A Sparse Global Principle-Based Optimization of Matrix Erasure Coding–Decoding Algorithm in Large-Scale Storage Systems

As the scale of storage increases, the probability of the entire system failing due to hardware failures, human operational errors, virus attacks, terrorist attacks, power outages, fires, earthquakes, and other natural disasters has significantly increased due to the failure of storage nodes. To address this issue, this paper optimizes the matrix erasure coding decoding algorithm using the sparse global principle, thereby improving the fault tolerance and resilience of the storage system and ensuring high data availability and system reliability. First, based on Cauchy’s theorem, this paper optimizes matrix decoding by proposing the Cauchy matrix. Then, by combining the sparse principle and the global principle, this paper optimizes the decoding algorithm of the Cauchy matrix to improve the computational efficiency and accuracy of erasure coding–decoding. Finally, the performance analysis of the sparse random erasure-correcting code decoding algorithm shows that in the comparison of the recovery time of double nodes, the merging decoding algorithm takes a long time and has low efficiency due to the matrix inversion operation during the recovery of double nodes, and the cyclic iterative method has the highest efficiency. The efficiency of the matrix-based decoding algorithm in the recovery of double nodes is significantly better than that of the pseudo-inverse decoding method. When [Formula: see text], [Formula: see text], [Formula: see text] [Formula: see text]m/s and [Formula: see text] [Formula: see text]Mbit, the proposed algorithm has the best performance at (5,3) bitrates and can control the average repair time below 150[Formula: see text]s. When the repair interval is large, the average repair time of MSR code is larger with the increase of repair localization, which is basically about 200[Formula: see text]s, which is 50[Formula: see text]s longer than the performance of the erasure code decoding algorithm in this paper. Because the restoration interval is larger, the number of lost storage nodes is larger. Therefore, a single node is restored in regeneration mode rather than reconstruction mode. The restoration time in reconstruction mode is longer than that in regeneration mode.