一类新的(k+2,k) Hadamard MSR码

为降低分布式存储系统中节点的存储量,构造了一类新(k+2, k)Hadamard MSR码.该码的每个编码矩阵皆对应于2个值,供其对角元素选取.在编码矩阵中,这2个值循环出现,且不同的矩阵,循环出现的周期不同.基于这一特性构造了节点的修复方案,将失效节点中的个数据分成/2组,每一组重建2个数据,其他k+1个节点为每一组各提供1个数据.证明了若新码编码矩阵的对角元素可取的2个值不相等,则可最优修复系统节点;若所有编码矩阵对角元素可取的2个值的和为同一不为0的值,则可最优修复第1个校验节点;若所有编码矩阵对角元素可取的2个值的逆的和为1,则可最优修复第2个校验节点.新码的节点存储量降低到了Hadamard MSR码的理论界,可最优修复任意系统节点和1个校验节点. 

A New (k+2, k) Hadamard Minimum Storage Regenerating Code

To reduce the storage capacity of nodes in distributed storage systems, a new (k+2, k) Hadamard Minimum Storage Regenerating (MSR) code was constructed. Each coding matrix is related to two values, from which the diagonal elements of this coding matrix are selected. These two values appear in the coding matrix in a repeating pattern, but with different repeating cycles for different matrices. Based on the structure of the coding matrix, a repair strategy was constructed. The repair strategy divides symbols in the failed node into /2 groups with two symbols in each group, then the two symbols are recovered by downloading one symbol from each of the other k+1 nodes. If the two values related to each coding matrix are unequal, the new Hadamard MSR code can optimally repair systematic nodes. If the sum of two values related to each coding matrix is nonzero and the k values are the same, the new Hadamard MSR code can optimally repair the first parity node. If the sum of the inverse of two values related to each coding matrix is one, the new Hadamard MSR code can optimally repair the second parity node. The new code reduces the storage capacity to the bond for Hadamard MSR code. Further, it can optimally repair all systematic nodes and one parity node.