A construction of Maximally Recoverable LRCs for small number of local groups
A construction of Maximally Recoverable LRCs for small number of local groups
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DOI：
10.1109/isit54713.2023.10206554
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发表时间：
2022-12
期刊：
影响因子：
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通讯作者：
Manik Dhar;Sivakanth Gopi
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文献类型：
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作者：
Manik Dhar;Sivakanth Gopi
最大可恢复局部重建码（MR LRC）是为分布式存储设计的代码，以在给定的存储冗余和局部性的情况下提供对故障的最大恢复力。（n，r，h，a，g）-MR LRC具有被划分成大小为r = n/g的g个局部组的n个坐标，其中每个局部组具有“a”个局部奇偶校验并且存在附加的“h”个全局奇偶校验。这样的代码可以纠正每个本地组中的“a”擦除和任何附加擦除。在小的字段上的MR LRC的构造是可取的，因为字段大小决定了在实践中的编码和解码效率。在这项工作中，我们给出了大小为q = O（n）h+（g−1）a− h/g的域上的（n，r，h，a，g）-MR-LRC的一个新的构造，它推广了Hu和Yekhanin（ISIT 2016）的构造。当存在少量本地组时，这改进了现有技术，这在MR LRC的实际部署中是真实的。
Maximally Recoverable Local Reconstruction Codes (MR LRCs) are codes designed for distributed storage to provide maximum resilience to failures for a given amount of storage redundancy and locality. An (n, r, h, a, g)-MR LRC has n coordinates divided into g local groups of size r = n/g, where each local group has ‘a’ local parity checks and there are an additional ‘h’ global parity checks. Such a code can correct ‘a’ erasures in each local group and any additional erasures. Constructions of MR LRCs over small fields is desirable since field size determines the encoding and decoding efficiency in practice. In this work, we give a new construction of (n, r, h, a, g)-MR-LRCs over fields of size q = O(n)h+(g−1)a−⌈h/g⌉ which generalizes a construction of Hu and Yekhanin (ISIT 2016). This improves upon state of the art when there are a small number of local groups, which is true in practical deployments of MR LRCs.