Iterative Hard-Decision Decoding Algorithms for Binary Reed-Muller Codes

In this paper, novel hard-decision iterative decoding algorithms for binary Reed-Muller (RM) codes are presented. First, two algorithms are devised based on the majority-logic decoding algorithm with reliability measures of the received sequence. The bit-flipping (BF) and the normalized bit-flipping...

Celý popis

Uložené v:

Podrobná bibliografia
Vydané v:	IEEE access Ročník 10; s. 1
Hlavní autori:	Ni, Yong-Ting, Nguyen, Duc Nhat, Liao, Feng-Kai, Kao, Tzu-Chieh, Chen, Chao-Yu
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Piscataway IEEE 01.01.2022 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:	Algorithms Binary codes Binary system bit-flipping Codes Decoding Generators Iterative decoding Iterative methods majority-logic decoding Maximum likelihood decoding Normalizing Polar codes Reed-Muller code Reed-Muller codes Reliability
ISSN:	2169-3536, 2169-3536
On-line prístup:	Získať plný text
Tagy:	Pridať tag Žiadne tagy, Buďte prvý, kto otaguje tento záznam!

Abstract	In this paper, novel hard-decision iterative decoding algorithms for binary Reed-Muller (RM) codes are presented. First, two algorithms are devised based on the majority-logic decoding algorithm with reliability measures of the received sequence. The bit-flipping (BF) and the normalized bit-flipping (NBF) decoding algorithms are hard-decision decoding algorithms. According to the updated hard reliability measures, the BF and NBF algorithms flip one bit of the received hard-decision sequence at a time in each iteration. The NBF decoding algorithm performs better than the BF decoding algorithm by normalizing the reliability measures of the information bits. Moreover, the BF and NBF algorithms are modified to flip multiple bits in one iteration to reduce the average number of iterations. The modified decoding algorithms are called the multiple-bits-flipping (MBF) algorithm and the normalized multiple-bits-flipping (NMBF) algorithm, respectively. The proposed algorithms have low computational complexities and can converge rapidly after a small number of iterations. The simulation results show that the proposed hard-decision decoding algorithms outperform the conventional decoding algorithm.
AbstractList	In this paper, novel hard-decision iterative decoding algorithms for binary Reed-Muller (RM) codes are presented. First, two algorithms are devised based on the majority-logic decoding algorithm with reliability measures of the received sequence. The bit-flipping (BF) and the normalized bit-flipping (NBF) decoding algorithms are hard-decision decoding algorithms. According to the updated hard reliability measures, the BF and NBF algorithms flip one bit of the received hard-decision sequence at a time in each iteration. The NBF decoding algorithm performs better than the BF decoding algorithm by normalizing the reliability measures of the information bits. Moreover, the BF and NBF algorithms are modified to flip multiple bits in one iteration to reduce the average number of iterations. The modified decoding algorithms are called the multiple-bits-flipping (MBF) algorithm and the normalized multiple-bits-flipping (NMBF) algorithm, respectively. The proposed algorithms have low computational complexities and can converge rapidly after a small number of iterations. The simulation results show that the proposed hard-decision decoding algorithms outperform the conventional decoding algorithm.
Author	Ni, Yong-Ting Nguyen, Duc Nhat Liao, Feng-Kai Kao, Tzu-Chieh Chen, Chao-Yu
Author_xml	– sequence: 1 givenname: Yong-Ting surname: Ni fullname: Ni, Yong-Ting organization: Department of Engineering Science, National Cheng Kung University, Tainan 701, Taiwan, R.O.C – sequence: 2 givenname: Duc Nhat surname: Nguyen fullname: Nguyen, Duc Nhat organization: Department of Engineering Science, National Cheng Kung University, Tainan 701, Taiwan, R.O.C – sequence: 3 givenname: Feng-Kai surname: Liao fullname: Liao, Feng-Kai organization: Department of Engineering Science, National Cheng Kung University, Tainan 701, Taiwan, R.O.C – sequence: 4 givenname: Tzu-Chieh surname: Kao fullname: Kao, Tzu-Chieh organization: Department of Engineering Science, National Cheng Kung University, Tainan 701, Taiwan, R.O.C – sequence: 5 givenname: Chao-Yu surname: Chen fullname: Chen, Chao-Yu organization: Department of Engineering Science, National Cheng Kung University, Tainan 701, Taiwan, R.O.C
BookMark	eNpNUcFq3DAQFSWFJmm-IBdDz95IGkmWjlsn7S6kBJL2LGRrtNXiWKnkDfTv642X0LnMY-a9NwPvgpyNaURCrhldMUbNzbpt756eVpxyvgKmKSj9gZxzpkwNEtTZf_gTuSplT-fS80g252SznTC7Kb5itXHZ17fYxxLTWM0g-TjuqvWwSzlOv59LFVKuvsbR5b_VI6KvfxyGAXPVJo_lM_kY3FDw6tQvya9vdz_bTX3_8H3bru_rHqSeamM00A51x5Er3QvPPPZCycAUuEajVyA647T3vQgYaEdh3kNnJNd9CAiXZLv4-uT29iXH5_kdm1y0b4OUd9blKfYDWu2l8sKFzoERrGscCu4dNJ4ZQCmPXl8Wr5ec_hywTHafDnmc37dcNZIKIRnMLFhYfU6lZAzvVxm1xwTskoA9JmBPCcyq60UVEfFdYRptmGDwD-yRg24
CODEN	IAECCG
Cites_doi	10.1109/TIT.2009.2021379 10.1109/TIT.2005.864443 10.1109/ISIT44484.2020.9174087 10.1109/TIT.1962.1057683 10.1109/ISTC.2018.8625281 10.1109/18.817523 10.1109/TCOMM.2014.2345069 10.1109/TSP.2015.2439211 10.1109/18.370093 10.1109/ISIT.2019.8849320 10.1109/TIT.1954.1057465 10.1109/IREPGELC.1954.6499441 10.1109/LCOMM.2004.825737 10.1049/el.2011.3334 10.1109/MCOM.2014.6852102 10.1109/LCOMM.2008.080017 10.1109/LCOMM.2012.090312.121501 10.1109/ISIT.2019.8849214 10.1109/TIT.2004.826632 10.1109/26.774831 10.1109/TIT.2005.864425 10.1109/26.768759 10.1109/TIT.2004.831835 10.1109/TIT.2020.2977917 10.1109/TIT.2015.2410251
ContentType	Journal Article
Copyright	Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2022
Copyright_xml	– notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2022
DBID	97E ESBDL RIA RIE AAYXX CITATION 7SC 7SP 7SR 8BQ 8FD JG9 JQ2 L7M L~C L~D DOA
DOI	10.1109/ACCESS.2022.3180368
DatabaseName	IEEE All-Society Periodicals Package (ASPP) 2005–Present IEEE Xplore Open Access Journals IEEE All-Society Periodicals Package (ASPP) 1998–Present IEEE Electronic Library (IEL) CrossRef Computer and Information Systems Abstracts Electronics & Communications Abstracts Engineered Materials Abstracts METADEX Technology Research Database Materials Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional DOAJ Directory of Open Access Journals
DatabaseTitle	CrossRef Materials Research Database Engineered Materials Abstracts 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 METADEX Computer and Information Systems Abstracts Professional
DatabaseTitleList	Materials Research Database
Database_xml	– sequence: 1 dbid: DOA name: DOAJ Directory of Open Access Journals url: https://www.doaj.org/ sourceTypes: Open Website – sequence: 2 dbid: RIE name: IEEE/IET Electronic Library (IEL) (UW System Shared) url: https://ieeexplore.ieee.org/ sourceTypes: Publisher
DeliveryMethod	fulltext_linktorsrc
Discipline	Engineering
EISSN	2169-3536
EndPage	1
ExternalDocumentID	oai_doaj_org_article_8d56d4afba3941b7ae42da37d193e55e 10_1109_ACCESS_2022_3180368 9789141
Genre	orig-research
GrantInformation_xml	– fundername: Ministry of Science and Technology Taiwan grantid: MOST 109--2628--E--006--008--MY3; MOST 110--2224--E--305--001 funderid: 10.13039/501100004663
GroupedDBID	0R~ 5VS 6IK 97E AAJGR ABAZT ABVLG ACGFS ADBBV ALMA_UNASSIGNED_HOLDINGS BCNDV BEFXN BFFAM BGNUA BKEBE BPEOZ EBS ESBDL GROUPED_DOAJ IPLJI JAVBF KQ8 M43 M~E O9- OCL OK1 RIA RIE RNS 4.4 AAYXX AGSQL CITATION EJD 7SC 7SP 7SR 8BQ 8FD JG9 JQ2 L7M L~C L~D
ID	FETCH-LOGICAL-c358t-99830be8b2e268c4d1dec465f163a78ed634b9a8ddc4fef0b03ec43b9528cffe3
IEDL.DBID	DOA
ISICitedReferencesCount	0
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000809369600001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	2169-3536
IngestDate	Fri Oct 03 12:52:48 EDT 2025 Sun Jun 29 12:22:56 EDT 2025 Sat Nov 29 06:32:10 EST 2025 Wed Aug 27 02:24:35 EDT 2025
IsDoiOpenAccess	true
IsOpenAccess	true
IsPeerReviewed	true
IsScholarly	true
Language	English
License	https://creativecommons.org/licenses/by/4.0/legalcode
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c358t-99830be8b2e268c4d1dec465f163a78ed634b9a8ddc4fef0b03ec43b9528cffe3
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ORCID	0000-0002-3717-5600
OpenAccessLink	https://doaj.org/article/8d56d4afba3941b7ae42da37d193e55e
PQID	2675044513
PQPubID	4845423
PageCount	1
ParticipantIDs	crossref_primary_10_1109_ACCESS_2022_3180368 proquest_journals_2675044513 doaj_primary_oai_doaj_org_article_8d56d4afba3941b7ae42da37d193e55e ieee_primary_9789141
PublicationCentury	2000
PublicationDate	2022-01-01
PublicationDateYYYYMMDD	2022-01-01
PublicationDate_xml	– month: 01 year: 2022 text: 2022-01-01 day: 01
PublicationDecade	2020
PublicationPlace	Piscataway
PublicationPlace_xml	– name: Piscataway
PublicationTitle	IEEE access
PublicationTitleAbbrev	Access
PublicationYear	2022
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	ref13 ref12 ref15 Ni (ref26) ref14 ref11 ref10 ref2 ref1 ref17 ref16 ref19 ref18 MacWilliams (ref28) 1977 ref24 ref23 ref25 ref20 ref22 ref21 ref8 ref7 ref9 ref4 ref3 ref6 ref5 Green (ref27) 1966; 4
References_xml	– ident: ref12 doi: 10.1109/TIT.2009.2021379 – ident: ref9 doi: 10.1109/TIT.2005.864443 – ident: ref11 doi: 10.1109/ISIT44484.2020.9174087 – ident: ref25 doi: 10.1109/TIT.1962.1057683 – ident: ref15 doi: 10.1109/ISTC.2018.8625281 – start-page: 1 volume-title: Proc. Int. Symp. Inf. Theory Appl. (ISITA) ident: ref26 article-title: An iterative bit-flipping decoding algorithm for binary Reed–Müller codes – ident: ref6 doi: 10.1109/18.817523 – ident: ref17 doi: 10.1109/TCOMM.2014.2345069 – ident: ref20 doi: 10.1109/TSP.2015.2439211 – ident: ref3 doi: 10.1109/18.370093 – ident: ref21 doi: 10.1109/ISIT.2019.8849320 – ident: ref2 doi: 10.1109/TIT.1954.1057465 – ident: ref1 doi: 10.1109/IREPGELC.1954.6499441 – ident: ref23 doi: 10.1109/LCOMM.2004.825737 – ident: ref18 doi: 10.1049/el.2011.3334 – ident: ref14 doi: 10.1109/MCOM.2014.6852102 – ident: ref16 doi: 10.1109/LCOMM.2008.080017 – volume: 4 start-page: 247 issue: 37 year: 1966 ident: ref27 article-title: A serial orthogonal decoder publication-title: JPL Space Programs Summary – ident: ref13 doi: 10.1109/LCOMM.2012.090312.121501 – ident: ref22 doi: 10.1109/ISIT.2019.8849214 – ident: ref7 doi: 10.1109/TIT.2004.826632 – ident: ref4 doi: 10.1109/26.774831 – ident: ref8 doi: 10.1109/TIT.2005.864425 – ident: ref24 doi: 10.1109/26.768759 – ident: ref5 doi: 10.1109/TIT.2004.831835 – volume-title: The Theory of Error-Correcting Codes year: 1977 ident: ref28 – ident: ref10 doi: 10.1109/TIT.2020.2977917 – ident: ref19 doi: 10.1109/TIT.2015.2410251
SSID	ssj0000816957
Score	2.22795
Snippet	In this paper, novel hard-decision iterative decoding algorithms for binary Reed-Muller (RM) codes are presented. First, two algorithms are devised based on...
SourceID	doaj proquest crossref ieee
SourceType	Open Website Aggregation Database Index Database Publisher
StartPage	1
SubjectTerms	Algorithms Binary codes Binary system bit-flipping Codes Decoding Generators Iterative decoding Iterative methods majority-logic decoding Maximum likelihood decoding Normalizing Polar codes Reed-Muller code Reed-Muller codes Reliability
SummonAdditionalLinks	– databaseName: IEEE Electronic Library (IEL) dbid: RIE link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1Lb9QwEB6VigMcWqCgLhTkA8cGkvh93C5URYIKIZB6s2J7DJVgU-1u-f0dO-6qCC6cYiVx5HwTex7OfAPwWokYuDGiCUmTg2L62JiUk91t6zuDqRtSkfRHfX5uLi7s5x043ubCIGL5-Qzf5GbZy49juM6hsswGa7ucpX5PazXlam3jKbmAhJW6Egt1rX07XyzoHcgF7HvyTA0t1eYP5VM4-mtRlb9W4qJeTvf_b2CPYK-akWw-yf0x7ODyCTy8Qy54AGcfCmEyrWYsb88372o1HUaNMWssNv_5fVxdbn78WjMyXdlJSc1lX0ifNZ8yK_eKLcaI66fw7fT918VZU-smNIFLs2nIg-KtR-N77JUJInYRg1Ayke01aINRceHtYGIMImFqfcvpOvdW9iakhPwZ7C7HJR4CGxRSPzKalEoieWFkTDp5a4NMdDAzOL4F1F1N9BiuuBWtdRP-LuPvKv4zOMmgb2_N3NblBKHp6lRxJkoVxZD8wK3ovB5Q9HHgOpKtiVLiDA6yBLYPqeDP4OhWhK7Ow7XrVaavF7Ljz__d6wU8yAOcgipHsLtZXeNLuB9-by7Xq1flE7sB6r_Qig priority: 102 providerName: IEEE
Title	Iterative Hard-Decision Decoding Algorithms for Binary Reed-Muller Codes
URI	https://ieeexplore.ieee.org/document/9789141 https://www.proquest.com/docview/2675044513 https://doaj.org/article/8d56d4afba3941b7ae42da37d193e55e
Volume	10
WOSCitedRecordID	wos000809369600001&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: PRVAON databaseName: DOAJ Directory of Open Access Journals customDbUrl: eissn: 2169-3536 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000816957 issn: 2169-3536 databaseCode: DOA dateStart: 20130101 isFulltext: true titleUrlDefault: https://www.doaj.org/ providerName: Directory of Open Access Journals – providerCode: PRVHPJ databaseName: ROAD: Directory of Open Access Scholarly Resources customDbUrl: eissn: 2169-3536 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000816957 issn: 2169-3536 databaseCode: M~E dateStart: 20130101 isFulltext: true titleUrlDefault: https://road.issn.org providerName: ISSN International Centre
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LT9tAEF5VEYf2gKBQkRKiPXCshdf78OwxBKJUIlFVFYnbyvuilUqCkpQjv53ZtUFBHHrhYlt-rL3f2DPz2d5vCDlVwjsOIAoXayQoUPkCYhrsrkvLIETWxGzpq3o-h5sb_WOr1Ff6J6yVB26BOwMvlRdNtA3Xgtm6CaLyDa89Zh5BypC8b1nrLTKVfTAwpWXdyQyxUp-NxmPsERLCqkKeCui44VUoyor9XYmVN345B5vJHtntskQ6aq9un3wIi8_k05Z24AGZfs96yOisaPr6Xlx0xXIoLixTQKKjv7dLpP6_79YUM1N6nkfe0p8YropZEt1e0fHSh_UhuZ5c_hpPi64sQuG4hE2BBImXNoCtQqXACc98cELJiKlVU0PwigurG_DeiRhiaUuO27nVsgIXY-BfSG-xXIQjQhsV8DjMiZSKIloB0sc6Wq2djDiDPvn2jJC5b9UvTGYNpTYtoCYBajpA--Q8ofiya5KuzivQoKYzqPmfQfvkINngpRGkuZoJ1ieDZ5uY7jFbm0oldXohGf_6Hqc-Jh9Td9o3LAPS26z-hROy4x42f9arYb7DcDp7vBzmcYJPrPnWbQ
linkProvider	Directory of Open Access Journals
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1Lb9QwEB5VBalwANqCWCjgQ49NSfyKfdwuVFuxXVVVK_Vmxfa4VIIN2t3y-7EddwWCC6dYSRw538SehzPfABxK7h1TilcutNFBUdRXKqRkd13bRmFoupAlPWvnc3Vzoy-24GiTC4OI-eczPE7NvJfve3efQmWJDVY3KUv9keCc1kO21iaikkpIaNEWaqGm1h_Hk0l8i-gEUhp9UxUXa_WH-sks_aWsyl9rcVYwp8__b2gv4FkxJMl4kPwubOFiD57-Ri-4D9OzTJkc1zOSNuirT6WeDomNPuksMv522y_v1l-_r0g0XslJTs4ll1GjVeeJl3tJJr3H1Uu4Pv18NZlWpXJC5ZhQ6yr6UKy2qCxFKpXjvvHouBQhWl9dq9BLxq3ulPeOBwy1rVm8zqwWVLkQkL2C7UW_wNdAOomxXzSbpAw8WK6ED22wWjsR4kGN4OgBUPNjIMgw2bGotRnwNwl_U_AfwUkCfXNrYrfOJyKapkwWo7yQnnfBdkzzxrYdcuo71vpobaIQOIL9JIHNQwr4Izh4EKEpM3FlqEwE9lw07M2_e32AnenV-czMzuZf3sKTNNghxHIA2-vlPb6Dx-7n-m61fJ8_t1_qK9PR
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=Iterative+Hard-Decision+Decoding+Algorithms+for+Binary+Reed-Muller+Codes&rft.jtitle=IEEE+access&rft.au=Ni%2C+Yong-Ting&rft.au=Nguyen%2C+Duc+Nhat&rft.au=Liao%2C+Feng-Kai&rft.au=Kao%2C+Tzu-Chieh&rft.date=2022-01-01&rft.issn=2169-3536&rft.eissn=2169-3536&rft.volume=10&rft.spage=59373&rft.epage=59382&rft_id=info:doi/10.1109%2FACCESS.2022.3180368&rft.externalDBID=n%2Fa&rft.externalDocID=10_1109_ACCESS_2022_3180368
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2169-3536&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2169-3536&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2169-3536&client=summon