Constructions Of Locally Repairable Codes Based On Tanner Graph

Nowadays,the continuous progress of science and technology has led to the repid growth of data volume.Therefore,the Distributed Storage System(DSS)which provides higher storage efficiency and data reliability has been widely used.At the same time,in order to further optimize the repair efficiency of DSS,the erasure code technology which uses relatively less redundancy for data storage is studied.Among them,due to the feature that locally repairable code(LRC)can complete the repair process by accessing other r nodes at most which in the same local group of the error node,LRC codes have received a lot of attention.At present,there have been many achievements in the study of LRC codes,most of which can be divided into two parts:the study of parameter performance and the design of construction method.In terms of parameters,it mainly analyzes the minimum distance,locality and other parameters of the code;In terms of construction,methods such as matrix-based that including generate or check matrix,cyclic or nested matrix,graph-based methods that including Tanner graph and hypergraph,and other polynomial-based or vector space-based are proposedThis paper studies the construction method of LRC codes.The main innovations and research contents of this paper are as follows:On the one hand,after learning and summarizing the construction method based on Tanner Graph,a new construction method which takes parameters average information locality,average locality and update complexity into account is proposed and optimizes the parameters mentioned.By analyzing the characteristics of Tanner Graph,firstly,the average information locality ri is optimized by designing the part of the local check nodes.Secondly,after analyzing the characteristics of local groups,the average locality r is optimized by constructing overlapping groups in different situations.Thirdly,on the basis of ensuring the minimum distance,the update complexity is optimized by designing the global check nodes.Finally,the algorithm complexity is analyzed and compared.The result shows that the proposed method optimizes the performance above and reduces the complexity of constructing LRC when the conditions are satisfied.On the other hand,by learning the method of constructing LRC with availability,the above construction method is extended.Under the situation of further considering the parameter availability,a construction of(r,t=2)i LRC also based on Tanner Graph is proposed,and relevant prerequisites and explanations are given according to the structural design characteristics of the method.Any LRC codes with parameter(n,k,r)can be constructed if the conditions are satisfied.Firstly,the number of information variable nodes contained in the local group is relatively reduced by designing of the local group's structure and prepare for the construction of availability.Secondly,on the basis of the combination,a method for constructing the availability of information variable nodes is proposed.Finally,the features of the proposed construction are explained,and through comparison,analysis and examples,it shows that the proposed method can not only construct LRC with(r,t=2)i property,but also expand the applicable range of codes with the same property.That is,the new construction method proposed can obtain multiple code results with the same property when the conditions are satisfied.