基于正交拉丁方的局部修复码构造  

Construction of locally repairable codes based on orthogonal Latin square

作　　者：刘帅帅 王静[1] 刘哲 徐忠环 LIU Shuaishuai;WANG Jing;LIU Zhe;XU Zhonghuan(School of Information Engineering,Chang’an University,Xi’an 710064,China)

机构地区：[1]长安大学信息工程学院,陕西西安710064

出　　处：《浙江大学学报（工学版）》2024年第3期501-509,共9页Journal of Zhejiang University：Engineering Science

基　　金：国家自然科学基金资助项目(62001059,62072054);陕西省自然科学基金资助项目(2021GY-019)。

摘　　要：针对目前具有(r,t)局部性的局部修复码码率较低且构造过程中计算复杂度过高的问题,提出基于正交拉丁方的二元局部修复码构造方法.根据正交拉丁方元素与矩阵位置的对应关系构造关联矩阵,得到具有全符号局部性的局部修复码(AS-LRCs),该码的码率和码长渐近边界条件,且最小距离较大.利用关联矩阵级联单位矩阵构造信息位具有(r,t=2)局部性的单校验局部修复码,该码的最小距离和码率均满足最优边界条件,为最优局部修复码.考虑到实际分布式存储系统中存在高故障率节点,利用正交拉丁方完备组构造具有信息位局部性的高可用性单校验局部修复码(IS-LRCs),可以灵活选择可用性t,提高了系统的鲁棒性与灵活性.The construction of binary locally repairable codes based on orthogonal Latin square was proposed,to resolve the problems of low code rate and high computational complexity of locally repairable codes with (r,t)-locality.The incidence matrix was derived according to the corresponding relationship between the orthogonal Latin square elements and the positions of the digital matrix,and then the all symbol-locally repairable codes(AS-LRCs)were constructed based on the incidence matrix above.The AS-LRCs boasted asymptotically boundary conditions in terms of code rate and code length,and desired minimum distance.The single-check locally repairable codes with information (r,t=2)-locality were constructed by utilizing the incidence matrix concatenated with an identity matrix.The minimum distance and the code rate of the single-check locally repairable codes reached the optimal boundary conditions,making them be optimal locally repairable codes.Considering that there are nodes with high failure rate in practical distributed storage systems,the single-check information symbol-locally repairable codes(IS-LRCs)with high availability were further constructed through the orthogonal Latin square complete groups,of which the availability parameter can be selected flexibly,and the robustness and the flexibility of distributed storage systems were improved.

关 键 词：分布式存储系统 局部修复码 正交拉丁方 最小距离 节点故障率 

分 类 号：TN911.2[电子电信—通信与信息系统]