The Research On Multi-node Repair Problem Of Distributed Storage System

Distributed storage system stores data in a number of independent nodes through the use of multiple storage devices in the network,so as to realize the massive data storage.The large number of nodes in the storage system will frequently lead to node failure,thus in order to ensure the reliability of the stored data,it is necessary to save a considerable amount of redundant data in the system,so that when some nodes are unavailable,they can use the remaining nodes to reconstruct the original ones,and the failed nodes are generated by using redundancy data.As a new data redundancy technology,the regenerating code has been a hotspot which can effectively be used to reduce the bandwidth resources consumed by the distributed system to repair the failed nodes.For the single failure node case,the coding strategy for the exact repair has been much improved and it is becoming better and better.However,the repair of failure nodes in the distributed storage system is usually triggered continuously which means that the repair of multi-node failure is required.For this reason,this thesis mainly studies the multi-node simultaneous repair mechanism and its related issues when the number of the unavailable nodes achieves a certain fixed value.First of all,the encoding form of the minimum storage point for the multi-node cooperative repair model is studied.It is known that Suh and Ramchandran constructed a class of the minimal storage regenerating code which can exactly repair a single failed node by using the interference alignment technique of the communication system.This thesis illustrates that the Suh-Ramchandran code can be employed for the multi-node failure cooperative repair case through an(n=7;k=3)code.In order to state the cooperative repair process more clearly,this thesis re-describes a class of codes with parameters(n=2k+s;k)based on the Suh-Ramchandran codes,and shows that the directly constructed codes can achieve the optimal repair bandwidth for multiple systematic failures repair.Next,in this thesis we discuss the minimum capacity cut of the centralized multi-node repair model by using the cut-type analysis,and we get a more general array condition which meeting the minimal cut capacity.This generalizes some earlier results.According to the form of the minimum capacity cut we obtained,this thesis uses a simple method of linear programming to derive a theoretical bound on the storage-bandwidth which is tighter than the known ones.Then,the parameters for the two extreme cases,that is,the minimum storage multi-node regeneration code and the minimum bandwidth multi-node regeneration code are given.Compared with the single-node repair model and the multi-node cooperative repair model,it can be seen that the centralized multi-node model has the least repair bandwidth when repairing multiple failure nodes.By analyzing the storage and bandwidth resources under some special parameters,some minimum storage multi-node regeneration code and minimum bandwidth multi-node regeneration code are proposed under the centralized multi-node repair model.Finally,a class of regenerating codes with multi-node exact repair is presented by connecting a small number of specific surviving nodes.Papailiopoulos et al.constructed a class of simple generation codes by using MDS codes that can achieve arbitrary code rate.Moreover,it has the ability to carry out exact repair by connecting f surviving nodes through simple XORs operations when single node failure happens.In this thesis,we present a new method which can exactly repair multi-node simultaneously by modifying the parity data of the simple regenerating code.The node storage and repair bandwidth of the modified regeneration codes only relate to the value f,and the node storage is closer to the minimum theoretical value as f increases.Meanwhile,when repairing multi-node failure,the proposed method not only can access the data stored on the remaining nodes directly without any calculation,but also have the properties of simple repair operation and local repair-ability,so it can be applied to distributed storage systems.