Analytical Lower Bound on the Lifting Degree of Multiple-Edge QC-LDPC Codes With Girth 6
Multiple-edge protographs have some advantages over single-edge protographs, such as potentially having larger minimum Hamming distance. However, most of results in the literature are related to the construction of single-edge quasi-cyclic low-density parity-check codes (QC-LDPC) codes and little re...
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| Veröffentlicht in: | IEEE communications letters 2018-08, Vol.22 (8), p.1528-1531 |
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| creator | Sadeghi, Mohammad-Reza Amirzade, Farzane |
| description | Multiple-edge protographs have some advantages over single-edge protographs, such as potentially having larger minimum Hamming distance. However, most of results in the literature are related to the construction of single-edge quasi-cyclic low-density parity-check codes (QC-LDPC) codes and little research has been done for the construction of multiple-edge QC-LDPC codes. In this letter, for the first time, necessary and sufficient conditions for the exponent matrices to have multiple-edge QC-LDPC codes with girth 6 are provided. As a consequence of this letter, a lower bound on the lifting degree of regular and irregular multiple-edge QC-LDPC codes with girth 6 is derived. We also present QC-LDPC codes whose lifting degrees meet our proposed lower bound. These codes have shorter lengths compared with single-edge QC-LDPC codes. Another contribution of this letter is presenting a technique to reduce the size of the search space to find these codes. |
| doi_str_mv | 10.1109/LCOMM.2018.2841873 |
| format | Article |
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However, most of results in the literature are related to the construction of single-edge quasi-cyclic low-density parity-check codes (QC-LDPC) codes and little research has been done for the construction of multiple-edge QC-LDPC codes. In this letter, for the first time, necessary and sufficient conditions for the exponent matrices to have multiple-edge QC-LDPC codes with girth 6 are provided. As a consequence of this letter, a lower bound on the lifting degree of regular and irregular multiple-edge QC-LDPC codes with girth 6 is derived. We also present QC-LDPC codes whose lifting degrees meet our proposed lower bound. These codes have shorter lengths compared with single-edge QC-LDPC codes. Another contribution of this letter is presenting a technique to reduce the size of the search space to find these codes.</description><identifier>ISSN: 1089-7798</identifier><identifier>EISSN: 1558-2558</identifier><identifier>DOI: 10.1109/LCOMM.2018.2841873</identifier><identifier>CODEN: ICLEF6</identifier><language>eng</language><publisher>New York: IEEE</publisher><subject>Binary system ; Codes ; Computer science ; difference matrices ; Error correcting codes ; girth ; Hamming distance ; Hoisting ; Indexes ; lifting degree ; Linear matrix inequalities ; Low density parity check codes ; Lower bounds ; Matrices ; Multiple-edge QC-LDPC codes ; Parity check codes ; protographs</subject><ispartof>IEEE communications letters, 2018-08, Vol.22 (8), p.1528-1531</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2018</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c295t-2c47fd739a3f4aca5c13d65585282c45703ea24d917aa361079a9aab328b55373</citedby><cites>FETCH-LOGICAL-c295t-2c47fd739a3f4aca5c13d65585282c45703ea24d917aa361079a9aab328b55373</cites><orcidid>0000-0002-7676-4168 ; 0000-0002-8665-7921</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/8368304$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,780,784,796,27924,27925,54758</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/8368304$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Sadeghi, Mohammad-Reza</creatorcontrib><creatorcontrib>Amirzade, Farzane</creatorcontrib><title>Analytical Lower Bound on the Lifting Degree of Multiple-Edge QC-LDPC Codes With Girth 6</title><title>IEEE communications letters</title><addtitle>COML</addtitle><description>Multiple-edge protographs have some advantages over single-edge protographs, such as potentially having larger minimum Hamming distance. However, most of results in the literature are related to the construction of single-edge quasi-cyclic low-density parity-check codes (QC-LDPC) codes and little research has been done for the construction of multiple-edge QC-LDPC codes. In this letter, for the first time, necessary and sufficient conditions for the exponent matrices to have multiple-edge QC-LDPC codes with girth 6 are provided. As a consequence of this letter, a lower bound on the lifting degree of regular and irregular multiple-edge QC-LDPC codes with girth 6 is derived. We also present QC-LDPC codes whose lifting degrees meet our proposed lower bound. These codes have shorter lengths compared with single-edge QC-LDPC codes. Another contribution of this letter is presenting a technique to reduce the size of the search space to find these codes.</description><subject>Binary system</subject><subject>Codes</subject><subject>Computer science</subject><subject>difference matrices</subject><subject>Error correcting codes</subject><subject>girth</subject><subject>Hamming distance</subject><subject>Hoisting</subject><subject>Indexes</subject><subject>lifting degree</subject><subject>Linear matrix inequalities</subject><subject>Low density parity check codes</subject><subject>Lower bounds</subject><subject>Matrices</subject><subject>Multiple-edge QC-LDPC codes</subject><subject>Parity check codes</subject><subject>protographs</subject><issn>1089-7798</issn><issn>1558-2558</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNo9kE9LAzEQxYMoWKtfQC8Bz1vzZ7NJjnWtVdhSBUVvId2dbVPWpia7SL-9W1u8vBmY94aZH0LXlIwoJfquyOez2YgRqkZMpVRJfoIGVAiVsF5O-54onUip1Tm6iHFNCFFM0AH6HG9ss2tdaRtc-B8I-N53mwr7DW5XgAtXt26zxA-wDADY13jWNa3bNpBMqiXg1zwpHl5ynPsKIv5w7QpPXeg1u0RntW0iXB3rEL0_Tt7yp6SYT5_zcZGUTIs2YWUq60pybXmd2tKKkvIq628WTPUzIQkHy9JKU2ktzyiR2mprF5yphRBc8iG6PezdBv_dQWzN2nehfyoaRqmknDK5d7GDqww-xgC12Qb3ZcPOUGL2BM0fQbMnaI4E-9DNIeQA4D-geKY4SfkvQbZp6Q</recordid><startdate>20180801</startdate><enddate>20180801</enddate><creator>Sadeghi, Mohammad-Reza</creator><creator>Amirzade, Farzane</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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However, most of results in the literature are related to the construction of single-edge quasi-cyclic low-density parity-check codes (QC-LDPC) codes and little research has been done for the construction of multiple-edge QC-LDPC codes. In this letter, for the first time, necessary and sufficient conditions for the exponent matrices to have multiple-edge QC-LDPC codes with girth 6 are provided. As a consequence of this letter, a lower bound on the lifting degree of regular and irregular multiple-edge QC-LDPC codes with girth 6 is derived. We also present QC-LDPC codes whose lifting degrees meet our proposed lower bound. These codes have shorter lengths compared with single-edge QC-LDPC codes. 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| source | IEEE Xplore |
| subjects | Binary system Codes Computer science difference matrices Error correcting codes girth Hamming distance Hoisting Indexes lifting degree Linear matrix inequalities Low density parity check codes Lower bounds Matrices Multiple-edge QC-LDPC codes Parity check codes protographs |
| title | Analytical Lower Bound on the Lifting Degree of Multiple-Edge QC-LDPC Codes With Girth 6 |
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