A Formula for the I/O Cost of Linear Repair Schemes and Application to Reed-Solomon Codes
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910293099020288 |
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| author | Liu, Zhongyan Zhang, Zhifang |
| author_facet | Liu, Zhongyan Zhang, Zhifang |
| contents | Node repair is a crucial problem in erasure-code-based distributed storage systems. An important metric for repair efficiency is the I/O cost which equals the total amount of data accessed at helper nodes to repair a failed node. In this work, a general formula for computing the I/O cost of linear repair schemes is derived from a new perspective, i.e., by investigating the Hamming weight of a related linear space. Applying the formula to Reed-Solomon (RS) codes, we obtain lower bounds on the I/O cost for full-length RS codes with two and three parities. Furthermore, we build linear repair schemes for the RS codes with improved I/O cost. For full-length RS codes with two parities, our scheme meets the lower bound on the I/O cost. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04912 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Formula for the I/O Cost of Linear Repair Schemes and Application to Reed-Solomon Codes Liu, Zhongyan Zhang, Zhifang Information Theory Node repair is a crucial problem in erasure-code-based distributed storage systems. An important metric for repair efficiency is the I/O cost which equals the total amount of data accessed at helper nodes to repair a failed node. In this work, a general formula for computing the I/O cost of linear repair schemes is derived from a new perspective, i.e., by investigating the Hamming weight of a related linear space. Applying the formula to Reed-Solomon (RS) codes, we obtain lower bounds on the I/O cost for full-length RS codes with two and three parities. Furthermore, we build linear repair schemes for the RS codes with improved I/O cost. For full-length RS codes with two parities, our scheme meets the lower bound on the I/O cost. |
| title | A Formula for the I/O Cost of Linear Repair Schemes and Application to Reed-Solomon Codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2401.04912 |