最优局部修复码的构造

Construction of Optimal Locally Repairable Codes

局部修复码(LRCs)作为纠删码的一种,被广泛应用于分布式存储系统中;针对目前局部修复码在满足最小距离最优界时码率不高且局部性的参数限制大的问题,提出一种基于方形网络的最优局部修复码构造方法,利用方形网络构造局部修复码的校验矩阵,从校验矩阵入手构造局部修复码,此码达到了最优码率界,但是其局部性有所限制;进一步将方形网络水平方向和垂直方向上的关联矩阵进行扩展,用方形网络的扩展矩阵构造局部修复码的校验矩阵,所构造的局部修复码在局部性上的性能有所提升;和现有局部修复码进行对比分析,构造的局部修复码不仅满足最小距离最优界,同时达到了局部修复码的码率最优界,可适用于任意局部性的情况,对二元最优局部修复码的构造具有借鉴意义。

As one of erasure codes,locally repairable codes(LRCs)are widely used in distributed storage systems.Aiming at the problem that current LRCs have low code rate and large locality parameter restriction when meeting the minimum distance and optimal bound,an optimal locally repairable code construction method based on square network is proposed.The square network is used to construct the check matrix of the LRCs,and the locally repairable codes are constructed by starting with the check matrix,which achieves the optimal rate bound,but its locality is limited.By further extending the incidence matrix in horizontal and vertical directions of the square network,the check matrix of the LCRs is constructed by using the extended matrix of square network.the performance of the constructed LCRs is improved in locality.And compared with existing LCRs,the constructed LCRs not only meet the minimum distance optimal bound,but also reach the rate optimal bound of the LCRs,which can be applied to any locality,it has reference significance for the construction of bivariate optimal LCRs.