Universal and Dynamic Locally Repairable Codes With Maximal Recoverability via Sum-Rank Codes
Universal and Dynamic Locally Repairable Codes With Maximal Recoverability via Sum-Rank Codes
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DOI：
10.1109/tit.2019.2924888
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发表时间：
2019-06
影响因子：
2.5
通讯作者：
Umberto Martínez-Peñas;F. Kschischang
中科院分区：
文献类型：
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作者：
Umberto Martínez-Peñas;F. Kschischang
可在局部维修代码（LRC）中以相等或不平等的位置，局部距离和本地域大小，获得具有和总和的显式两层体系结构，并具有不相关的本地组，并实现了最大的恢复（MR）所有本地线性代码的家庭（无论MDS与否），直到指定的最大位置$ r $。本地字段）可以有效地进行动态修改，而无需全局重新编码或架构或外部代码的更改，在保留MR属性时，可以轻松适应存储中的新配置或新的热和冷数据。添加，删除或更新，而无需全局重新编码。 $。对于平等的地区，这些全球领域小于以前的MR-LRC的$ r \ leq h $（全球均等）。对于有限的地区和大量本地群体，给定结构的全球擦除校正复杂性与具有本地复制的Tamo – Barg代码或Reed-Barg代码或Reed-solomon代码相当，虽然当地代码的笛卡尔产物与局部复制和笛卡尔产品相同，而当$ r = 1 $和$ h = 0 $时，局部维修效率还可以适应所有类型的层次结构和参数的层次MR-LRC。降低现场尺寸，以较低的信息率为代价。
Locally repairable codes (LRCs) are considered with equal or unequal localities, local distances, and local field sizes. An explicit two-layer architecture with a sum-rank outer code is obtained, having disjoint local groups and achieving maximal recoverability (MR) for all families of local linear codes (MDS or not) simultaneously, up to a specified maximum locality $r $ . Furthermore, the local linear codes (thus the localities, local distances, and local fields) can be efficiently and dynamically modified without global recoding or changes in architecture or outer code, while preserving the MR property, easily adapting to new configurations in storage or new hot and cold data. In addition, local groups and file components can be added, removed or updated without global recoding. The construction requires global fields of size roughly $g^{r} $ , for $g $ local groups and maximum or specified locality $r $ . For equal localities, these global fields are smaller than those of previous MR-LRCs when $r \leq h $ (global parities). For unequal localities, they provide an exponential field size reduction on all previous best known MR-LRCs. For bounded localities and a large number of local groups, the global erasure-correction complexity of the given construction is comparable to that of Tamo–Barg codes or Reed–Solomon codes with local replication, while local repair is as efficient as for the Cartesian product of the local codes. Reed–Solomon codes with local replication and Cartesian products are recovered from the given construction when $r=1 $ and $h = 0 $ , respectively. The given construction can also be adapted to provide hierarchical MR-LRCs for all types of hierarchies and parameters. Finally, subextension subcodes and sum-rank alternant codes are introduced to obtain further exponential field size reductions, at the expense of lower information rates.