| Recent efforts have been focusing on locally repairable code(LRC)to address the urgent problems of multiple-node failures and hot data managements in the distributed storage systems(DSSs).Specifically,the failure nodes can be repaired separately by t disjoint repair groups whose sizes do not exceed r,and the design of the block structure can optimize the performance of code storage and repair.Among them,single-parity(r,t)-LRC with each repair group contains a single parity node can achieve a higher code rate while attain the distance bounds of LRC.Meanwhile,to speed up the repair rate of the hot data,two typical scenarios,i.e.,unequal locality and unequal recovery,are introduced into the LRC with multiple repair groups.This thesis mainly analyzes the minimum distance bound and proposes the code construction method under the above two scenarios,and the main research content of this thesis can be divided into the following two parts:In the first part,we derive the minimum distance bound of the LRC with multiple repair groups.The LRC with information(r,t)-locality proposed by Bhadane and Thangaraj is proved to be achievable,i.e.,there exists a code whose minimum distance reaches the derived bound.Since the code rate of the code that meets the above bounds is low,in order to obtain codes with a higher code rate,the single-parity(k_r,t)-LRC and single-parity(r,t)-LRC are attained by accounting for the unequal locality and unequal recovery into the single-parity(r,t)-LRC.Next,the local groups of block single-parity(k_r,t)-LRC is designed as a block diagonal matrix which makes the code easier to construct,and the counterpart of block single-parity(r,t)-LRC is vertical partitioning,which is beneficial to reduce the average information locality of the code when repairing one or two error nodes in parallel reading.Then the associated minimum distance bounds of block single-parity(k_r,t)-LRC and block single-parity(r,t)-LRC are attained.In the second part,we mainly investigate the code construction rules of binary block single-parity(r,t)-LRC and block single-parity(k_r,t)-LRC.First,we prove that the optimal minimum distance binary block single-parity(k_r,t)-LRC and block single-parity(r,t)-LRC can be effectively constructed by some irregular low-density parity-check(LDPC)code.Based on Mac Kay and PEG algorithm,this thesis construct the above two classes of codes,and proves that obtained codes can reach the minimum distance bound of LRC.Finally,through the analysis of the average information locality of the block single-parity(r,t)-LRC,this thesis finds that when the same code length n,dimension k,the minimum distance d,and availability t are given,compared with the existing single-parity(r,t)-LRC that can reach the minimum distance,the block single-parity(r,t)-LRC has a smaller average information locality when repairing one or two error nodes in parallel reading.For storage systems with hot data,the proposed binary codes seem promising for system implementations since the encoding,repairing,parallel reading,and data reconstruction can be performed by simple XOR operations. |
