFVEUS4JFVRwk5KsVLmQQKhRW2g3fqRahTL1tlvKtL6LMVvoc3fFhS_R8p-52_G71-GfndtOrPBQYPcX7x9A6gN61gN9G60tZpfmI3qqrhaT-WzHgeQvcpKPRw |
| linkProvider | IEEE |
| 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=Information-Theoretically+Secure+Erasure+Codes+for+Distributed+Storage&rft.jtitle=IEEE+transactions+on+information+theory&rft.au=Rashmi%2C+K.+V.&rft.au=Shah%2C+Nihar+B.&rft.au=Ramchandran%2C+Kannan&rft.au=Kumar%2C+P.+Vijay&rft.date=2018-03-01&rft.issn=0018-9448&rft.eissn=1557-9654&rft.volume=64&rft.issue=3&rft.spage=1621&rft.epage=1646&rft_id=info:doi/10.1109%2FTIT.2017.2769101&rft.externalDBID=n%2Fa&rft.externalDocID=10_1109_TIT_2017_2769101 |
| 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 |