论文标题
具有多个维修度的最佳维修/访问MDS阵列代码
Optimal Repair/Access MDS Array Codes with Multiple Repair Degrees
论文作者
论文摘要
在文献中，具有最佳维修属性的大多数已知高利率$（N，K）$ MDS阵列代码仅支持单个维修学位（即，在维修过程中与之联系的辅助节点的数量）$ d $，其中$ k \ le d \ le d \ le d \ le n-1 $。但是，在实际存储系统中，可用节点的数量经常更改。因此，首选具有多个维修度的$（N，K）$ MDS数组代码，并为所有节点提供最佳维修属性。据我们所知，只有两个MDS阵列代码在文献中具有这样的属性，Ye和Barg提出了这些特性（IEEETrans。Inform。Theoloy，63（10），2001- 2014年，2014年，2017年）。但是，它们的子包装水平相对较大。在本文中，我们提出了一种通用的构造方法，该方法可以将一些维修学位的一些MDS阵列代码转换为具有多个修复程度和一组节点的最佳维修属性的MDS阵列代码，而其余节点的维修效率/程度可以保留。作为通用构造方法的应用，在一个小有限的字段上获得了具有多个维修度的高速MDS阵列代码的明确构造，所有节点的最佳访问属性是获得了多个维修度的。特别是，子包装水平远小于Ye和Barg所提出的有关相同参数$ n $和$ k $的两个代码中的水平。
In the literature, most of the known high-rate $(n,k)$ MDS array codes with the optimal repair property only support a single repair degree (i.e., the number of helper nodes contacted during a repair process) $d$, where $k\le d\le n-1$. However, in practical storage systems, the number of available nodes changes frequently. Thus, it is preferred to construct $(n,k)$ MDS array codes with multiple repair degrees and the optimal repair property for all nodes. To the best of our knowledge, only two MDS array codes have such properties in the literature, which were proposed by Ye and Barg (IEEE Trans. Inform. Theory, 63(10), 2001-2014, 2017). However, their sub-packetization levels are relatively large. In this paper, we present a generic construction method that can convert some MDS array codes with a single repair degree into the ones with multiple repair degrees and optimal repair property for a set of nodes, while the repair efficiency/degrees of the remaining nodes can be kept. As an application of the generic construction method, an explicit construction of high-rate MDS array code with multiple repair degrees and the optimal access property for all nodes is obtained over a small finite field. Especially, the sub-packetization level is much smaller than that of the two codes proposed by Ye and Barg concerning the same parameters $n$ and $k$.
