Abstract: Erasure coding algorithms are widely applied in both single-data-center and multi-data-center environments.Current research on erasure coding algorithms primarily focuses on storage cost and repair bandwidth.However,challenges such as how to perform repairs across multiple data centers with limited dedicated bandwidth and switch constraints,and how to balance key factors like reliability and fault tolerance,have not been thoroughly analyzed or addressed.This study targets the three-data-center scenario,which is one of the most common multi-data-center configurations.First,it identifies four crucial factors for erasure coding in system design:redundancy,reliability,fault tolerance,and decoding bandwidth.Based on these factors,it then proposes ansingle-data-center local reconstruction code(S-LRC) algorithm that achieves optimal bandwidth repair within a single data center.Building on the S-LRC algorithm,it further develops the global local reconstruction code(G-LRC) algorithm to accommodate the architecture of a three-data-center setup.Compared to traditional coding schemes,the proposed G-LRC algorithm offers higher reliability,greater fault tolerance,and a lower decoding bandwidth penalty.Specifically,for two-node failures,the decoding bandwidth penalty of G-LRC is only 1/7～2/7 of that of traditional schemes.Finally,the G-LRC algorithm is implemented and validated in a large file storage system,where an optimal decoding decision algorithm is designed to reduce repair bandwidth,addressing the deployment challenges of non maximum distance separable(non-MDS) codes in practical systems.

Key words: Three data center, Erasure code, Local reconstruction code, Maximum recovery code, Reed-solomon code