Construction of Reed-Solomon Erasure Codes With Four Parities Based on Systematic Vandermonde Matrices

IF 3.6 2区计算机科学 Q2 COMPUTER SCIENCE, HARDWARE & ARCHITECTURE

IEEE Transactions on Computers Pub Date : 2024-04-10 DOI:10.1109/TC.2024.3387069

Leilei Yu;Yunghsiang S. Han

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.

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基于系统范德蒙德矩阵构建四奇偶校验的里德-所罗门纠错码

2021 年，Tang 等人提出了一种具有四个奇偶校验符号的里德-所罗门（RS）擦除码的改进结构，以加速基于里德-穆勒（RM）变换的 RS 算法的计算。其思路是将原始范德蒙德奇偶校验矩阵变为系统范德蒙德奇偶校验矩阵。然而，这种构造依赖于计算机搜索，并要求 RS 码的信息向量大小不超过 52 美元。本文改进了其想法，提出了一种纯代数的构造。所提出的方法具有更明确的构造、更宽的码字长度范围和有竞争力的编码/测度解码计算复杂度。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

IEEE Transactions on Computers 工程技术-工程：电子与电气

CiteScore

6.60

自引率

5.40%

发文量

199

审稿时长

6.0 months

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.