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/allerton.2018.8635867
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发表时间：
2018-09
期刊：
影响因子：
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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
本地维修代码（LRC）被视为具有相等或不平等的地方，局部距离和局部田地尺寸的情况。获得具有与总和的总代码的显式两层体系结构，具有不相交的本地组，并同时获得所有局部线性代码（MDS）的家族（MR）的最大可恢复性（MR），最多可达到规定的最大局部性r。此外，局部线性代码（因此，位置，局部距离和本地字段）可以进行有效，动态修改，而无需全局重新编码或体系结构或外部代码的变化，同时保留MR，很容易适应新的热和冷数据。此外，无需全局重新编码即可添加，删除或更新本地组和文件组件。该构造需要大约$ g^{r} $的全局字段，对于本地组和最大位置r。对于平等的地区，这些全球领域比以前的MR-LRC（全球平等）小于以前的MR-LRC。对于不平等的地区，它们可为所有以前最著名的MR-LRC提供指数级的域尺寸。对于有限的地区和许多本地群体，给定结构的全球擦除校正复杂性可与具有局部复制的tamo-barg代码或芦苇 - 固体代码相当本地代码。当$ r = 1 $和$ h = 0 $时，从给定的结构中回收了带有本地复制和笛卡尔产品的芦苇 - 固体代码。最后，引入了亚延伸子代码和总和替代代码，以获得进一步的指数尺寸降低，但以较低的信息速率为代价。
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 are obtained, having disjoint local groups and achieving maximal recoverability (MR) for all families of local linear codes (MDS or not) simultaneously, up to a prescribed 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 MR, easily adapting to 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 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. Finally, subextension subcodes and sum-rank alternant codes are introduced to obtain further exponential field size reductions, at the expense of lower information rates.