具有灵活容错能力的局部修复码构造

Construction of Locally Repairable Codes with Flexible Fault Tolerance

摘要:

局部修复码能有效应对分布式存储系统中多节点故障的修复难题，针对现有局部修复码容错能力不灵活且码率较低的问题，提出一类基于循环置换矩阵构造局部修复码的方法；该方法采用循环置换矩阵构造校验矩阵，并由校验矩阵生成局部修复码，经验证，与现有的局部修复码相比，构造的码实现了最小距离最优和码长最优，同时具有更高的码率和更灵活的可用性参数选择，但其容错能力受可用性参数的限制；进一步，在上述局部修复码构造的基础上，通过对校验矩阵进行克罗内克列积运算，提出了另一类局部修复码的构造方法，该类局部修复码实现了最小距离最优，并提高了系统容错能力的灵活性，可通过调整局部容错参数δ的取值实现灵活的容错能力，满足了分布式存储系统在可调容错能力上的应用需求。

Abstract:

Locally repairable codes can effectively address the challenge of multi-node failure recovery in distributed storage systems. To overcome the limitations of existing locally repairable codes, such as inflexible fault tolerance and low code rates, a method for constructing locally repairable codes based on cyclic permutation matrices is proposed. This method utilizes cyclic permutation matrices to construct a parity-check matrix, from which the locally repairable codes are generated. Experimental validation shows that, compared to existing locally repairable codes, the constructed codes achieve optimal minimum distance and optimal code length, while offering higher code rates and more flexible availability parameter choices. However, their fault tolerance capability is constrained by the availability parameters. Furthermore, based on the aforementioned construction of locally repairable codes, another class of locally repairable codes is proposed by applying the Kronecker column-wise product operation to the parity-check matrix. This class of locally repairable codes achieves optimal minimum distance and enhances the flexibility of system fault tolerance. By adjusting the value of the local fault tolerance parameter δ , flexible fault tolerance capabilities can be achieved, meeting the application requirements of distributed storage systems for adjustable fault tolerance.