Research And Construction Of Locally Repairable Codes Based On Packings

Distributed data storage has become the mainstream method for large-scale data storage in enterprises and institutions because of its advantages of mass storage,easy expansion and low cost.However,with the continuous expansion of the system scale,the load of the data storage disks continues to increase,and data failures on storage nodes are a common phenomenon,which affects the reliability of data storage.The multi-copy technology can greatly improve the reliability of data storage by creating data copies and writing to multiple different storage nodes,but it has the problem of excessive storage overhead.The locally repairable code adopts the method of grouping data nodes to generate additional check nodes to achieve intra-group repair.It has excellent performance of high repair efficiency and low storage overhead,and has become a key technology for distributed data storage.Locally repairable codes are further divided into two types: single repair set and multiple repair sets.Compared with a single repair set,local repair codes with multiple repair se ts are better in parallel read ability.Therefore,how to design locally repairable codes with multiple repair sets according to application requirements is a hot research topic.This thesis proposes a method to construct locally repairable codes with multiple repair sets based on packings,and provides an explicit structure for the code.In addition,the locally repairable code can still reach the optimal bound proposed by Rawat in 2016 when the repair set size reaches 4.The main research contents are as follows:1)First,two structures of resolvable balanced incomplete block design and resolvable group divisible design in combinatorial design theory are used to construct two types of parameters k(28)0,4(mod 12).In order to expand the value range of k,use cyclic packings with parameter k(28)6(mod 12)to construct two types of 0,2(mod 4)-regular packings with parameter k(28)6(mod 12).Then,another new parameter k(28)5(mod 12)of 0,2(mod 4)-regular packing with block size {4,3} is constructed for the first time by using a type of parameter k(28)6(mod 12)of cyclic packings.Based on the parameter k(28)5(mod 12),all the remaining parameters of the 0,2(mod 4)-regular packing with a block size of 4 are constructed again by combining and adding.The above construction not only proves the existence of all parameters of the r egular packings with a block size of 4,but also expands the value range of the number of occurrences of each element in the regular packings in its block.2)Using the correspondence between the generator matrix of locally repairable codes and the blocks of regular packings,in the case that each repair set contains only one check symbol,an optimal locally repairable codes with a repair set size of up to 4is constructed using regular packings with a block size of 4,and the code can reac h the optimal bound.Then,the parameters of the optimal locally repairable codes constructed in this thesis are compared with the parameters of some representative construction methods.The results show that the locally repairable codes constructed in this thesis perform better in terms of parameter value range,storage cost and high bit rate.