基于混合型正交表构造部分重复码*

考虑到分布式存储系统中数据的存储和节点修复，提出一种基于混合型正交表的异构部分重复(fractional repetition, FR)码构造算法，并证明了该异构FR码是一般好的一般部分重复(generalized fractional repetition, GFR)码。具体地，利用混合型正交表中的水平对构造关联矩阵，根据关联矩阵对数据块在存储节点进行存放。另外，利用分组的方法在混合型正交表的基础上构造分组部分重复码,可以在局部组内实现单故障节点的精确无编码修复，修复局部性为2或3，且能够对多个故障节点进行快速有效的修复。性能分析和实验仿真可知，所构造的分组FR码与RS码和简单再生码相比，在修复故障节点时具有较小的修复带宽开销和修复局部性，修复效率得到了提升

Construction of fractional repetition codes based on mixed orthogonal array

For data storage and node repair in distributed storage systems, heterogeneous fractional repetition (FR) codes are constructed based on mixed orthogonal array. It is proved that the constructed heterogeneous FR codes are universally good generalized fractional repetition (GFR) codes. Concretely, the incidence matrix of FR codes is obtained by using the horizontal pairs in the mixed orthogonal array, and the data blocks are stored in the nodes of distributed storage systems. In addition, the grouping method is used to construct the grouping FR codes on the basis of the mixed orthogonal array, realizing the precise non coding repair of a single fault node within the local repair group, and the repair locality is 2 or 3. Moreover, the grouping FR codes can repair multiple fault nodes quickly and efficiently. Performance analyses and experimental simulations show that, compared with RS codes and simple regeneration codes, the constructed grouping FR codes have lower repair bandwidth overhead and repair locality, and the repair efficiency is also improved.