A Generic Transformation for Optimal Node Repair in MDS Array Codes Over F2
A Generic Transformation for Optimal Node Repair in MDS Array Codes Over F2
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DOI：
10.1109/tcomm.2021.3126751
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发表时间：
2019-01
影响因子：
8.3
通讯作者：
Jie Li;Xiaohu Tang;C. Hollanti
中科院分区：
文献类型：
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作者：
Jie Li;Xiaohu Tang;C. Hollanti
对于高速率线性系统最大距离可分离码（MDS），大多数早期结构都能最优地修复所有系统节点，但不能修复所有奇偶节点。幸运的是，Li等人在IEEE Trans中首先解决了这个问题。通知。理论，64(9),6257-6267,2018)，其中提出了一种转换，可以将任何非二进制MDS数组代码转换为另一个具有所需属性的代码。但是，该转换不适用于二进制MDS数组代码。在本文中，我们提出了另一种将任意$[n, k]$二进制MDS数组代码转换为新代码的通用变换，该变换赋予任意$r=n-k\ ge2 $选择的节点最优修复带宽和最优重建访问属性，同时在某些条件下保留剩余$k$节点的归一化修复带宽/重建访问。作为两个直接应用，我们证明了1)通过多次变换，任意二进制MDS阵列代码都可以转化为对所有节点具有最优重建访问的二进制MDS阵列代码；2)任意系统节点具有最优修复带宽或最优重建访问的二进制MDS阵列代码都可以转化为对所有节点具有相应最优性的二进制MDS阵列代码。
For high-rate linear systematic maximum distance separable (MDS) codes, most early constructions could initially optimally repair all the systematic nodes but not all the parity nodes. Fortunately, this issue was first solved by Li et al. in (IEEE Trans. Inform. Theory, 64(9), 6257-6267, 2018), where a transformation that can convert any nonbinary MDS array code into another one with desired properties was proposed. However, the transformation does not work for binary MDS array codes. In this paper, we address this issue by proposing another generic transformation that can convert any $[n, k]$ binary MDS array code into a new one, which endows any $r=n-k\ge 2$ chosen nodes with optimal repair bandwidth and optimal rebuilding access properties, and at the same time, preserves the normalized repair bandwidth/rebuilding access for the remaining $k$ nodes under some conditions. As two immediate applications, we show that 1) by applying the transformation multiple times, any binary MDS array code can be converted into one with optimal rebuilding access for all nodes, 2) any binary MDS array code with optimal repair bandwidth or optimal rebuilding access for the systematic nodes can be converted into one with the corresponding optimality property for all nodes.