{"title":"Construction of Reed-Solomon Erasure Codes With Four Parities Based on Systematic Vandermonde Matrices","authors":"Leilei Yu;Yunghsiang S. Han","doi":"10.1109/TC.2024.3387069","DOIUrl":null,"url":null,"abstract":"In 2021, Tang et al. proposed an improved construction of Reed-Solomon (RS) erasure codes with four parity symbols to accelerate the computation of Reed-Muller (RM) transform-based RS algorithm. The idea is to change the original Vandermonde parity-check matrix into a systematic Vandermonde parity-check matrix. However, the construction relies on a computer search and requires that the size of the information vector of RS codes does not exceed \n<inline-formula><tex-math>$52$</tex-math></inline-formula>\n. This paper improves its idea and proposes a purely algebraic construction. The proposed method has a more explicit construction, a wider range of codeword lengths, and competitive encoding/erasure decoding computational complexity.","PeriodicalId":13087,"journal":{"name":"IEEE Transactions on Computers","volume":"73 7","pages":"1875-1882"},"PeriodicalIF":3.6000,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Transactions on Computers","FirstCategoryId":"94","ListUrlMain":"https://ieeexplore.ieee.org/document/10496475/","RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, HARDWARE & ARCHITECTURE","Score":null,"Total":0}
引用次数: 0
Abstract
In 2021, Tang et al. proposed an improved construction of Reed-Solomon (RS) erasure codes with four parity symbols to accelerate the computation of Reed-Muller (RM) transform-based RS algorithm. The idea is to change the original Vandermonde parity-check matrix into a systematic Vandermonde parity-check matrix. However, the construction relies on a computer search and requires that the size of the information vector of RS codes does not exceed
$52$
. This paper improves its idea and proposes a purely algebraic construction. The proposed method has a more explicit construction, a wider range of codeword lengths, and competitive encoding/erasure decoding computational complexity.
期刊介绍：
The IEEE Transactions on Computers is a monthly publication with a wide distribution to researchers, developers, technical managers, and educators in the computer field. It publishes papers on research in areas of current interest to the readers. These areas include, but are not limited to, the following: a) computer organizations and architectures; b) operating systems, software systems, and communication protocols; c) real-time systems and embedded systems; d) digital devices, computer components, and interconnection networks; e) specification, design, prototyping, and testing methods and tools; f) performance, fault tolerance, reliability, security, and testability; g) case studies and experimental and theoretical evaluations; and h) new and important applications and trends.
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
