M. Borges-Quintana, M. Borges-Trenard, Irene Marquez Corbella, E. Martínez-Moro
{"title":"梯度下降译码的代数观点","authors":"M. Borges-Quintana, M. Borges-Trenard, Irene Marquez Corbella, E. Martínez-Moro","doi":"10.1109/CIG.2010.5592830","DOIUrl":null,"url":null,"abstract":"There are two gradient descent decoding procedures for binary codes proposed independently by Liebler and by Ashikhmin and Barg. Liebler in his paper [15] mentions that both algorithms have the same philosophy but in fact they are rather different. The purpose of this communication is to show that both algorithms can be seen as two ways of understanding the reduction process algebraic monoid structure related to the code. The main tool used for showing this is the Gröbner representation of the monoid associated to the linear code.","PeriodicalId":354925,"journal":{"name":"2010 IEEE Information Theory Workshop","volume":"124 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2010-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"13","resultStr":"{\"title\":\"An algebraic view to gradient descent decoding\",\"authors\":\"M. Borges-Quintana, M. Borges-Trenard, Irene Marquez Corbella, E. Martínez-Moro\",\"doi\":\"10.1109/CIG.2010.5592830\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"There are two gradient descent decoding procedures for binary codes proposed independently by Liebler and by Ashikhmin and Barg. Liebler in his paper [15] mentions that both algorithms have the same philosophy but in fact they are rather different. The purpose of this communication is to show that both algorithms can be seen as two ways of understanding the reduction process algebraic monoid structure related to the code. The main tool used for showing this is the Gröbner representation of the monoid associated to the linear code.\",\"PeriodicalId\":354925,\"journal\":{\"name\":\"2010 IEEE Information Theory Workshop\",\"volume\":\"124 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2010-08-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"13\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2010 IEEE Information Theory Workshop\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/CIG.2010.5592830\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2010 IEEE Information Theory Workshop","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CIG.2010.5592830","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
There are two gradient descent decoding procedures for binary codes proposed independently by Liebler and by Ashikhmin and Barg. Liebler in his paper [15] mentions that both algorithms have the same philosophy but in fact they are rather different. The purpose of this communication is to show that both algorithms can be seen as two ways of understanding the reduction process algebraic monoid structure related to the code. The main tool used for showing this is the Gröbner representation of the monoid associated to the linear code.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
