Locally repairable codes with multiple (ri, δi)-localities
Locally repairable codes with multiple (ri, δi)-localities
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DOI：
10.1109/isit.2017.8006887
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发表时间：
2017-02
期刊：
影响因子：
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通讯作者：
Bin Chen;Shutao Xia;Jie Hao
中科院分区：
文献类型：
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作者：
Bin Chen;Shutao Xia;Jie Hao
在分布式存储系统中，为了降低磁盘I/O和修复成本，引入了局部可修复代码（lrc）。为了容忍多节点故障，进一步提出了具有(r, δ)-局域的lrc。由于热数据在分布式存储系统中并不少见，Zeh et al.和Kadhe et al.最近都在关注具有多个位置或不等位置的lrc (ml - lrc)，这表明代码符号之间的位置可以不同。ml - lrc在降低热数据修复成本方面很有吸引力。在本文中，我们将ml -LRC推广到多节点失效的（r, δ）局域情况，并定义了一个具有多个（ri, δi）i [s]局域（s >2）的LRC，其中r1 2 s。这种代码确保某些热数据可以更快地修复，并且在某些情况下具有更好的容错能力，因为ri相对较小，δι较大。然后，我们利用再生集技术推导出lrc最小距离的类单态上界。最后，我们得到了一类最优ml - lrc的显式和结构化结构，并将其进一步推广到多个（ri, δi）i [s]局部的情况。
In distributed storage systems, locally repairable codes (LRCs) are introduced to realize low disk I/O and repair cost. In order to tolerate multiple node failures, the LRCs with (r, δ)-localitty are further proposed. Since hot data is not uncommon in a distributed storage system, both Zeh et al. and Kadhe et al. focus on the LRCs with multiple localities or unequal localities (ML-LRCs) recently, which said that the localities among the code symbols can be different. ML-LRCs are attractive and useful in reducing repair cost for hot data. In this paper, we generalize the ML-LRCs to the (r, δ)-locality case of multiple node failures, and define an LRC with multiple (ri, δi)i ∊ [s] localities (s > 2), where r1 2 s. Such codes ensure that some hot data could be repaired more quickly and have better failure-tolerance in certain cases because of relatively smaller ri and larger δι. Then, we derive a Singleton-like upper bound on the minimum distance for the proposed LRCs by employing the regenerating-set technique. Finally, we obtain a class of explicit and structured constructions of optimal ML-LRCs, and further extend them to the cases of multiple (ri, δi)i ∊ [s] localities.