{"title":"一类率为1/3的拟循环LDPC码的代数设计","authors":"R. M. Tanner","doi":"10.1109/GLOBECOM46510.2021.9685071","DOIUrl":null,"url":null,"abstract":"An algebraic design procedure is given for constructing rate 1/3 quasi-cyclic LDPC codes with Tanner graphs with girth 6. Parity check matrices consist of 2 × 3 block matrices of circulants of size p, a prime, exhibiting invariance under the action of a subgroup of the multiplicative group mod p. The group invariance converts the problem of avoiding short cycles into that of choosing orbits to solve connectivity constraints. A series of very low density H matrix codes constructed show surprisingly good minimum distances.","PeriodicalId":200641,"journal":{"name":"2021 IEEE Global Communications Conference (GLOBECOM)","volume":"100 2","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Algebraic Design of a Class of Rate 1/3 Quasi-Cyclic LDPC Codes\",\"authors\":\"R. M. Tanner\",\"doi\":\"10.1109/GLOBECOM46510.2021.9685071\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"An algebraic design procedure is given for constructing rate 1/3 quasi-cyclic LDPC codes with Tanner graphs with girth 6. Parity check matrices consist of 2 × 3 block matrices of circulants of size p, a prime, exhibiting invariance under the action of a subgroup of the multiplicative group mod p. The group invariance converts the problem of avoiding short cycles into that of choosing orbits to solve connectivity constraints. A series of very low density H matrix codes constructed show surprisingly good minimum distances.\",\"PeriodicalId\":200641,\"journal\":{\"name\":\"2021 IEEE Global Communications Conference (GLOBECOM)\",\"volume\":\"100 2\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2021 IEEE Global Communications Conference (GLOBECOM)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/GLOBECOM46510.2021.9685071\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2021 IEEE Global Communications Conference (GLOBECOM)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/GLOBECOM46510.2021.9685071","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Algebraic Design of a Class of Rate 1/3 Quasi-Cyclic LDPC Codes
An algebraic design procedure is given for constructing rate 1/3 quasi-cyclic LDPC codes with Tanner graphs with girth 6. Parity check matrices consist of 2 × 3 block matrices of circulants of size p, a prime, exhibiting invariance under the action of a subgroup of the multiplicative group mod p. The group invariance converts the problem of avoiding short cycles into that of choosing orbits to solve connectivity constraints. A series of very low density H matrix codes constructed show surprisingly good minimum distances.
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