On Repairing Iteration Number Of Locally Repairable Codes

As a family of Erasure Codes(ECs),Locally Repairable Codes can recover any code symbol only use at most r other code symbols.With this feature,Locally Repairable Codes(LRCs)in distributed storage system have broad prospects.At present,there have been many researches on Locally Repairable Codes with multiple erasure tolerance,such as Codes with Sequential Repair ability,Codes with Parallel Repair ability,and Codes with both Sequential and Parallel Repair ability are called(n,k,r,tavl,tseq)-Exact Locally Repair Codes(ELRCs).Multiple failed symbols commonly divided into serval ordered disjoint sets in the repair process.The number of disjoint sets is called the iteration number of repairing.The iteration number of repairing can greatly influence the repair efficiency of multiple erasure.Excessive iteration number of repairing process can cause too many failed symbols to wait for other symbols to be fixed.And in the distributed storage system with LRC,excessive iteration number can cause the reduction of system availability.This thesis is focused on the iteration number of Locally Repairable Codes with multiple erasure tolerance,mainly in the following aspects:On the one hand,we study the iteration number upper bounds of(n,k,r,tavl,tseq)-ELRC with joint sequential-parallel repair.Firstly,we use a Hyper Graph based presentation of any parity check matrix and transform the complicated repairing process into the deleting process of vertices and hyper edges.Secondly,we give a tight iteration number upper bound for any(n,k,r,2,tseq)-ELRC,and prove there can always be an failed index set holds the equality sign.Thirdly,we give a constructive proof of an existing iteration number upper bound for any(n,k,r≥2,3,tseq)-ELRC.Then,we give a tight iteration number upper bound for any(n,k,r=1,tavl,tseq)-ELRC.Finally,we compare the two tighter bound we give in this thesis to the existing results.On the other hand,we study the repair mode with iteration number priority.At first,the merit and demerit of Locally Repairable Codes with availability and sequential repair tolerance have been analysed in this thesis.Then,instead of trying to get a Locally Repairable Codes with low or given iteration number,we give a repairing mode with iteration number priority:search a repair set disj oint to the error index set with lowest cardinal number.Then,we make a feasibility analysis to the repair method.In the next part,we give a Simulated Annealing based repair method.Finally,by analog simulation,we compare the sequential mode,parallel mode,joint sequential-parallel mode to the repair mode with iteration number priority.