Girth Analysis of Tanner's (3, 17)-Regular QC-LDPC Codes Based on Euclidean Division Algorithm
In this paper, the girth distribution of the Tanner's (3, 17)-regular quasi-cyclic LDPC (QC-LDPC) codes with code length 17p is determined, where p is a prime and p \equiv 1~(\bmod ~51) . By analyzing their cycle structure, five equivalent types of cycles with length not more than 10 are o...
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| Veröffentlicht in: | IEEE access 2019, Vol.7, p.94917-94930 |
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| creator | Xu, Hengzhou Duan, Yake Miao, Xiaoxiao Zhu, Hai |
| description | In this paper, the girth distribution of the Tanner's (3, 17)-regular quasi-cyclic LDPC (QC-LDPC) codes with code length 17p is determined, where p is a prime and p \equiv 1~(\bmod ~51) . By analyzing their cycle structure, five equivalent types of cycles with length not more than 10 are obtained. The existence of these five types of cycles is transmitted into polynomial equations in a 51st unit root of the prime field \mathbb {F}_{p} . By using the Euclidean division algorithm to check the existence of solutions for such polynomial equations, the girth values of the Tanner's (3, 17)-regular QC-LDPC codes are obtained. |
| doi_str_mv | 10.1109/ACCESS.2019.2929587 |
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By analyzing their cycle structure, five equivalent types of cycles with length not more than 10 are obtained. The existence of these five types of cycles is transmitted into polynomial equations in a 51st unit root of the prime field <inline-formula> <tex-math notation="LaTeX">\mathbb {F}_{p} </tex-math></inline-formula>. By using the Euclidean division algorithm to check the existence of solutions for such polynomial equations, the girth values of the Tanner's (3, 17)-regular QC-LDPC codes are obtained.]]></description><identifier>ISSN: 2169-3536</identifier><identifier>EISSN: 2169-3536</identifier><identifier>DOI: 10.1109/ACCESS.2019.2929587</identifier><identifier>CODEN: IAECCG</identifier><language>eng</language><publisher>Piscataway: IEEE</publisher><subject>Algorithms ; Codes ; Encoding ; Euclidean division algorithm ; girth ; Hardware ; Indexes ; LDPC codes ; Low density parity check codes ; Mathematical analysis ; Parity check codes ; Polynomials ; prime field ; quasi-cyclic (QC) ; Technological innovation ; Training</subject><ispartof>IEEE access, 2019, Vol.7, p.94917-94930</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2019</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c408t-eca5aaa9fef576c6f829612250ce74e7117df1b8a16a74b21d3301d61ea367683</citedby><cites>FETCH-LOGICAL-c408t-eca5aaa9fef576c6f829612250ce74e7117df1b8a16a74b21d3301d61ea367683</cites><orcidid>0000-0001-9403-4460</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/8765603$$EHTML$$P50$$Gieee$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,864,2100,4014,27624,27914,27915,27916,54924</link.rule.ids></links><search><creatorcontrib>Xu, Hengzhou</creatorcontrib><creatorcontrib>Duan, Yake</creatorcontrib><creatorcontrib>Miao, Xiaoxiao</creatorcontrib><creatorcontrib>Zhu, Hai</creatorcontrib><title>Girth Analysis of Tanner's (3, 17)-Regular QC-LDPC Codes Based on Euclidean Division Algorithm</title><title>IEEE access</title><addtitle>Access</addtitle><description><![CDATA[In this paper, the girth distribution of the Tanner's (3, 17)-regular quasi-cyclic LDPC (QC-LDPC) codes with code length <inline-formula> <tex-math notation="LaTeX">17p </tex-math></inline-formula> is determined, where <inline-formula> <tex-math notation="LaTeX">p </tex-math></inline-formula> is a prime and <inline-formula> <tex-math notation="LaTeX">p \equiv 1~(\bmod ~51) </tex-math></inline-formula>. By analyzing their cycle structure, five equivalent types of cycles with length not more than 10 are obtained. The existence of these five types of cycles is transmitted into polynomial equations in a 51st unit root of the prime field <inline-formula> <tex-math notation="LaTeX">\mathbb {F}_{p} </tex-math></inline-formula>. By using the Euclidean division algorithm to check the existence of solutions for such polynomial equations, the girth values of the Tanner's (3, 17)-regular QC-LDPC codes are obtained.]]></description><subject>Algorithms</subject><subject>Codes</subject><subject>Encoding</subject><subject>Euclidean division algorithm</subject><subject>girth</subject><subject>Hardware</subject><subject>Indexes</subject><subject>LDPC codes</subject><subject>Low density parity check codes</subject><subject>Mathematical analysis</subject><subject>Parity check codes</subject><subject>Polynomials</subject><subject>prime field</subject><subject>quasi-cyclic (QC)</subject><subject>Technological innovation</subject><subject>Training</subject><issn>2169-3536</issn><issn>2169-3536</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>ESBDL</sourceid><sourceid>RIE</sourceid><sourceid>DOA</sourceid><recordid>eNpNUVtLHDEUHoqFivoLfAn0oQqdbU4yuT2u41aFhV60rw3HSbJmGSeazBb89x0dEc_LOXx8FzhfVR0DXQBQ823Ztqvr6wWjYBbMMCO0-lDtM5Cm5oLLvXf3p-qolC2dRk-QUPvV34uYxzuyHLB_KrGQFMgNDoPPXwo54V8JqNP6t9_seszkV1uvz3-2pE3OF3KGxTuSBrLadX10HgdyHv_FEido2W9SjuPd_WH1MWBf_NHrPqj-fF_dtJf1-sfFVbtc111D9Vj7DgUimuCDULKTQTMjgTFBO68arwCUC3CrESSq5paB45yCk-CRSyU1P6iuZl-XcGsfcrzH_GQTRvsCpLyxmMfY9d6aBrToqJKcs0aFoNGAY1QBCofOweT1efZ6yOlx58tot2mXpwcVyxohJEyJcmLxmdXlVEr24S0VqH3uxc692Ode7Gsvk-p4VkXv_ZtCKykk5fw_WFKFgA</recordid><startdate>2019</startdate><enddate>2019</enddate><creator>Xu, Hengzhou</creator><creator>Duan, Yake</creator><creator>Miao, Xiaoxiao</creator><creator>Zhu, Hai</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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By analyzing their cycle structure, five equivalent types of cycles with length not more than 10 are obtained. The existence of these five types of cycles is transmitted into polynomial equations in a 51st unit root of the prime field <inline-formula> <tex-math notation="LaTeX">\mathbb {F}_{p} </tex-math></inline-formula>. By using the Euclidean division algorithm to check the existence of solutions for such polynomial equations, the girth values of the Tanner's (3, 17)-regular QC-LDPC codes are obtained.]]></abstract><cop>Piscataway</cop><pub>IEEE</pub><doi>10.1109/ACCESS.2019.2929587</doi><tpages>14</tpages><orcidid>https://orcid.org/0000-0001-9403-4460</orcidid><oa>free_for_read</oa></addata></record> |
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| subjects | Algorithms Codes Encoding Euclidean division algorithm girth Hardware Indexes LDPC codes Low density parity check codes Mathematical analysis Parity check codes Polynomials prime field quasi-cyclic (QC) Technological innovation Training |
| title | Girth Analysis of Tanner's (3, 17)-Regular QC-LDPC Codes Based on Euclidean Division Algorithm |
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