<p>Erasure codes are being widely implemented in distributed storage systems to achieve fault tolerance with high storage efficiency. Reed-Solomon code is commonly deployed in data centers due to its optimal storage efficiency, but it requires massive bandwidth for node repair. Minimum Storage Regenerating code (MSR) and Locally Repairable (LR) code are proposed to reduce <i>repair bandwidth</i>, which is defined as the amount of data communicated during node repair. However, MSR code usually carries a heavy disk I/O burden and LR code is not optimal in storage efficiency. In this paper, we take disk I/O, storage efficiency, repair bandwidth and sub-packetization level into consideration together, and propose novel constructions of maximum distance separable array codes with low disk I/O, reduced repair bandwidth and very small sub-packetization level of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$l={\cal{O}}(r)$</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mi>l</mi> <mo>=</mo> <mrow> <mrow> <mi mathvariant="script">O</mi> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> </math></EquationSource> </InlineEquation>. We focus on the repair of systematic nodes since they are more likely to fail than parity nodes. Specifically, the proposed codes achieve the cut-set bound on repair bandwidth for systematic nodes when the code rate <InlineEquation ID="IEq2"> <EquationSource Format="TEX">${k\over n}={1\over 2}$</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <mfrac> <mi>k</mi> <mi>n</mi> </mfrac> </mrow> <mo>=</mo> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </math></EquationSource> </InlineEquation>, and for <InlineEquation ID="IEq3"> <EquationSource Format="TEX">${k\over n}>{1\over 2}$</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <mfrac> <mi>k</mi> <mi>n</mi> </mfrac> </mrow> <mo>></mo> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </math></EquationSource> </InlineEquation>, the repair bandwidth is less than twice of the cut-set bound. Compared with new advanced piggybacking codes, the proposed codes obtain a significant reduction on repair bandwidth for systematic nodes while also consuming less disk I/Os. In terms of average repair bandwidth of all nodes, the proposed codes are intuitively better than the existing advanced piggybacking codes.</p>

MDS array codes with low disk I/O and small repair bandwidth

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发表日期：

2025年12月2日

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Lei Li,
Chenhao Ying,
Liang Chen,
Yuanyuan Dong,
Jie Li,
Yuan Luo

摘要

Erasure codes are being widely implemented in distributed storage systems to achieve fault tolerance with high storage efficiency. Reed-Solomon code is commonly deployed in data centers due to its optimal storage efficiency, but it requires massive bandwidth for node repair. Minimum Storage Regenerating code (MSR) and Locally Repairable (LR) code are proposed to reduce repair bandwidth, which is defined as the amount of data communicated during node repair. However, MSR code usually carries a heavy disk I/O burden and LR code is not optimal in storage efficiency. In this paper, we take disk I/O, storage efficiency, repair bandwidth and sub-packetization level into consideration together, and propose novel constructions of maximum distance separable array codes with low disk I/O, reduced repair bandwidth and very small sub-packetization level of $l={\cal{O}}(r)$ $l = O (r)$ . We focus on the repair of systematic nodes since they are more likely to fail than parity nodes. Specifically, the proposed codes achieve the cut-set bound on repair bandwidth for systematic nodes when the code rate ${k\over n}={1\over 2}$ $\frac{k}{n} = \frac{1}{2}$ , and for ${k\over n}>{1\over 2}$ $\frac{k}{n} > \frac{1}{2}$ , the repair bandwidth is less than twice of the cut-set bound. Compared with new advanced piggybacking codes, the proposed codes obtain a significant reduction on repair bandwidth for systematic nodes while also consuming less disk I/Os. In terms of average repair bandwidth of all nodes, the proposed codes are intuitively better than the existing advanced piggybacking codes.