LDPC Codes for Compressed Sensing
We present a mathematical connection between channel coding and compressed sensing. In particular, we link, on the one hand, channel coding linear programming decoding (CC-LPD), which is a well-known relaxation of maximum-likelihood channel decoding for binary linear codes, and, on the other hand, c...
Saved in:
| Published in | IEEE transactions on information theory Vol. 58; no. 5; pp. 3093 - 3114 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
New York, NY
IEEE
01.05.2012
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.2011.2181819 |
Cover
Loading…
| Abstract | We present a mathematical connection between channel coding and compressed sensing. In particular, we link, on the one hand, channel coding linear programming decoding (CC-LPD), which is a well-known relaxation of maximum-likelihood channel decoding for binary linear codes, and, on the other hand, compressed sensing linear programming decoding (CS-LPD), also known as basis pursuit, which is a widely used linear programming relaxation for the problem of finding the sparsest solution of an underdetermined system of linear equations. More specifically, we establish a tight connection between CS-LPD based on a zero-one measurement matrix over the reals and CC-LPD of the binary linear channel code that is obtained by viewing this measurement matrix as a binary parity-check matrix. This connection allows the translation of performance guarantees from one setup to the other. The main message of this paper is that parity-check matrices of "good" channel codes can be used as provably "good" measurement matrices under basis pursuit. In particular, we provide the first deterministic construction of compressed sensing measurement matrices with an order-optimal number of rows using high-girth low-density parity-check codes constructed by Gallager. |
|---|---|
| AbstractList | We present a mathematical connection between channel coding and compressed sensing. In particular, we link, on the one hand, channel coding linear programming decoding (CC-LPD), which is a well-known relaxation of maximum-likelihood channel decoding for binary linear codes, and, on the other hand, compressed sensing linear programming decoding (CS-LPD), also known as basis pursuit, which is a widely used linear programming relaxation for the problem of finding the sparsest solution of an underdetermined system of linear equations. More specifically, we establish a tight connection between CS-LPD based on a zero-one measurement matrix over the reals and CC-LPD of the binary linear channel code that is obtained by viewing this measurement matrix as a binary parity-check matrix. This connection allows the translation of performance guarantees from one setup to the other. The main message of this paper is that parity-check matrices of "good" channel codes can be used as provably "good" measurement matrices under basis pursuit. In particular, we provide the first deterministic construction of compressed sensing measurement matrices with an order-optimal number of rows using high-girth low-density parity-check codes constructed by Gallager. We present a mathematical connection between channel coding and compressed sensing. In particular, we link, on the one hand, channel coding linear programming decoding (CC-LPD), which is a well-known relaxation of maximum-likelihood channel decoding for binary linear codes, and, on the other hand, compressed sensing linear programming decoding (CS-LPD), also known as basis pursuit, which is a widely used linear programming relaxation for the problem of finding the sparsest solution of an underdetermined system of linear equations. More specifically, we establish a tight connection between CS-LPD based on a zero-one measurement matrix over the reals and CC-LPD of the binary linear channel code that is obtained by viewing this measurement matrix as a binary parity-check matrix. This connection allows the translation of performance guarantees from one setup to the other. The main message of this paper is that parity-check matrices of "good" channel codes can be used as provably "good" measurement matrices under basis pursuit. In particular, we provide the first deterministic construction of compressed sensing measurement matrices with an order-optimal number of rows using high-girth low-density parity-check codes constructed by Gallager. [PUBLICATION ABSTRACT] |
| Author | Smarandache, R. Dimakis, A. G. Vontobel, P. O. |
| Author_xml | – sequence: 1 givenname: A. G. surname: Dimakis fullname: Dimakis, A. G. email: dimakis@usc.edu organization: Dept. of Electr. Eng.-Syst., Univ. of Southern California, Los Angeles, CA, USA – sequence: 2 givenname: R. surname: Smarandache fullname: Smarandache, R. email: rsmarand@sciences.sdsu.edu organization: Dept. of Math. & Stat., San Diego State Univ., San Diego, CA, USA – sequence: 3 givenname: P. O. surname: Vontobel fullname: Vontobel, P. O. email: pascal.vontobel@ieee.org organization: Hewlett-Packard Labs., Palo Alto, CA, USA |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=25827491$$DView record in Pascal Francis |
| BookMark | eNp9kE1LAzEQhoNUsK3eBS8VEbxszWQzu8lR1q9CQcF6Dmk2KynbbE22B_-9KS09eJA5zAw873y8IzLwnbeEXAKdAlB5v5gtpowCTBmIFPKEDAGxzGSBfECGlILIJOfijIxiXKWWI7AhuZ4_vleTqqttnDRdSNV6E2yMtp58WB-d_zonp41uo7045DH5fH5aVK_Z_O1lVj3MM5Mj7zPUYJHVfCmawpSyMFYzQ6mkXKAQ0GhT6hpzjQWiboCDWBY51pJpWtJlTvMxudvP3YTue2tjr9YuGtu22ttuGxVQxmT6QpQJvfmDrrpt8Om6RFGZl1CiSNTtgdLR6LYJ2hsX1Sa4tQ4_iqFgJZeQOLrnTOhiDLY5IkDVzluVvFU7b9XB2yQp_kiM63XvOt8H7dr_hFd7obPWHvcUkCNSzH8BiE2Dzw |
| CODEN | IETTAW |
| CitedBy_id | crossref_primary_10_1007_s40012_016_0144_6 crossref_primary_10_1109_TSP_2014_2386300 crossref_primary_10_1016_j_compeleceng_2018_01_014 crossref_primary_10_1016_j_amc_2019_124965 crossref_primary_10_1109_TIT_2013_2265693 crossref_primary_10_1109_LSP_2016_2585181 crossref_primary_10_1109_ACCESS_2018_2824329 crossref_primary_10_1049_el_2015_3447 crossref_primary_10_4028_www_scientific_net_AMM_644_650_1007 crossref_primary_10_1049_iet_ipr_2015_0117 crossref_primary_10_20535_S0021347013020015 crossref_primary_10_1109_TCCN_2020_2988479 crossref_primary_10_1109_JSEN_2018_2810329 crossref_primary_10_1109_TW_2013_060413_121184 crossref_primary_10_1109_LCOMM_2020_3040535 crossref_primary_10_1109_LSP_2013_2271533 crossref_primary_10_1137_20M1381988 crossref_primary_10_1007_s11767_012_0870_3 crossref_primary_10_1155_2021_9980774 crossref_primary_10_1016_j_ins_2017_11_056 crossref_primary_10_1049_trit_2018_1011 crossref_primary_10_3233_JIFS_179294 crossref_primary_10_1109_TCOMM_2019_2926080 crossref_primary_10_7498_aps_66_090703 crossref_primary_10_1109_TIT_2016_2587772 crossref_primary_10_1016_j_amc_2021_126901 crossref_primary_10_1109_TVLSI_2020_2967477 crossref_primary_10_1109_TIT_2017_2677965 crossref_primary_10_1109_TIT_2012_2208584 crossref_primary_10_1007_s10589_019_00114_9 crossref_primary_10_1109_TIT_2021_3088090 crossref_primary_10_1109_JETCAS_2012_2218512 crossref_primary_10_3390_electronics12092063 crossref_primary_10_1109_TSP_2020_2990154 crossref_primary_10_1109_LSP_2017_2749043 crossref_primary_10_1016_j_bspc_2015_02_016 crossref_primary_10_1016_j_sigpro_2020_107951 crossref_primary_10_1109_ACCESS_2024_3521957 crossref_primary_10_1016_j_memori_2023_100060 crossref_primary_10_1109_TCSI_2018_2803627 crossref_primary_10_1109_LSP_2021_3072572 crossref_primary_10_1007_s00542_017_3351_7 crossref_primary_10_1186_1687_6180_2013_181 crossref_primary_10_1109_LSP_2013_2267656 crossref_primary_10_1587_transcom_2018EBP3247 crossref_primary_10_1007_s11277_017_5079_1 crossref_primary_10_1109_TIT_2019_2921757 crossref_primary_10_1109_TSP_2022_3216708 crossref_primary_10_1016_j_sigpro_2023_109173 crossref_primary_10_3390_s22218260 crossref_primary_10_1109_TMTT_2021_3100499 crossref_primary_10_1049_iet_com_2018_6015 crossref_primary_10_1109_LSP_2015_2447934 crossref_primary_10_1109_TIT_2023_3239163 crossref_primary_10_1587_transinf_2018EDP7324 crossref_primary_10_1007_s11235_017_0294_3 crossref_primary_10_1002_dac_3023 crossref_primary_10_1016_j_image_2019_05_009 crossref_primary_10_3390_e23050605 crossref_primary_10_1049_iet_spr_2016_0026 crossref_primary_10_1142_S0129054117500071 crossref_primary_10_17163_ings_n23_2020_07 crossref_primary_10_1007_s12209_016_2746_3 crossref_primary_10_1109_TAES_2017_2671978 crossref_primary_10_1109_LCOMM_2025_3538910 crossref_primary_10_1587_transcom_2016EBP3018 crossref_primary_10_12677_HJWC_2016_62008 crossref_primary_10_3390_e24081024 crossref_primary_10_1109_TSP_2017_2757915 crossref_primary_10_1109_TSP_2020_3000637 crossref_primary_10_1155_2023_1434736 crossref_primary_10_1109_TIT_2023_3283967 |
| Cites_doi | 10.1109/ITA.2010.5454077 10.1109/TSP.2007.914344 10.7551/mitpress/4347.001.0001 10.1109/ALLERTON.2008.4797558 10.1017/CBO9780511791338 10.1016/j.acha.2008.07.002 10.1109/TIT.2011.2137330 10.1145/375551.375608 10.1109/ALLERTON.2008.4797639 10.1109/TIT.2009.2025528 10.1002/ett.4460090308 10.1109/ISIT.2009.5205910 10.1109/TIT.2007.907501 10.1109/TIT.2009.2032726 10.1109/ISIT.2004.1365106 10.1109/TIT.2009.2016006 10.1109/JPROC.2010.2045092 10.1109/JSTSP.2010.2043161 10.1007/s00454-006-1235-1 10.1109/TIT.2008.926452 10.1109/ISIT.1994.394711 10.1007/978-1-4613-0165-3_5 10.1145/1536414.1536418 10.1145/509907.510003 10.1090/S0894-0347-08-00610-3 10.1109/TSP.2010.2082536 10.1016/j.jco.2007.04.002 10.1109/TIT.2013.2264715 10.1214/08-AOS653 10.1109/ICASSP.2008.4518375 10.1007/s00365-007-9003-x 10.1109/TIT.2006.887523 10.1109/ALLERTON.2009.5394826 10.1109/TIT.2005.862083 10.1109/JCN.2010.6388466 10.1109/ITW.2007.4313110 10.1109/TSP.2010.2049997 10.1109/TIT.2008.924700 10.1006/aima.1996.0050 10.1109/TIT.2007.909108 10.1109/TIT.2004.842696 10.1109/18.556667 10.1016/j.aim.2006.12.010 10.1109/TIT.1981.1056404 10.1109/ISIT.2011.6034170 10.1109/TIT.2003.811926 10.1109/TIT.2006.871582 10.1109/ITW.2006.1633805 10.1137/090748160 10.1109/ALLERTON.2008.4797608 10.1109/ISIT.2005.1523344 10.1109/CCC.2007.38 10.1109/TIT.2005.858979 |
| ContentType | Journal Article |
| Copyright | 2015 INIST-CNRS Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) May 2012 |
| Copyright_xml | – notice: 2015 INIST-CNRS – notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) May 2012 |
| DBID | 97E RIA RIE AAYXX CITATION IQODW 7SC 7SP 8FD JQ2 L7M L~C L~D F28 FR3 |
| DOI | 10.1109/TIT.2011.2181819 |
| 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 ANTE: Abstracts in New Technology & Engineering Engineering Research Database |
| 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 Engineering Research Database ANTE: Abstracts in New Technology & Engineering |
| DatabaseTitleList | Technology Research Database 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 | 3114 |
| ExternalDocumentID | 2643550691 25827491 10_1109_TIT_2011_2181819 6135505 |
| Genre | orig-research Feature |
| 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 F28 FR3 |
| ID | FETCH-LOGICAL-c354t-5a1e52d4b8f6c796cea2c0090485881fac7ad53a5655af1418b635d92a070b303 |
| IEDL.DBID | RIE |
| ISSN | 0018-9448 |
| IngestDate | Fri Jul 11 03:58:16 EDT 2025 Mon Jun 30 03:31:59 EDT 2025 Mon Jul 21 09:14:41 EDT 2025 Tue Jul 01 02:34:31 EDT 2025 Thu Apr 24 23:11:51 EDT 2025 Tue Aug 26 17:18:12 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 5 |
| Keywords | Performance evaluation Approximation guarantee High density pseudocodeword Linear channel Binary code Linear code Relaxation graph cover Linear equation zero-infinity operator Sparse representation Parity check codes Deterministic approach Binary channel Linear programming linear programming decoding basis pursuit Channel coding Maximum likelihood decoding sparse approximation pseudoweight Error correcting code Compressed sensing Parity check |
| Language | English |
| License | https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html CC BY 4.0 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c354t-5a1e52d4b8f6c796cea2c0090485881fac7ad53a5655af1418b635d92a070b303 |
| Notes | SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23 |
| PQID | 1009371758 |
| PQPubID | 36024 |
| PageCount | 22 |
| ParticipantIDs | proquest_journals_1009371758 pascalfrancis_primary_25827491 crossref_primary_10_1109_TIT_2011_2181819 ieee_primary_6135505 proquest_miscellaneous_1022901887 crossref_citationtrail_10_1109_TIT_2011_2181819 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2012-05-01 |
| PublicationDateYYYYMMDD | 2012-05-01 |
| PublicationDate_xml | – month: 05 year: 2012 text: 2012-05-01 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 | 2012 |
| 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 | ref57 ref13 ref12 ref59 ref15 ref53 ref55 ref11 ref54 ref10 ref17 ref16 koetter (ref47) 2006 ref18 vontobel (ref8) 2005 lu (ref38) 2008 zhang (ref19) 2005 ref51 ref50 ref46 ref45 ref42 ref41 ref44 ref43 wiberg (ref27) 1996 ref49 ref9 ref4 ref3 ref6 ref40 dimakis (ref2) 2010 ref35 ref34 forney jr (ref28) 2001; 123 ref36 ref31 ref30 ref33 ref32 feldman (ref5) 2003 ref1 ref39 zhang (ref37) 0 gallager (ref14) 1963 guruswami (ref58) 2008 lin (ref56) 2004 chandar (ref48) 2008 ref24 ref23 ref26 ref25 ref64 ref20 ref63 ref22 ref65 ref21 massey (ref52) 1977; 56 koetter (ref7) 2003 ref29 cands (ref62) 2009; 37 ref60 ref61 |
| References_xml | – ident: ref41 doi: 10.1109/ITA.2010.5454077 – ident: ref59 doi: 10.1109/TSP.2007.914344 – year: 1963 ident: ref14 publication-title: Low-Density Parity-Check Codes doi: 10.7551/mitpress/4347.001.0001 – start-page: 209 year: 2008 ident: ref38 article-title: Counter braids: Asymptotic optimality of the message passing decoding algorithm publication-title: Proc 46th Allerton Conf Commun Control Comput doi: 10.1109/ALLERTON.2008.4797558 – ident: ref23 doi: 10.1017/CBO9780511791338 – year: 2004 ident: ref56 publication-title: Error Control Coding – year: 0 ident: ref37 article-title: On the iterative decoding of high rate LDPC codes with applications in compressed sensing publication-title: IEEE Trans Inf Theory – ident: ref36 doi: 10.1016/j.acha.2008.07.002 – ident: ref61 doi: 10.1109/TIT.2011.2137330 – ident: ref50 doi: 10.1145/375551.375608 – ident: ref11 doi: 10.1109/ALLERTON.2008.4797639 – ident: ref32 doi: 10.1109/TIT.2009.2025528 – ident: ref55 doi: 10.1002/ett.4460090308 – year: 2005 ident: ref19 publication-title: A Simple Proof for Recoverability of -Minimization Go Over or Under? – ident: ref30 doi: 10.1109/ISIT.2009.5205910 – ident: ref29 doi: 10.1109/TIT.2007.907501 – ident: ref63 doi: 10.1109/TIT.2009.2032726 – year: 2008 ident: ref58 article-title: Euclidean sections with sublinear randomness and error-correction over the reals publication-title: Proc 12th Int Workshop Random Comput – ident: ref9 doi: 10.1109/ISIT.2004.1365106 – ident: ref57 doi: 10.1109/TIT.2009.2016006 – ident: ref44 doi: 10.1109/JPROC.2010.2045092 – ident: ref60 doi: 10.1109/JSTSP.2010.2043161 – ident: ref20 doi: 10.1007/s00454-006-1235-1 – ident: ref10 doi: 10.1109/TIT.2008.926452 – ident: ref25 doi: 10.1109/ISIT.1994.394711 – start-page: 75 year: 2003 ident: ref7 article-title: Graph covers and iterative decoding of finite-length codes publication-title: Proc 3rd Int Symp Turbo Codes Related Topics – volume: 123 start-page: 101 year: 2001 ident: ref28 publication-title: Codes Systems and Graphical Models (Minneapolis MN 1999) doi: 10.1007/978-1-4613-0165-3_5 – ident: ref13 doi: 10.1145/1536414.1536418 – year: 1996 ident: ref27 publication-title: Codes and decoding on general graphs – year: 2010 ident: ref2 article-title: Channel coding LP decoding and compressed sensing LP decoding: Further connections publication-title: Proc 2010 Int Zrich Seminar Commun – ident: ref45 doi: 10.1145/509907.510003 – ident: ref22 doi: 10.1090/S0894-0347-08-00610-3 – ident: ref64 doi: 10.1109/TSP.2010.2082536 – ident: ref43 doi: 10.1016/j.jco.2007.04.002 – ident: ref54 doi: 10.1109/TIT.2013.2264715 – volume: 37 start-page: 2145 year: 2009 ident: ref62 article-title: Near-ideal model selection by <formula formulatype="inline"> <tex Notation="TeX">$\ell_{1}$</tex></formula> minimization publication-title: Ann Statist doi: 10.1214/08-AOS653 – ident: ref18 doi: 10.1109/ICASSP.2008.4518375 – ident: ref49 doi: 10.1007/s00365-007-9003-x – ident: ref12 doi: 10.1109/TIT.2006.887523 – ident: ref1 doi: 10.1109/ALLERTON.2009.5394826 – ident: ref15 doi: 10.1109/TIT.2005.862083 – year: 2003 ident: ref5 publication-title: Decoding error-correcting codes via linear programming – ident: ref42 doi: 10.1109/JCN.2010.6388466 – ident: ref31 doi: 10.1109/ITW.2007.4313110 – ident: ref65 doi: 10.1109/TSP.2010.2049997 – year: 2006 ident: ref47 article-title: On the block error probability of LP decoding of LDPC codes publication-title: Proc Inaugural Workshop Center Inf Theory Appl – ident: ref24 doi: 10.1109/TIT.2008.924700 – year: 2008 ident: ref48 publication-title: A Negative Result Concerning Explicit Matrices with the Restricted Isometry Property – ident: ref53 doi: 10.1006/aima.1996.0050 – ident: ref35 doi: 10.1109/TIT.2007.909108 – ident: ref6 doi: 10.1109/TIT.2004.842696 – ident: ref39 doi: 10.1109/18.556667 – ident: ref26 doi: 10.1016/j.aim.2006.12.010 – ident: ref40 doi: 10.1109/TIT.1981.1056404 – ident: ref34 doi: 10.1109/ISIT.2011.6034170 – ident: ref21 doi: 10.1109/TIT.2003.811926 – ident: ref4 doi: 10.1109/TIT.2006.871582 – ident: ref51 doi: 10.1109/ITW.2006.1633805 – ident: ref16 doi: 10.1137/090748160 – volume: 56 year: 1977 ident: ref52 publication-title: Algebraic Topology An Introduction – ident: ref17 doi: 10.1109/ALLERTON.2008.4797608 – ident: ref33 doi: 10.1109/ISIT.2005.1523344 – ident: ref46 doi: 10.1109/CCC.2007.38 – ident: ref3 doi: 10.1109/TIT.2005.858979 – year: 2005 ident: ref8 article-title: Graph-cover decoding and finite-length analysis of message-passing iterative decoding of LDPC codes publication-title: CoRR |
| SSID | ssj0014512 |
| Score | 2.413276 |
| Snippet | We present a mathematical connection between channel coding and compressed sensing. In particular, we link, on the one hand, channel coding linear programming... |
| SourceID | proquest pascalfrancis crossref ieee |
| SourceType | Aggregation Database Index Database Enrichment Source Publisher |
| StartPage | 3093 |
| SubjectTerms | Applied sciences Approximation guarantee Approximation methods basis pursuit Channel coding Channels Coding theory Coding, codes Compressed Compressed sensing Data compression Decoding Detection Exact sciences and technology graph cover Information theory Information, signal and communications theory Linear programming linear programming decoding Low density parity check codes Mathematical analysis Matrices Matrix Matrix methods Maximum likelihood decoding Maximum likelihood method pseudocodeword pseudoweight Sampling, quantization Signal and communications theory sparse approximation Sparse matrices Telecommunications and information theory Vectors zero-infinity operator |
| Title | LDPC Codes for Compressed Sensing |
| URI | https://ieeexplore.ieee.org/document/6135505 https://www.proquest.com/docview/1009371758 https://www.proquest.com/docview/1022901887 |
| Volume | 58 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV1LS8NAEB5qT3qwWhWjtaTgRTBtN82mm6NUSxUrgi14C_uKByUV21789c7khS_EW2An7GZmZ2cmM_sNwClaJYULTDzeNxigCME9hRGYN-xjLBCGvjEhXXCe3oWTeXDzyB9rcF7dhbHWZsVntkuPWS7fLPSafpX10PSQQ70BGxi45Xe1qoxBwFmODM5QgXGeMiXZj3qz61mO1UnmTBCmzicTlPVUoYpIuUSmJHk3ix8Hc2Ztxg2YluvMi0yeu-uV6ur3bxCO__2QHdgu3E73It8nu1CzaRMaZUsHt9DwJmx9wifcg87t5f3IHS2MXbro3LpEn4GNG_eBCt_Tp32Yj69mo4lX9FTw9IAHK49LZrlvAiWSUA-jUFvpa_SzUJG5ECyReigNH0j087hMWMCEQpfERL7Es0GhvTuAerpI7SG4g0QqmWQugQ54YIUMBUZXbBAkwlfD0IFeyeZYF4Dj1PfiJc4Cj34Uo2BiEkxcCMaBs-qN1xxs4w_aPeJrRVew1IH2F0lW4z4XGIBHzIFWKdq4UNclATcTLiDGTg50qmFUNMqeyNQu1kRD0PgMD-Wj36c-hk1coJ9XQ7agvnpb2xP0WFaqnW3VD39n4vQ |
| linkProvider | IEEE |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV1LT8MwDLYGHIADb0RhQJG4INFt6ZouPaLBtMGGkBgStyqvcgB1iG0Xfj12X-IlxK1SXCW149iunc8Ap2iVFC4w8XjLYIAiBPcURmBep4WxQBj6xoR0wXl0G_YfgutH_liD8-oujLU2Kz6zDXrMcvlmouf0q6yJpocc6gVYQrvPWX5bq8oZBJzl2OAMVRhnKpOSrag5HoxztE4yaIJQdT4ZoayrCtVEyimyJcn7Wfw4mjN701uHUbnSvMzkuTGfqYZ-_wbi-N9P2YC1wvF0L_Kdsgk1m27BetnUwS10fAtWPyEUbsPJ8PKu63Ynxk5ddG9dos_gxo17T6Xv6dMOPPSuxt2-V3RV8HSbBzOPS2a5bwIlklB3olBb6Wv0tFCVuRAskbojDW9L9PS4TFjAhEKnxES-xNNBocXbhcV0kto9cNuJVDLJnAId8MAKGQqMr1g7SISvOqEDzZLNsS4gx6nzxUuchR6tKEbBxCSYuBCMA2fVG6853MYftNvE14quYKkDR18kWY37XGAIHjEH6qVo40JhpwTdTMiAGD05cFINo6pR_kSmdjInGgLHZ3gs7_8-9TEs98ejYTwc3N4cwAou1s9rI-uwOHub20P0X2bqKNu2H4G-5j0 |
| 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=LDPC+Codes+for+Compressed+Sensing&rft.jtitle=IEEE+transactions+on+information+theory&rft.au=DIMAKIS%2C+Alexandros+G&rft.au=SMARANDACHE%2C+Roxana&rft.au=VONTOBEL%2C+Pascal+O&rft.date=2012-05-01&rft.pub=Institute+of+Electrical+and+Electronics+Engineers&rft.issn=0018-9448&rft.volume=58&rft.issue=5&rft.spage=3093&rft.epage=3114&rft_id=info:doi/10.1109%2FTIT.2011.2181819&rft.externalDBID=n%2Fa&rft.externalDocID=25827491 |
| 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 |