{"title":"论分组码的格子结构","authors":"F. Kschischang, V. Sorokine","doi":"10.1109/ISIT.1994.394681","DOIUrl":null,"url":null,"abstract":"Two main results will be presented: 1. The problem of minimizing the number of states in the trellis for a general (nonlinear) code at a given time index is NP-complete, and thus apparently computationally infeasible for large codes. 2. Minimal linear block code trellises correspond to configurations of non-attacking rooks on a triangular chess board. This correspondence can be used to enumerate the minimal trellises, and also to obtain insight into various bounds on the size of the trellises.<<ETX>>","PeriodicalId":331390,"journal":{"name":"Proceedings of 1994 IEEE International Symposium on Information Theory","volume":"77 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1994-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"191","resultStr":"{\"title\":\"On the trellis structure of block codes\",\"authors\":\"F. Kschischang, V. Sorokine\",\"doi\":\"10.1109/ISIT.1994.394681\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Two main results will be presented: 1. The problem of minimizing the number of states in the trellis for a general (nonlinear) code at a given time index is NP-complete, and thus apparently computationally infeasible for large codes. 2. Minimal linear block code trellises correspond to configurations of non-attacking rooks on a triangular chess board. This correspondence can be used to enumerate the minimal trellises, and also to obtain insight into various bounds on the size of the trellises.<<ETX>>\",\"PeriodicalId\":331390,\"journal\":{\"name\":\"Proceedings of 1994 IEEE International Symposium on Information Theory\",\"volume\":\"77 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1994-06-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"191\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of 1994 IEEE International Symposium on Information Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISIT.1994.394681\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of 1994 IEEE International Symposium on Information Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISIT.1994.394681","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Two main results will be presented: 1. The problem of minimizing the number of states in the trellis for a general (nonlinear) code at a given time index is NP-complete, and thus apparently computationally infeasible for large codes. 2. Minimal linear block code trellises correspond to configurations of non-attacking rooks on a triangular chess board. This correspondence can be used to enumerate the minimal trellises, and also to obtain insight into various bounds on the size of the trellises.<>
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