Repair of Algebraic Geometry Codes of Two Failed Nodes

Abstract

For distributed storage systems using coding technology, the problem often is the node repair problem. When a storage node fails, in order to ensure the effective transmission of information, it is necessary to recover the invalid node data. The research in the repair mode is at most accurate repair. The method of retrieving the information of the invalid node by accurately accessing the information of the existing node. The commonly used regenerative code is the MDS code. Recently, Venkatesan Guruswami et al. obtained the optimal RS code (measured by sub-symbol). However, the code length of the RS code Limited by the number of elements in the finite field, Chaoping Xing et al. can break through this limitation by using algebraic geometric code repair. Based on Xing, this paper discusses the repair and bandwidth problems for two failed nodes. Then, through the example of Hermitian code, the bandwidth is consistent with the results of Hoang Dau et al. but our symbol storage is small.