基于组合矩阵的精确修复MDS编码

Exact-Repair MDS Code Construction Using Compound-Matrix

针对分布式存储系统中精确修复故障节点数据的问题,构造了一类最小存储再生编码。本文利用线性无关矢量以及分块矩阵构造了编码的生成矩阵。所有编解码运算都属于GF(2)域,编码后的数据混合存放在存储节点中。采用该编码的存储系统,能够仅经过2k个基本异或运算精确修复任意单节点故障。修复故障的最小带宽为M×(k+1)/n,且在系统正常工作时,能够为单用户提供最高n×B的可用带宽。与其它最小存储再生码相比,编码矩阵简单,解码计算量较小,为用户提供较高的可用带宽。

A kind of minimum storage regenerating （MSR） code is constructed in this paper for exact-repair error node in the distributed storage systems. The generation matrix is built by using the compound-matrix and the linear independent vectors. The system data and the redundancy data are mixed and stored in each storage node. All the operations of the encoding and the decoding are belong to the GF（2）. Only after 2k basic XOR operations, the storage system can be exactly repaired for single node＇ s error with the minimum bandwidth ofM ~ （k ＋ 1 ）/n, and it can provide the maximum bandwidth of n x B for the single user in the normal conditions. Compared with the other MSR codes, the codes proposed by the paper have more straight forward structure and less decoding operation, and it can provide the most available bandwidth for users.