基于MOLS的最优二元局部修复码构造  

Construction of Optimal Binary Locally Repairable Codes Based on MOLS

作　　者：王娥 李静辉 杨佳蓉 WANG E;LI Jinghui;YANG Jiarong(Chang'an University,Xi'an 710064)

机构地区：[1]长安大学,西安710064

出　　处：《计算机与数字工程》2023年第2期396-400,共5页Computer & Digital Engineering

基　　金：国家自然科学基金项目(编号:62001059);陕西省重点研发计划项目(编号:2021GY-019)资助。

摘　　要：目前局部修复码(Locally Repairable Codes,LRCs)在分布式存储系统中的应用引起了广泛关注。为了减小LRCs的编码和修复复杂度,论文提出一种二元局部修复码(Binary Locally Repairable Codes,BLRCs)的构造算法。首先通过相互正交的拉丁方(Mutually Orthogonal Latin Squares,MOLS)构造特定参数的均衡不完全区组设计(Balanced Incomplete Block Design,BIBD),然后利用BIBD的关联矩阵构造BLRCs的生成矩阵,最后由生成矩阵构造具有信息符号(r,t)-局部性的BLRCs。理论分析表明,论文提出的基于MOLS构造的BLRCs满足最优最小距离界,是最优的二元局部修复码。特别地,当可用性t=2时,基于MOLS构造的BLRCs的码率达到了Parakash等提出的最优码率界。与基于阵列LDPC码构造的BLRCs,基于迭代矩阵构造的BLRCs和直积码相比,论文提出的基于MOLS构造的BLRCs的码率更高。The application of Locally Repairable Codes(LRCs)in distributed storage systems has attracted a lot of attention.In order to reduce the coding and repairing complexity of LRCs,this paper proposes a construction algorithm of Binary Locally Repairable Codes(BLRCs).Firstly,the balanced incomplete block design(BIBD)with specific parameters is constructed by mutually orthogonal latin squares(MOLS),then the incidence matrix of BIBD is used to construct the generator matrix of BLRCs,and finally,the BLRCs with information symbol(rt)-locality are constructed from the generator matrix.Theoretical analysis shows that the BLRCs constructed based on MOLS in this paper satisfy the minimum distance bound,which proves the codes are optimal BLRCs.In particular,when the availability t=2,the code rate of BLRCs constructed based on MOLS reaches the optimal code rate bound proposed by Parakash et al.Compared with BLRCs constructed based on array LDPC codes,iterative matrix and direct product codes,the code rate of BLRCs constructed based on MOLS in this paper is higher.

关 键 词：分布式存储系统 局部修复码 正交拉丁方 均衡不完全区组设计 最小距离 

分 类 号：O157.4[理学—数学] T316.4[理学—基础数学]