Balaji Srinivasan Babu, Ganesh Ramachandra Kini, P. V. Kumar
{"title":"A Rate-Optimal Construction of Codes with Sequential Recovery with Low Block Length","authors":"Balaji Srinivasan Babu, Ganesh Ramachandra Kini, P. V. Kumar","doi":"10.1109/NCC.2018.8600259","DOIUrl":null,"url":null,"abstract":"An erasure code is said to be a code with sequential recovery with parameters <tex>$r$</tex> and t, if for any <tex>$s$</tex> ≤ <tex>$t$</tex> erased code symbols, there is an s-step recovery process in which at each step we recover exactly one erased code symbol by contacting at most <tex>$r$</tex> other code symbols. In this paper, we give a construction of binary codes with sequential recovery that are rate-optimal for any value of <tex>$t$</tex> and any value <tex>$r$</tex> ≥ 3. Our construction is based on construction of certain kind of tree-like graphs with girth <tex>$t$</tex> + 1. We construct these graphs and hence the codes recursively.","PeriodicalId":121544,"journal":{"name":"2018 Twenty Fourth National Conference on Communications (NCC)","volume":"116 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2018 Twenty Fourth National Conference on Communications (NCC)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/NCC.2018.8600259","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 5
Abstract
An erasure code is said to be a code with sequential recovery with parameters $r$ and t, if for any $s$ ≤ $t$ erased code symbols, there is an s-step recovery process in which at each step we recover exactly one erased code symbol by contacting at most $r$ other code symbols. In this paper, we give a construction of binary codes with sequential recovery that are rate-optimal for any value of $t$ and any value $r$ ≥ 3. Our construction is based on construction of certain kind of tree-like graphs with girth $t$ + 1. We construct these graphs and hence the codes recursively.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
