{"title":"六边形信号星座的二维李氏纠错码","authors":"H. Morita, M. Fujisawa, S. Sakata","doi":"10.1109/ITW48936.2021.9611434","DOIUrl":null,"url":null,"abstract":"We construct linear codes over odd prime fields for correcting two-dimensional (2-D) Lee-errors on the hexagonal signal constellations. They are obtained by puncturing and enlarging either RS codes or BCH codes. We introduce 2-D Lee-weight on the hexagonal constellations in the same way as the method presented by the first author in ISIT’19, and propose an effective and efficient method for correcting Lee-errors of small weight. The concept of value-locator of an error, which was introduced implicitly by K. Nakamura in the late 1970s and early 1980s and inherited to the ISIT’19 paper, is a key for decoding Lee-error-correcting codes. Our method is based on the Buchberger algorithm for finding Gröbner bases of ideals in the multivariate polynomial ring. A result of simulations shows that our method works well for correcting Lee-errors of small weight.","PeriodicalId":325229,"journal":{"name":"2021 IEEE Information Theory Workshop (ITW)","volume":"8 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Two-dimensional Lee-Error-Correcting Codes on Hexagonal Signal Constellations\",\"authors\":\"H. Morita, M. Fujisawa, S. Sakata\",\"doi\":\"10.1109/ITW48936.2021.9611434\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We construct linear codes over odd prime fields for correcting two-dimensional (2-D) Lee-errors on the hexagonal signal constellations. They are obtained by puncturing and enlarging either RS codes or BCH codes. We introduce 2-D Lee-weight on the hexagonal constellations in the same way as the method presented by the first author in ISIT’19, and propose an effective and efficient method for correcting Lee-errors of small weight. The concept of value-locator of an error, which was introduced implicitly by K. Nakamura in the late 1970s and early 1980s and inherited to the ISIT’19 paper, is a key for decoding Lee-error-correcting codes. Our method is based on the Buchberger algorithm for finding Gröbner bases of ideals in the multivariate polynomial ring. A result of simulations shows that our method works well for correcting Lee-errors of small weight.\",\"PeriodicalId\":325229,\"journal\":{\"name\":\"2021 IEEE Information Theory Workshop (ITW)\",\"volume\":\"8 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-10-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2021 IEEE Information Theory Workshop (ITW)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ITW48936.2021.9611434\",\"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 Information Theory Workshop (ITW)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ITW48936.2021.9611434","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Two-dimensional Lee-Error-Correcting Codes on Hexagonal Signal Constellations
We construct linear codes over odd prime fields for correcting two-dimensional (2-D) Lee-errors on the hexagonal signal constellations. They are obtained by puncturing and enlarging either RS codes or BCH codes. We introduce 2-D Lee-weight on the hexagonal constellations in the same way as the method presented by the first author in ISIT’19, and propose an effective and efficient method for correcting Lee-errors of small weight. The concept of value-locator of an error, which was introduced implicitly by K. Nakamura in the late 1970s and early 1980s and inherited to the ISIT’19 paper, is a key for decoding Lee-error-correcting codes. Our method is based on the Buchberger algorithm for finding Gröbner bases of ideals in the multivariate polynomial ring. A result of simulations shows that our method works well for correcting Lee-errors of small weight.
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