{"title":"A transform approach for analyzing and constructing quasi-cyclic low-density parity-check codes","authors":"Qiuju Diao, Qin Huang, Shu Lin, K. Abdel-Ghaffar","doi":"10.1109/ITA.2011.5743557","DOIUrl":null,"url":null,"abstract":"An approach for studying quasi-cyclic codes based on matrix transformations via Fourier transforms and row and column permutations is presented. These transformations put a parity-check matrix in the form of an array of circulant matrices into a diagonal array of matrices of the same size over an extension field. The approach is used to characterize certain structural properties of low-density parity-check (LDPC) codes such as the girths of their Tanner graphs. Many constructions of quasi-cyclic LDPC codes can be unified under the proposed approach.","PeriodicalId":326414,"journal":{"name":"2011 Information Theory and Applications Workshop","volume":"18 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2011-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"13","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2011 Information Theory and Applications Workshop","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ITA.2011.5743557","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 13
Abstract
An approach for studying quasi-cyclic codes based on matrix transformations via Fourier transforms and row and column permutations is presented. These transformations put a parity-check matrix in the form of an array of circulant matrices into a diagonal array of matrices of the same size over an extension field. The approach is used to characterize certain structural properties of low-density parity-check (LDPC) codes such as the girths of their Tanner graphs. Many constructions of quasi-cyclic LDPC codes can be unified under the proposed approach.