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Optimal locally repairable codes with local minimum storage regeneration via rank-metric codes

机译:最佳本地可修复代码,通过等级度量代码实现本地最小存储再生

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This paper presents a new explicit construction for locally repairable codes (LRCs) for distributed storage systems. The codes possess all-symbols locality and maximal possible minimum distance, or equivalently, can tolerate the maximal number of node failures. This construction, based on maximum rank distance (MRD) Gabidulin codes, provides minimum distance optimal vector and scalar LRCs for a wide range of parameters. In addition, vector LRCs that allow for efficient local repair of failed nodes are considered. Towards this, the paper derives an upper bound on the amount of data that can be stored on DSS employing minimum distance optimal LRCs with given repair bandwidth, and presents codes which attain this bound by combining MRD and minimum storage regenerating (MSR) codes.
机译:本文提出了一种新的显式构造,用于分布式存储系统的本地可修复代码(LRC)。这些代码具有所有符号的局部性和最大可能的最小距离,或者等效地,可以容忍最大数量的节点故障。这种结构基于最大秩距离(MRD)Gabidulin码,可为各种参数提供最小距离的最佳矢量和标量LRC。另外,考虑了允许对故障节点进行有效本地修复的矢量LRC。为此,本文推导了可以使用具有给定修复带宽的最小距离最佳LRC在DSS上存储的数据量的上限,并提出了通过组合MRD和最小存储再生(MSR)码达到此界限的代码。

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