可用性不等的全符号局部修复码构造

Construction of all-symbol locally repairable codes with unequal availability

摘要:

现有的可用性不等的全符号局部修复码存在参数取值受限与码率较低的问题。为了解决该问题,基于饱和正交表构造一类可用性不等的全符号局部修复码,实现了较高码率。具体而言,根据饱和正交表生成关联矩阵,对关联矩阵进行矩阵变换以及克罗内克积操作,构造了信息符号具有高可用性的全符号局部修复码,以及信息位可用性不等的全符号局部修复码。理论分析表明,信息符号具有高可用性的全符号局部修复码参数取值灵活,且在局部性r=2时维度和码长都达到最优；与现有的全符号局部修复码相比,信息位可用性不等的全符号局部修复码在码率性能上更具优势。

Abstract:

The existing all-symbol locally repairable codes with unequal availability have limited parameter values, and low code rates. In order to solve the problems above, this paper constructs a class of all-symbol locally repairable codes with unequal availability based on saturated orthogonal arrays, which achieves higher code rates. Specifically, the association matrix is generated based on the saturated orthogonal array, and the matrix transformations as well as the Kronecker product operations are performed on the association matrix to generate all-symbol locally repairable codes with high availability of information symbols and unequal availability of information bits. Theoretical analyses show that all-symbol locally repairable codes with high availability of information symbols have flexible parameter values and are optimal in dimension and code length at locality r=2. Compared with the existing all-symbol locally repairable codes, the constructed all-symbol locally repairable codes with unequal availability of information bits perform better in terms of code rate.