Maringer, G., Polyanskii, N. A., Vorobyev, I. V., Welter, L.
{"title":"反馈插入-删除代码","authors":"Maringer, G., Polyanskii, N. A., Vorobyev, I. V., Welter, L.","doi":"10.1134/s0032946021030029","DOIUrl":null,"url":null,"abstract":"<p>A new problem of transmitting information over the adversarial insertion-deletion channel with feedback is introduced. Assume that the encoder transmits <span>\\(n\\)</span> binary symbols one by one over a channel in which some symbols can be deleted and some additional symbols can be inserted. After each transmission, the encoder is notified about insertions or deletions that have occurred within the previous transmission, and the encoding strategy can be adapted accordingly. The goal is to design an encoder that is able to transmit error-free as much information as possible under the assumption that the total number of deletions and insertions is limited by <span>\\(\\tau n\\)</span>, <span>\\(0<\\tau<1\\)</span>. We show how this problem can be reduced to the problem of transmitting messages over the substitution channel. Thereby, the maximal asymptotic rate of feedback insertion-deletion codes is completely established. The maximal asymptotic rate for the adversarial substitution channel has been partially determined by Berlekamp and later completed by Zigangirov. However, the analysis of the lower bound by Zigangirov is quite complicated. We revisit Zigangirov's result and present a more elaborate version of his proof.</p>","PeriodicalId":54581,"journal":{"name":"Problems of Information Transmission","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2021-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Feedback Insertion-Deletion Codes\",\"authors\":\"Maringer, G., Polyanskii, N. A., Vorobyev, I. V., Welter, L.\",\"doi\":\"10.1134/s0032946021030029\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>A new problem of transmitting information over the adversarial insertion-deletion channel with feedback is introduced. Assume that the encoder transmits <span>\\\\(n\\\\)</span> binary symbols one by one over a channel in which some symbols can be deleted and some additional symbols can be inserted. After each transmission, the encoder is notified about insertions or deletions that have occurred within the previous transmission, and the encoding strategy can be adapted accordingly. The goal is to design an encoder that is able to transmit error-free as much information as possible under the assumption that the total number of deletions and insertions is limited by <span>\\\\(\\\\tau n\\\\)</span>, <span>\\\\(0<\\\\tau<1\\\\)</span>. We show how this problem can be reduced to the problem of transmitting messages over the substitution channel. Thereby, the maximal asymptotic rate of feedback insertion-deletion codes is completely established. The maximal asymptotic rate for the adversarial substitution channel has been partially determined by Berlekamp and later completed by Zigangirov. However, the analysis of the lower bound by Zigangirov is quite complicated. We revisit Zigangirov's result and present a more elaborate version of his proof.</p>\",\"PeriodicalId\":54581,\"journal\":{\"name\":\"Problems of Information Transmission\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2021-10-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Problems of Information Transmission\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.1134/s0032946021030029\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Problems of Information Transmission","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1134/s0032946021030029","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
A new problem of transmitting information over the adversarial insertion-deletion channel with feedback is introduced. Assume that the encoder transmits \(n\) binary symbols one by one over a channel in which some symbols can be deleted and some additional symbols can be inserted. After each transmission, the encoder is notified about insertions or deletions that have occurred within the previous transmission, and the encoding strategy can be adapted accordingly. The goal is to design an encoder that is able to transmit error-free as much information as possible under the assumption that the total number of deletions and insertions is limited by \(\tau n\), \(0<\tau<1\). We show how this problem can be reduced to the problem of transmitting messages over the substitution channel. Thereby, the maximal asymptotic rate of feedback insertion-deletion codes is completely established. The maximal asymptotic rate for the adversarial substitution channel has been partially determined by Berlekamp and later completed by Zigangirov. However, the analysis of the lower bound by Zigangirov is quite complicated. We revisit Zigangirov's result and present a more elaborate version of his proof.
期刊介绍:
Problems of Information Transmission is of interest to researcher in all fields concerned with the research and development of communication systems. This quarterly journal features coverage of statistical information theory; coding theory and techniques; noisy channels; error detection and correction; signal detection, extraction, and analysis; analysis of communication networks; optimal processing and routing; the theory of random processes; and bionics.