{"title":"一类QC-LDPC码的可逆循环矩阵","authors":"M. Baldi, F. Bambozzi, F. Chiaraluce","doi":"10.1109/ISITA.2008.4895413","DOIUrl":null,"url":null,"abstract":"This paper presents a new class of easily invertible circulant matrices, defined by exploiting the isomorphism from the ring Mn of n times n circulant matrices over GF(p) to the ring Rn = GF(p)[x]/(xn - 1) of the polynomials modulo (xn - 1). Such class contains matrices free of 4-length cycles that, if sparse, can be included in the parity check matrix of QC-LDPC codes. Bounds for the weight of their inverses are also determined, that are useful for designing sparse generator matrices for these error correcting codes.","PeriodicalId":338675,"journal":{"name":"2008 International Symposium on Information Theory and Its Applications","volume":"49 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2008-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A class of invertible circulant matrices for QC-LDPC codes\",\"authors\":\"M. Baldi, F. Bambozzi, F. Chiaraluce\",\"doi\":\"10.1109/ISITA.2008.4895413\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper presents a new class of easily invertible circulant matrices, defined by exploiting the isomorphism from the ring Mn of n times n circulant matrices over GF(p) to the ring Rn = GF(p)[x]/(xn - 1) of the polynomials modulo (xn - 1). Such class contains matrices free of 4-length cycles that, if sparse, can be included in the parity check matrix of QC-LDPC codes. Bounds for the weight of their inverses are also determined, that are useful for designing sparse generator matrices for these error correcting codes.\",\"PeriodicalId\":338675,\"journal\":{\"name\":\"2008 International Symposium on Information Theory and Its Applications\",\"volume\":\"49 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2008-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2008 International Symposium on Information Theory and Its Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISITA.2008.4895413\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2008 International Symposium on Information Theory and Its Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISITA.2008.4895413","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A class of invertible circulant matrices for QC-LDPC codes
This paper presents a new class of easily invertible circulant matrices, defined by exploiting the isomorphism from the ring Mn of n times n circulant matrices over GF(p) to the ring Rn = GF(p)[x]/(xn - 1) of the polynomials modulo (xn - 1). Such class contains matrices free of 4-length cycles that, if sparse, can be included in the parity check matrix of QC-LDPC codes. Bounds for the weight of their inverses are also determined, that are useful for designing sparse generator matrices for these error correcting codes.
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