基于拉丁方的最优局部修复码构造  

Construction of Optimal Locally Repairable Codes Based on Latin Square

作　　者：王娥 王静[1] 李静辉 杨佳蓉 WANG E;WANG Jing;LI Jinghui;YANG Jiarong(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,西安710064

出　　处：《北京邮电大学学报》2023年第5期8-14,共7页Journal of Beijing University of Posts and Telecommunications

基　　金：国家自然科学基金项目(62072054)。

摘　　要：使用构造的具有(r,t)-局部性的局部修复码(LRCs)难以同时实现最小距离最优和码率最优。对此,提出一种基于拉丁方的LRCs构造算法,将拉丁方中的数字元素按照一定规律转换为二进制元素,再结合矩阵的克罗内克积构造所需的校验矩阵,从而构造具有(r,2)-局部性的单校验二元局部修复码(BLRCs)。进一步提出了基于正交拉丁方的LRCs构造算法,并用于构造具有任意可用性t的BLRCs。理论分析结果表明,构造的这2种LRCs的最小距离均达到了最优的最小距离界。与基于直积码和基于阵列低密度奇偶校验码构造的LRCs相比,所提算法实现了更优的码率。At present,locally repairable codes(LRCs)with(r,t)-locality are seldom able to achieve the optimal minimum distance and optimal code rate at the same time.Therefore,a construction algorithm of LRCs based on latin square is proposed.More specifically,the digits in latin square are replaced by binary numbers according to certain rules,and then the required check matrix can be constructed by the kronecker product.Thus,binary locally repairable codes(BLRCs)with(r,2)-locality of information symbols are constructed.Furthermore,a construction algorithm of LRCs based on mutually orthogonal latin square is proposed,which could construct BLRCs with arbitrary availability.Theoretical analyses show that,both of the two constructed codes satisfies the minimum distance bound,and their code rates are higher than that of the LRCs constructed based on direct product codes and array low density parity check codes,and the LRCs based on latin square achieve the optimal code rate.

关 键 词：分布式存储系统 局部修复码 拉丁方 正交拉丁方 

分 类 号：TN911.2[电子电信—通信与信息系统]