Bounds on the maximum-likelihood decoding error probability of low-density parity-check codes
We derive both upper and lower bounds on the decoding error probability of maximum-likelihood (ML) decoded low-density parity-check (LDPC) codes. The results hold for any binary-input symmetric-output channel. Our results indicate that for various appropriately chosen ensembles of LDPC codes, reliab...
Saved in:
| Published in: | IEEE transactions on information theory Vol. 47; no. 7; pp. 2696 - 2710 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
IEEE
01.11.2001
|
| Subjects: | |
| ISSN: | 0018-9448 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | We derive both upper and lower bounds on the decoding error probability of maximum-likelihood (ML) decoded low-density parity-check (LDPC) codes. The results hold for any binary-input symmetric-output channel. Our results indicate that for various appropriately chosen ensembles of LDPC codes, reliable communication is possible up to channel capacity. However, the ensemble averaged decoding error probability decreases polynomially, and not exponentially. The lower and upper bounds coincide asymptotically, thus showing the tightness of the bounds. However, for ensembles with suitably chosen parameters, the error probability of almost all codes is exponentially decreasing, with an error exponent that can be set arbitrarily close to the standard random coding exponent. |
|---|---|
| AbstractList | We derive both upper and lower bounds on the decoding error probability of maximum-likelihood (ML) decoded low-density parity-check (LDPC) codes. The results hold for any binary-input symmetric-output channel. Our results indicate that for various appropriately chosen ensembles of LDPC codes, reliable communication is possible up to channel capacity. However, the ensemble averaged decoding error probability decreases polynomially, and not exponentially. The lower and upper bounds coincide asymptotically, thus showing the tightness of the bounds. However, for ensembles with suitably chosen parameters, the error probability of almost all codes is exponentially decreasing, with an error exponent that can be set arbitrarily close to the standard random coding exponent. We derive both upper and lower bounds on the decoding error probability of maximum-likelihood (ML) decoded low-density parity-check (LDPC) codes. The results hold for any binary-input symmetric-output channel. Our results indicate that for various appropriately chosen ensembles of LDPC codes, reliable communication is possible up to channel capacity. However, the ensemble averaged decoding error probability decreases polynomially, and not exponentially. The lower and upper bounds coincide asymptotically, thus showing the tightness of the bounds. However, for ensembles with suitably chosen parameters, the error probability of almost all codes is exponentially decreasing, with an error exponent that can be set arbitrarily close to the standard random coding exponent |
| Author | Miller, G. Burshtein, D. |
| Author_xml | – sequence: 1 givenname: G. surname: Miller fullname: Miller, G. organization: Dept. of Electr. Eng. Syst., Tel Aviv Univ., Israel – sequence: 2 givenname: D. surname: Burshtein fullname: Burshtein, D. |
| BookMark | eNp9kL1PwzAUxD0UibYwsDJ5QjCk9UvixBmh4kuqxAIjihz7mZomcbFTQf97UqViQIjpdHq_Oz3dhIxa1yIhZ8BmAKyYg5gVvIh5OiJjxkBERZqKYzIJ4b23KYd4TF5v3LbVgbqWdiukjfyyzbaJarvG2q6c01Sjctq2bxS9d55uvKtkZWvb7agztHafkcY27O1G-l4itUK1pn0Iwwk5MrIOeHrQKXm5u31ePETLp_vHxfUyUkmedRFoKEyag9IJxCKRlWI8M4mIc6FjITnTHBKDBlVlpGBZJlmVFpKbOJe8yuNkSi6G3v67jy2GrmxsUFjXskW3DWUsQGSM8x68_BeELIeE5QXsO-cDqrwLwaMple1kZ13beWnrEli5X7kEUQ4r94mrX4mNt430uz_Z84G1iPjDHY7fT9yJlQ |
| CODEN | IETTAW |
| CitedBy_id | crossref_primary_10_1109_TMAG_2002_801877 crossref_primary_10_1109_TIT_2006_883619 crossref_primary_10_1109_TIT_2004_824918 crossref_primary_10_1109_TIT_2013_2294373 crossref_primary_10_1109_TIT_2004_824917 crossref_primary_10_1109_TIT_2005_853320 crossref_primary_10_1109_TIT_2020_3037533 crossref_primary_10_1109_TIT_2007_892807 crossref_primary_10_1109_TIT_2006_883541 crossref_primary_10_1109_TSP_2004_823508 crossref_primary_10_1109_TIT_2005_846431 crossref_primary_10_1109_TIT_2005_856942 crossref_primary_10_1587_transfun_E95_A_790 crossref_primary_10_1137_070686615 crossref_primary_10_1109_JSAC_2015_2507758 crossref_primary_10_1109_TIT_2016_2647724 crossref_primary_10_1109_TIT_2002_801408 crossref_primary_10_1088_1742_6596_143_1_012018 crossref_primary_10_1109_TIT_2003_820012 crossref_primary_10_1109_TIT_2006_871615 crossref_primary_10_1109_TIT_2013_2252394 crossref_primary_10_1109_TIT_2017_2678531 crossref_primary_10_1109_JSAC_2009_090815 crossref_primary_10_1109_TIT_2011_2158489 crossref_primary_10_1109_TIT_2015_2449852 crossref_primary_10_1109_TIT_2009_2015992 crossref_primary_10_1109_TIT_2015_2496352 crossref_primary_10_1109_TIT_2004_828064 crossref_primary_10_1109_TIT_2007_899543 crossref_primary_10_1109_TIT_2015_2504100 crossref_primary_10_1109_TIT_2005_855604 crossref_primary_10_1109_TIT_2003_813560 crossref_primary_10_1109_18_910588 crossref_primary_10_1109_TIT_2015_2453267 crossref_primary_10_1109_TIT_2008_928274 crossref_primary_10_1109_TIT_2009_2018344 crossref_primary_10_1109_TCOMM_2004_826242 crossref_primary_10_1109_18_971742 crossref_primary_10_1088_0305_4470_36_43_032 crossref_primary_10_1109_TIT_2009_2039084 crossref_primary_10_1109_TIT_2011_2132570 crossref_primary_10_1109_TIT_2003_818403 crossref_primary_10_1109_TIT_2008_2011443 crossref_primary_10_1109_TIT_2007_915705 crossref_primary_10_1109_TIT_2005_850144 crossref_primary_10_1109_TIT_2012_2184673 crossref_primary_10_1109_TCOMM_2010_082710_090195 crossref_primary_10_1109_TIFS_2011_2139208 crossref_primary_10_1109_TIT_2010_2043781 crossref_primary_10_1109_TWC_2007_05725 crossref_primary_10_1109_18_992777 crossref_primary_10_1109_TIT_2016_2567638 crossref_primary_10_1109_JSAC_2014_140517 crossref_primary_10_1109_TIT_2007_907448 crossref_primary_10_1109_TIT_2003_815805 |
| Cites_doi | 10.1109/4234.831034 10.1109/18.335935 10.1007/978-3-7091-2945-6 10.7551/mitpress/4347.001.0001 10.1109/18.910576 10.1109/18.782147 10.1002/0471200611 10.1109/18.910577 10.1109/18.992777 10.1109/18.748992 10.1109/18.556667 10.1109/icc.1993.397441 |
| ContentType | Journal Article |
| DBID | RIA RIE AAYXX CITATION 7SC 7SP 8FD F28 FR3 JQ2 L7M L~C L~D |
| DOI | 10.1109/18.959254 |
| DatabaseName | IEEE All-Society Periodicals Package (ASPP) 1998–Present IEEE Electronic Library (IEL) CrossRef Computer and Information Systems Abstracts Electronics & Communications Abstracts Technology Research Database ANTE: Abstracts in New Technology & Engineering Engineering 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 Engineering Research Database Advanced Technologies Database with Aerospace ANTE: Abstracts in New Technology & Engineering Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Computer and Information Systems Abstracts 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 Computer Science |
| EndPage | 2710 |
| ExternalDocumentID | 10_1109_18_959254 959254 |
| 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 AAYXX CITATION 7SC 7SP 8FD F28 FR3 JQ2 L7M L~C L~D |
| ID | FETCH-LOGICAL-c376t-1d19f471cd31283abc056f38278d28a50d513fefecbfa8066a0b49a5f27a5b723 |
| IEDL.DBID | RIE |
| ISICitedReferencesCount | 117 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000171700300002&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 | Sat Sep 27 22:38:21 EDT 2025 Sun Sep 28 02:14:00 EDT 2025 Sat Nov 29 08:03:09 EST 2025 Tue Nov 18 22:38:04 EST 2025 Tue Aug 26 21:00:30 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 7 |
| Language | English |
| License | https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c376t-1d19f471cd31283abc056f38278d28a50d513fefecbfa8066a0b49a5f27a5b723 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 ObjectType-Article-2 ObjectType-Feature-1 |
| PQID | 1671307912 |
| PQPubID | 23500 |
| PageCount | 15 |
| ParticipantIDs | proquest_miscellaneous_1671307912 ieee_primary_959254 proquest_miscellaneous_28186055 crossref_primary_10_1109_18_959254 crossref_citationtrail_10_1109_18_959254 |
| PublicationCentury | 2000 |
| PublicationDate | 2001-11-01 |
| PublicationDateYYYYMMDD | 2001-11-01 |
| PublicationDate_xml | – month: 11 year: 2001 text: 2001-11-01 day: 01 |
| PublicationDecade | 2000 |
| PublicationTitle | IEEE transactions on information theory |
| PublicationTitleAbbrev | TIT |
| PublicationYear | 2001 |
| Publisher | IEEE |
| Publisher_xml | – name: IEEE |
| References | ref12 ref11 ref10 Zyablov (ref13) 1976; 11 ref2 ref1 ref8 ref7 ref9 ref4 ref3 ref6 ref5 |
| References_xml | – ident: ref10 doi: 10.1109/4234.831034 – ident: ref8 doi: 10.1109/18.335935 – ident: ref4 doi: 10.1007/978-3-7091-2945-6 – ident: ref3 doi: 10.7551/mitpress/4347.001.0001 – ident: ref6 doi: 10.1109/18.910576 – ident: ref11 doi: 10.1109/18.782147 – ident: ref2 doi: 10.1002/0471200611 – ident: ref9 doi: 10.1109/18.910577 – ident: ref5 doi: 10.1109/18.992777 – ident: ref7 doi: 10.1109/18.748992 – ident: ref12 doi: 10.1109/18.556667 – volume: 11 start-page: 18 issue: 1 year: 1976 ident: ref13 article-title: Estimation of the error-correction complexity for Gallager low-density codes publication-title: Probl. Inform. Transm. – ident: ref1 doi: 10.1109/icc.1993.397441 |
| SSID | ssj0014512 |
| Score | 2.0782835 |
| Snippet | We derive both upper and lower bounds on the decoding error probability of maximum-likelihood (ML) decoded low-density parity-check (LDPC) codes. The results... |
| SourceID | proquest crossref ieee |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 2696 |
| SubjectTerms | Asymptotic properties Channels Decoding Error detection coding Errors Exponents Tightness Upper bounds |
| Title | Bounds on the maximum-likelihood decoding error probability of low-density parity-check codes |
| URI | https://ieeexplore.ieee.org/document/959254 https://www.proquest.com/docview/1671307912 https://www.proquest.com/docview/28186055 |
| Volume | 47 |
| WOSCitedRecordID | wos000171700300002&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) issn: 0018-9448 databaseCode: RIE dateStart: 19630101 customDbUrl: isFulltext: true dateEnd: 99991231 titleUrlDefault: https://ieeexplore.ieee.org/ omitProxy: false ssIdentifier: ssj0014512 providerName: IEEE |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV07T8MwED4BYoCBRwFRngYxsKSNkziJR0AgBoQYQGJBkeOHVLVNUNry-PecnbQCUQa2JLpEkc_nu_P5vg_gjBlfKSG5J7jmXhRrtDmT-2hXJhRcGJxkDjL_Lrm_T5-f-UODs-16YbTW7vCZ7thLV8tXpZzYrbIuZxzzmUVYTJK4btWaFQwiRmtgcIr2iylHAyJEfd6laad-8YfrcVwqvxZg51Vu1v_1Pxuw1gSP5KLW9iYs6KIF61NiBtLYaQtWv6EMbsHLpaVOGpGyIBjtkaH46A0nQ2_Q6-tBz6IaE4U5qPVhRFdVWRFLMlPDd3-S0pBB-e4pe84dby1n4fjTQ03LPrHt8KNteLq5fry69RpWBU_iYjL2qKLcoEuSKkTfFIpcYgxkwjRIUhWkgvmK0dBoo2VuRIoRifDziAtmgkSwPAnCHVgqykLvAgmlFnHqaxmHccRNkFMmc27pkCIc-SBpw_l0wDPZQI5b5otB5lIPn2c0zepBbMPpTPS1xtmYJ9SySpgJTJ-eTJWYoW3YgocodDkZZTTGFNxPOA3acPyHjEXDwpSO7c399j6suENnrvnwAJbG1UQfwrJ8G_dG1ZGbgl8UCtxp |
| linkProvider | IEEE |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1Nj9MwEB1BQQIOu9BdRFmgBnHgkjZO4iQ-7iKqrrZUHIrUyypy_CFFbROUtkD_PWMnrUDbPXBLokkUeTyeGY_nPYCPzPhKCck9wTX3olijzZncR7syoeDC4CRzkPmTZDpN53P-rcXZdr0wWmt3-EwP7KWr5atKbu1W2ZAzjvnMQ3hkibNY06x1KBlEjDbQ4BQtGJOOFkaI-nxI00Hz6j_Ox7Gp3FmCnV8Znf7XHz2HkzZ8JJeNvl_AA1124XRPzUBaS-3Cs79wBs_g9sqSJ61JVRKM98hK_C5W25W3LBZ6WVhcY6IwC7VejOi6rmpiaWYaAO8dqQxZVr88ZU-6461lLdzsPNS1XBDbEL8-h--jL7PPY6_lVfAkLicbjyrKDTolqUL0TqHIJUZBJkyDJFVBKpivGA2NNlrmRqQYkwg_j7hgJkgEy5MgfAmdsir1KyCh1CJOfS3jMI64CXLKZM4tIVKEIx8kPfi0H_BMtqDjlvtimbnkw-cZTbNmEHvw4SD6o0HaOCbUtUo4COyfvt8rMUPrsCUPUepqu85ojEm4n3Aa9KB_j4zFw8Kkjr0--u0-PBnPvk6yyfX05gKeuiNorhXxDXQ29Va_hcfy56ZY1-_cdPwDuJHftA |
| 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=Bounds+on+the+maximum-likelihood+decoding+error+probability+of+low-density+parity-check+codes&rft.jtitle=IEEE+transactions+on+information+theory&rft.au=Miller%2C+G&rft.au=Burshtein%2C+D&rft.date=2001-11-01&rft.issn=0018-9448&rft.volume=47&rft.issue=7&rft.spage=2696&rft.epage=2710&rft_id=info:doi/10.1109%2F18.959254&rft.externalDBID=NO_FULL_TEXT |
| 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 |