最优局部修复码的构造

Construction of Optimal Locally Repairable Codes

摘要:

局部修复码(Locally Repairable Codes, 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,本文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,达到了最优码率界,但是其局部性不高。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,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。

Abstract:

Locally Repairable Codes (Locally Repairable Codes, LRCs), as one of the erasure codes, are widely used in distributed storage systems. Aiming at the problem that the current locally repairable code has low code rate and large locality parameter restriction when meeting the minimum distance optimal bound, this paper proposes a construction method of optimal locally repairable code based on the square network. It uses the square network to construct the check matrix of the locally repairable codes, and starts from the check matrix to construct the locally repairable codes, which achieves the optimal rate bound, but its locality is not high. By further extending the incidence matrix in horizontal and vertical directions of the square network, the performance of the locally repairable codes constructed are improved in locality. And compared with the existing locally repairable codes, the locally repairable codes constructed not only meet the minimum distance optimal bound, but also reach the rate optimal bound of the locally repairable codes, which can be applied to any locality. The construction has reference significance for the construction of bivariate optimal locally repairable codes.