Study Of Performance Optimization Of Coding Schemes In Distributed Storage Systems

In Distributed Storage Systems（DSSs）,data is stored through large network of nodes,but storage nodes are prone to failure.Redundancy has been introduced to ensure reliable data storage,replication is the simplest and most widely used redundancy technology,it has high storage overhead;Erasure codes can decrease the storage overhead,but the costs of repairing bandwidth are high.Ahlswede et al.introduced network coding techniques into DSSs and proposed modern storage coding techniques,in which regenerating codes can minimize repair bandwidth but add system disk I/O costs;Locally Repairable Codes（LRCs）can effectively repair faulty nodes,repair costs are reduced by using a small number of nodes in the repair process,and repair locality is better;Fractional Repetition（FR）codes do not require coding and decoding in the repair process,simplifying the node repair process.In this paper,three coding schemes with better performance are proposed based on existing LRCs and FR codes,as follows:（1）Considering that the existing LRCs construction parameters are limited and the code rate is not high,construction methods of LRCs based on matching and decomposition are proposed.Using perfect matching andt K₃-factor decomposition of complete graphs to construct the generation matrix of LRCs,the constructed codes can be localized in a wide range of choices,and LRCs with diverse parameters can be constructed according to the needs of distributed storage systems.After analysis,it is found that the constructed LRCs all achieve the optimal minimum distance,specifically,the code rate of the LRCs based on the perfect matching of the complete graph is also optimal.（2）In the study of LRCs,it is found that although most of the existing LRCs can achieve the minimum distance optimality,the overall code rate is still low.To address the above problems,the methods of constructed LRCs based on complete cyclic difference sets are proposed,and the constructed LRCs not only achieve the optimal minimum distance bound,but also the code rate is optimal at the availability t（28）2;In order to further improve the code rate,LRCs are constructed by Kronecker product of the correlation matrix based on the complete cyclic difference set with the full 1-row vector,whose code rate is closer to the optimal code rate bound than the existing LRCs.（3）Considering the different access conditions of hot and cold data in actual DSSs,the construction method of FR codes based on Paley matrix is proposed.Firstly,Paley matrix is used to construct the isomorphic FR codes.The minimum distance and reconstruction degree of the constructed FR codes reach the optimal boundary,but it cannot be applied to the flexible cold and hot data regulation system;Furthermore,by cascading Paley matrices of different orders,the FR codes with node storage capacity heterogeneous are constructed.To satisfy the different repetition degrees required for hot and cold data in DSSs,the FR codes with repetition degrees heterogeneous are constructed by adding the adjustment matrix to the correlation matrix and deleting the columns of the unit matrix.The theoretical studies reveal that the FR codes based on the Paley matrix can flexibly adjust the repetition degree in accordance with the actual data access condition,and its storage efficiency is more suitable for practical DSSs.