局部修复码的最优构造

分布式存储系统采用冗余策略来确保数据的可靠性和可用性,局部修复码(locally repairable codes,LRC)引起了广泛的关注,极大地减少了数据修复过程中所连接的节点数,在数据存储中作用极大.每个信息码元可以从其他t个不相交的集合中修复,且每个集合大小为r,称此类码具有(r,t)局部度.从校验矩阵入手,提...

Optimal Construction of Locally Repairable Codes

The distributed storage system adopts redundancy strategy to ensure the reliability and availability of data.Locally repairable codes(LRC)has attracted much attention,which greatly reduce the number of nodes connected in the process of data repair and play a great role in data storage.Each information symbol can be repaired from t other disjoint sets and each set size is r,we call codes have(r,t)local degree.Starting with the calibration matrix,two methods of constructing LRC with(r,t)local degree are proposed.The first one uses acyclic relative difference sets(RDS)with parametersλ=1 to construct the correlation matrix,and the other one proposes to construct the correlation matrix by using unital design,then adding the unit matrix to the right of the correlation matrix,and constructing the LRC check matrix.The LRC constructed by both methods are that a repair group contains a check node and can achieve arbitrary(r,t)local degree.Theoretical analysis shows that the minimum distance of the constructed two codes satisfies the minimum distance boundary,which proves that both codes are optimal LRC.The information rate of code constructed by acyclic relative difference sets is 1/2,and that of code constructed by unitary design is higher than 1/2 under certain conditions,and the code rate is r/ r+t.