m -ary Balanced Codes With Parallel Decoding

An m-ary block code, m = 2, 3, 4,..., of length n ϵ IN is called balanced if, and only if, every codeword is balanced; that is, the real sum of the codeword components, or weight, is equal to ⌊(m - 1)n/2⌋. This paper presents efficient encoding schemes to m-ary balanced codes with parallel (hence, f...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	IEEE transactions on information theory Jg. 61; H. 6; S. 3251 - 3264
Hauptverfasser:	Pelusi, Danilo, Elmougy, Samir, Tallini, Luca G., Bose, Bella
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York IEEE 01.06.2015 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:	Balanced codes Coding theory Combinatorics Decoding Electronics Encoding Frequency modulation Indexes Knuth's complementation method m-ary alphabet optical and magnetic recording parallel decoding scheme Redundancy Time complexity unidirectional error detection optical and magnetic recording Balanced codes parallel decoding scheme unidirectional error detection m -ary alphabet Knuth’s complementation method
ISSN:	0018-9448, 1557-9654
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Abstract	An m-ary block code, m = 2, 3, 4,..., of length n ϵ IN is called balanced if, and only if, every codeword is balanced; that is, the real sum of the codeword components, or weight, is equal to ⌊(m - 1)n/2⌋. This paper presents efficient encoding schemes to m-ary balanced codes with parallel (hence, fast) decoding. In fact, the decoding time complexity is O(1) digit operations. These schemes are a generalization to the m-ary alphabet of Knuth's complementation method with parallel decoding. Let ( n w ) m indicate the number of m-ary words w of length n and weight w ϵ(0,1, ... , (m - 1)n}. For any m ϵ IN, m ≥ 2, a simple implementation of the method is given which uses r ϵ IN check digits to balance k ≤ {(⌊(m-1) r /2⌋) m - (m mod 2 + [(m - 1)k] mod 2}}/(m - 1) information digits with an encoding time complexity of O(mk log m k) digit operations. A refined implementation of the parallel decoding method is also given with r check digits and k ≤ (m r -1)/(m -1) information digits, where the encoding time complexity is O(k√log m k). Thus, the proposed codes are less redundant than the m-ary balanced codes with parallel decoding found in the literature and yet maintain the same complexity.
AbstractList	An m-ary block code, m = 2, 3, 4,..., of length n ϵ IN is called balanced if, and only if, every codeword is balanced; that is, the real sum of the codeword components, or weight, is equal to ⌊(m - 1)n/2⌋. This paper presents efficient encoding schemes to m-ary balanced codes with parallel (hence, fast) decoding. In fact, the decoding time complexity is O(1) digit operations. These schemes are a generalization to the m-ary alphabet of Knuth's complementation method with parallel decoding. Let ( n w ) m indicate the number of m-ary words w of length n and weight w ϵ(0,1, ... , (m - 1)n}. For any m ϵ IN, m ≥ 2, a simple implementation of the method is given which uses r ϵ IN check digits to balance k ≤ {(⌊(m-1) r /2⌋) m - (m mod 2 + [(m - 1)k] mod 2}}/(m - 1) information digits with an encoding time complexity of O(mk log m k) digit operations. A refined implementation of the parallel decoding method is also given with r check digits and k ≤ (m r -1)/(m -1) information digits, where the encoding time complexity is O(k√log m k). Thus, the proposed codes are less redundant than the m-ary balanced codes with parallel decoding found in the literature and yet maintain the same complexity. An $m$ -ary block code, $m=2,3,4,ldots $ , of length $n !in ! ...mathbf...I...!...mathbf...I...mskip -7mu...mathbf...N... $ is called balanced if, and only if, every codeword is balanced; that is, the real sum of the codeword components, or weight, is equal to $ left lfloor... (m-1)n/2 ...right rfloor $ . This paper presents efficient encoding schemes to $m$ -ary balanced codes with parallel (hence, fast) decoding. In fact, the decoding time complexity is $O(1)$ digit operations. These schemes are a generalization to the $m$ -ary alphabet of Knuth's complementation method with parallel decoding. Let $binom...n... w..._...m...$ indicate the number of $m$ -ary words of length $n$ and weight $w !in !...0,1,ldots ,(m-1)n...$ . For any $m !in ! ...mathbf...I...!...mathbf...I...mskip -7mu...mathbf...N... $ , $mgeq 2$ , a simple implementation of the method is given which uses $r !in ! ...mathbf...I...!...mathbf...I...mskip -7mu...mathbf...N... $ check digits to balance $kleq ...binom...r... ... left lfloor... (m-1)r/2 ...right rfloor ..._...vphantom ...R_...R_...m...-...mbmod ...2...+[(m-1)k]bmod 2.../(m-1)$ information digits with an encoding time complexity of $O(mklog _...m...k)$ digit operations. A refined implementation of the parallel decoding method is also given with $r$ check digits and $kleq (m...r...-1)/(m-1)$ information digits, where the encoding time complexity is $O(ksqrt ...log _...m...k...)$ . Thus, the proposed codes are less redundant than the $m$ -ary balanced codes with parallel decoding found in the literature and yet maintain the same complexity. (ProQuest: ... denotes formulae/symbols omitted.)
Author	Elmougy, Samir Bose, Bella Tallini, Luca G. Pelusi, Danilo
Author_xml	– sequence: 1 givenname: Danilo surname: Pelusi fullname: Pelusi, Danilo email: dpelusi@unite.it organization: Fac. di Sci. della Comun., Univ. degli Studi di Teramo, Teramo, Italy – sequence: 2 givenname: Samir surname: Elmougy fullname: Elmougy, Samir email: mougy@ksu.edu.sa organization: Dept. of Comput. Sci., King Saud Univ., Riyadh, Saudi Arabia – sequence: 3 givenname: Luca G. surname: Tallini fullname: Tallini, Luca G. email: ltallini@unite.it organization: Fac. di Sci. della Comun., Univ. degli Studi di Teramo, Teramo, Italy – sequence: 4 givenname: Bella surname: Bose fullname: Bose, Bella email: bose@eecs.orst.edu organization: Sch. of Electr. Eng. & Comput. Sci., Oregon State Univ., Corvallis, OR, USA
BookMark	eNp9kE1LAzEQhoNUsK3eBS8LXt2az01y1PpVKOhhxWOI2Ylu2W5qsj34701p8eDB0_DCPPMyzwSN-tADQucEzwjB-rpe1DOKiZhRTjVh-giNiRCy1JXgIzTGmKhSc65O0CSlVY5cEDpGV-uitPG7uLWd7R00xTw0kIq3dvgsXmy0XQddcQcuNG3_cYqOve0SnB3mFL0-3Nfzp3L5_LiY3yxLl6uH0ntMHcf0vXJcaK8045CjBUyl5V4r6ioMllohvWOScY8bbAVVjriqkZJN0eX-7iaGry2kwazCNva50pBKcaGUIDpv4f2WiyGlCN5sYrvOzxiCzc6JyU7Mzok5OMlI9Qdx7WCHNvRDtG33H3ixB1sA-O2RBBPKGfsBgr1tbA
CODEN	IETTAW
CitedBy_id	crossref_primary_10_1109_TIT_2016_2555322 crossref_primary_10_1109_TIT_2017_2721423 crossref_primary_10_1109_TIT_2018_2868453 crossref_primary_10_1109_TIT_2017_2766668 crossref_primary_10_1109_TIT_2022_3203594 crossref_primary_10_1109_ACCESS_2019_2934847 crossref_primary_10_1016_j_eswa_2018_02_026 crossref_primary_10_1016_j_knosys_2019_105277 crossref_primary_10_1109_TCE_2017_015067 crossref_primary_10_3390_sym10110609 crossref_primary_10_1109_TIT_2018_2844834 crossref_primary_10_7717_peerj_cs_1883 crossref_primary_10_1049_iet_com_2016_0097 crossref_primary_10_1109_TIT_2017_2767034
Cites_doi	10.1109/TIT.1986.1057136 10.1109/ISIT.2009.5205824 10.1109/18.490545 10.1109/12.795122 10.1109/TIT.2008.2011441 10.1109/TC.2007.1014 10.1109/TIT.2007.915919 10.1109/JSAC.2010.100207 10.1016/S0166-218X(98)00129-2 10.1109/TIT.1973.1054929 10.1109/18.2610 10.1109/18.52490 10.1109/TIT.2006.885524 10.1109/TIT.2010.2040868 10.1109/TC.2005.18 10.1109/TIT.2011.2173633
ContentType	Journal Article
Copyright	Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Jun 2015
Copyright_xml	– notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Jun 2015
DBID	97E RIA RIE AAYXX CITATION 7SC 7SP 8FD JQ2 L7M L~C L~D
DOI	10.1109/TIT.2015.2429139
DatabaseName	IEEE Xplore (IEEE) IEEE All-Society Periodicals Package (ASPP) 1998–Present IEEE Electronic Library (IEL) 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
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
EISSN	1557-9654
EndPage	3264
ExternalDocumentID	3701035291 10_1109_TIT_2015_2429139 7101243
Genre	orig-research
GrantInformation_xml	– fundername: National Science Foundation grantid: CCF-1117215 funderid: 10.13039/100000001 – fundername: Italian MIUR grantid: PRIN 2009-2009EL7424 – fundername: NPST Program through King Saud University, Riyadh, Saudi Arabia grantid: 10-INF1165-02
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 JQ2 L7M L~C L~D
ID	FETCH-LOGICAL-c291t-ff02c402b6c459f8934e402ae027a4f982c60ea2a57fc3734f0d0a528c1c6d773
IEDL.DBID	RIE
ISICitedReferencesCount	16
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000354943600020&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	Mon Nov 10 02:54:06 EST 2025 Sat Nov 29 03:31:34 EST 2025 Tue Nov 18 22:05:35 EST 2025 Tue Aug 26 16:50:03 EDT 2025
IsPeerReviewed	true
IsScholarly	true
Issue	6
Keywords	optical and magnetic recording Balanced codes parallel decoding scheme unidirectional error detection m -ary alphabet Knuth’s complementation method
Language	English
License	https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c291t-ff02c402b6c459f8934e402ae027a4f982c60ea2a57fc3734f0d0a528c1c6d773
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
PQID	1684588519
PQPubID	36024
PageCount	14
ParticipantIDs	crossref_primary_10_1109_TIT_2015_2429139 ieee_primary_7101243 crossref_citationtrail_10_1109_TIT_2015_2429139 proquest_journals_1684588519
PublicationCentury	2000
PublicationDate	2015-June 2015-6-00 20150601
PublicationDateYYYYMMDD	2015-06-01
PublicationDate_xml	– month: 06 year: 2015 text: 2015-June
PublicationDecade	2010
PublicationPlace	New York
PublicationPlace_xml	– name: New York
PublicationTitle	IEEE transactions on information theory
PublicationTitleAbbrev	TIT
PublicationYear	2015
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 ref14 ref11 ref10 ref2 schouhamer immink (ref5) 2004 ref1 ref17 tallini (ref16) 2013 ref18 ref8 ref7 ref9 ref4 ref3 ref6
References_xml	– ident: ref7 doi: 10.1109/TIT.1986.1057136 – ident: ref9 doi: 10.1109/ISIT.2009.5205824 – ident: ref10 doi: 10.1109/18.490545 – ident: ref12 doi: 10.1109/12.795122 – ident: ref17 doi: 10.1109/TIT.2008.2011441 – ident: ref3 doi: 10.1109/TC.2007.1014 – ident: ref15 doi: 10.1109/TIT.2007.915919 – ident: ref6 doi: 10.1109/JSAC.2010.100207 – ident: ref11 doi: 10.1016/S0166-218X(98)00129-2 – start-page: 694 year: 2013 ident: ref16 article-title: On $L_{1}$ metric asymmetric/unidirectional error control codes, constrained weight codes and $\sigma $ -codes publication-title: Proc IEEE ISIT – ident: ref4 doi: 10.1109/TIT.1973.1054929 – ident: ref2 doi: 10.1109/18.2610 – ident: ref1 doi: 10.1109/18.52490 – ident: ref14 doi: 10.1109/TIT.2006.885524 – ident: ref18 doi: 10.1109/TIT.2010.2040868 – year: 2004 ident: ref5 publication-title: Codes for Mass Data Storage Systems – ident: ref13 doi: 10.1109/TC.2005.18 – ident: ref8 doi: 10.1109/TIT.2011.2173633
SSID	ssj0014512
Score	2.2778099
Snippet	An m-ary block code, m = 2, 3, 4,..., of length n ϵ IN is called balanced if, and only if, every codeword is balanced; that is, the real sum of the codeword... An $m$ -ary block code, $m=2,3,4,ldots $ , of length $n !in ! ...mathbf...I...!...mathbf...I...mskip -7mu...mathbf...N... $ is called balanced if, and only if,...
SourceID	proquest crossref ieee
SourceType	Aggregation Database Enrichment Source Index Database Publisher
StartPage	3251
SubjectTerms	Balanced codes Coding theory Combinatorics Decoding Electronics Encoding Frequency modulation Indexes Knuth's complementation method m-ary alphabet optical and magnetic recording parallel decoding scheme Redundancy Time complexity unidirectional error detection
Title	m -ary Balanced Codes With Parallel Decoding
URI	https://ieeexplore.ieee.org/document/7101243 https://www.proquest.com/docview/1684588519
Volume	61
WOSCitedRecordID	wos000354943600020&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) 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/eLvHCXMwlV3NS8MwFH9sw4MenG6K0yk5eBHWLW2Spj3qdOhl7DBxt9LmAwe6SdcJ_vcm_UJRBE9t4aW0vzR97-V9_AAuqSKK65A5LPGIY_QxdhKKY8cyuzNOJcU6yMkm-HQaLBbhrAGDuhZGKZUnn6mhPc1j-XIttnarbMRtMypKmtDk3C9qteqIAWVu0RncNQvY-BxVSBKHo_nD3OZwsaFRR7YL5jcVlHOq_PgR59pl0v7fcx3AfmlFouti2g-hoVYdaFcMDahcsB3Y-9JusAuDV-TE6Qe6semMQkk0Xku1QU_L7BnN4tSyqrygW-OPWn12BI-Tu_n43inZEhxh3ipztMaeMN5g4gvKQm3Apspcxso4njHVYeAJH6vYixnXgnBCNZY4Zl4gXOFLzskxtFbrlToBJBLBE2MrEC0ENXKJMlaZOVIitZYJ6cGoAjASZStxy2jxEuUuBQ4jA3lkIY9KyHtwVY94K9po_CHbtRDXciW6PehXcxSV62wTuX5gS22NGXr6-6gz2LX3LpK7-tDK0q06hx3xni036UX-CX0CctvASQ
linkProvider	IEEE
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3NT8IwFH9BNFEPoqgRRe3BiwmDsrZ0OypKICLhMCO3ZuvaSIJg-DDxv7fdxqLRmHjalrxm26_r3nt9Hz-AK6qI4tpnDotc4hh9jJ2I4tCxzO6M05hi7SVkE3ww8EYjf1iAWl4Lo5RKks9U3Z4msfx4Jld2q6zBbTMqSjZgk1Hq4rRaK48ZUNZMe4M3zRI2Xsc6KIn9RtALbBYXqxuFZPtgflNCCavKj19xol86pf892T7sZXYkukkn_gAKalqG0pqjAWVLtgy7XxoOHkLtFTnh_APd2oRGqWLUnsVqgZ7Hyxc0DOeWV2WC7oxHajXaETx17oN218n4Ehxp3mrpaI1dafzBqCUp87WBmypzGSrjeoZU-54rW1iFbsi4loQTqnGMQ-Z6silbMefkGIrT2VSdAJKR5JGxFoiWkhq5SBm7zBwpibWOI1KBxhpAIbNm4pbTYiISpwL7wkAuLOQig7wC1_mIt7SRxh-yhxbiXC5DtwLV9RyJbKUtRLPl2WJbY4ie_j7qEra7wWNf9HuDhzPYsfdJU72qUFzOV-octuT7cryYXySf0yehzsOQ
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=m%24+-ary+Balanced+Codes+With+Parallel+Decoding&rft.jtitle=IEEE+transactions+on+information+theory&rft.au=Pelusi%2C+Danilo&rft.au=Elmougy%2C+Samir&rft.au=Tallini%2C+Luca+G.&rft.au=Bose%2C+Bella&rft.date=2015-06-01&rft.issn=0018-9448&rft.eissn=1557-9654&rft.volume=61&rft.issue=6&rft.spage=3251&rft.epage=3264&rft_id=info:doi/10.1109%2FTIT.2015.2429139&rft.externalDBID=n%2Fa&rft.externalDocID=10_1109_TIT_2015_2429139
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