Construction of Binary Locally Repairable Codes With Optimal Distance and Code Rate
Construction of Binary Locally Repairable Codes With Optimal Distance and Code Rate
复制标题
DOI：
10.1109/lcomm.2021.3075520
复制
发表时间：
2021-07
期刊：
影响因子：
--
通讯作者：
Jing Wang;Keqin Shen;Xiangyang Liu;Chunlei Yu
中科院分区：
文献类型：
--
作者：
Jing Wang;Keqin Shen;Xiangyang Liu;Chunlei Yu
目前，对分布式存储系统中局部可修码（lrc）的研究表明，构造具有最优最小距离的二进制lrc （blrc）相对容易，但在最小距离上界条件下，构造具有最优码率的blrc仍然比较困难。为了解决这一问题，本文构造了具有最优最小距离和最优码率的blrc。所构造的线性码是具有信息符号局部性和可用性的线性码，每个修复组只有一个奇偶校验符号。具体而言，采用分组设计的方法，构建最优距离最小、最优码率为局部性$r=2$或可用性$t=2$的blrc。与W. Song等人提出的blrc相比，本文构建的blrc在码长和码率方面表现更好。在此基础上，利用单位矩阵变换的方法，构造了可用性$t=2$时具有最优距离和最优码率的blrc。与现有的基于图构造的blrc相比，该构造具有最小距离和码率的特点。
At present, the research on locally repairable codes (LRCs) in distributed storage systems indicates that, it is relatively easy to construct binary LRCs (BLRCs) with the optimal minimum distance, but under the condition of minimum distance upper bound, it remains difficult to construct the BLRCs with the optimal code rate. In order to solve the problem, BLRCs with optimal minimum distance and optimal code rate are constructed in this letter. The constructed linear codes are BLRCs with locality and availability of information symbols, and each repair group has only one parity symbol. Specifically, the method of block group design is adopted to construct the BLRCs with optimal minimum distance and optimal code rate of locality $r=2$ or availability $t=2$ . Compared with the BLRCs proposed by W. Song et al, the BLRCs constructed in this letter perform better in code length and code rate. Furthermore, using the method of identity matrix transformation, BLRCs with optimal minimum distance and optimal code rate for availability $t=2$ are also constructed. Compared with the existing BLRCs based on graph construction, this construction has the same characteristics of minimum distance and code rate.