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<p>The use of Reed–Solomon (RS) codes in distributed storage systems is ubiquitous. In recent years, the repair schemes for RS codes with one or multiple failed symbols that can lessen communication cost in the repair (i.e., repair bandwidth) have been presented in the literature. However, the existing distributed repair schemes of RS codes can only repair <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10623_2025_1679_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="55" /> </InlineMediaObject> <EquationSource Format="TEX">\(e=2,3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>e</mi> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation> erasures. In this paper, by elaborately constructing the trace polynomials, two distributed repair schemes for RS codes with <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10623_2025_1679_Article_IEq2.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">\(e\ge 4\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>e</mi> <mo>≥</mo> <mn>4</mn> </mrow> </math></EquationSource> </InlineEquation> erasures are proposed for the first time, where the obtained repair bandwidth of these distributed repair schemes is smaller than that of the naive repair scheme for RS codes (i.e., <i>k</i> full symbols).</p>

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Distributed repair schemes for Reed–Solomon codes with multiple erasures

  • 期刊论文

  • 发表日期：

    2025年7月3日

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  • Xing Lin

摘要

The use of Reed–Solomon (RS) codes in distributed storage systems is ubiquitous. In recent years, the repair schemes for RS codes with one or multiple failed symbols that can lessen communication cost in the repair (i.e., repair bandwidth) have been presented in the literature. However, the existing distributed repair schemes of RS codes can only repair \(e=2,3\) e = 2 , 3 erasures. In this paper, by elaborately constructing the trace polynomials, two distributed repair schemes for RS codes with \(e\ge 4\) e ≥ 4 erasures are proposed for the first time, where the obtained repair bandwidth of these distributed repair schemes is smaller than that of the naive repair scheme for RS codes (i.e., k full symbols).