{"title":"求解约束系统的Gilbert-Varshamov界","authors":"Keshav Goyal, H. M. Kiah","doi":"10.1109/ISIT50566.2022.9834754","DOIUrl":null,"url":null,"abstract":"We revisit the well-known Gilbert-Varshamov (GV) bound for constrained systems. In 1991, Kolesnik and Krachkovsky showed that GV bound can be determined via the solution of some optimization problem. Later, Marcus and Roth (1992) modified the optimization problem and improved the GV bound in many instances. In this work, we provide explicit numerical procedures to solve these two optimization problems and hence, compute the bounds. We then show the procedures can be further simplified when we plot the respective curves.","PeriodicalId":348168,"journal":{"name":"2022 IEEE International Symposium on Information Theory (ISIT)","volume":"8 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Evaluating the Gilbert-Varshamov Bound for Constrained Systems\",\"authors\":\"Keshav Goyal, H. M. Kiah\",\"doi\":\"10.1109/ISIT50566.2022.9834754\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We revisit the well-known Gilbert-Varshamov (GV) bound for constrained systems. In 1991, Kolesnik and Krachkovsky showed that GV bound can be determined via the solution of some optimization problem. Later, Marcus and Roth (1992) modified the optimization problem and improved the GV bound in many instances. In this work, we provide explicit numerical procedures to solve these two optimization problems and hence, compute the bounds. We then show the procedures can be further simplified when we plot the respective curves.\",\"PeriodicalId\":348168,\"journal\":{\"name\":\"2022 IEEE International Symposium on Information Theory (ISIT)\",\"volume\":\"8 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-06-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2022 IEEE International Symposium on Information Theory (ISIT)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISIT50566.2022.9834754\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2022 IEEE International Symposium on Information Theory (ISIT)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISIT50566.2022.9834754","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Evaluating the Gilbert-Varshamov Bound for Constrained Systems
We revisit the well-known Gilbert-Varshamov (GV) bound for constrained systems. In 1991, Kolesnik and Krachkovsky showed that GV bound can be determined via the solution of some optimization problem. Later, Marcus and Roth (1992) modified the optimization problem and improved the GV bound in many instances. In this work, we provide explicit numerical procedures to solve these two optimization problems and hence, compute the bounds. We then show the procedures can be further simplified when we plot the respective curves.
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