Research On Matrix-based Erasure Code Decoding Algorithm

The erasure code is a kind of forward error correction coding which is widely used.Its encoding process uses a certain linear law(ie,encode algorithm)to calculate the data to obtain redundant data to achieve fault tolerance.The decoding of erasure code is a process of reconstructing failed data elements using different decoding algorithms,and may also be referred to as failure data reconstruction.In the current research on erasure codes,more research on encoding algorithms and less research on decoding algorithms,but the decoding algorithm is also an important part in the data recovery process.The efficiency impact is also critical.The commonly used erasure code decoding algorithms have some problems such as low efficiency and poor algorithm performance.Therefore,improving the efficiency and performance of the erasure code decoding algorithm is also an important research aspect in the current coding theory field.Therefore,based on the research of the erasure code and the commonly used erasure code decoding algorithm,this paper proposes a matrix-based erasure code decoding algorithm.The specific contents include:(1)Definition and properties of the correlation matrix of the decoding algorithm.The two matrices often used in the erasure code field are: generator matrix and check matrix.In this paper,a new matrix is defined based on the properties of the two matrices,which is represented as the decoding algorithm correlation matrix.Referred to as the correlation matrix,and summarize the three properties of the correlation matrix.Each row of the correlation matrix is a linear representation of an element(including data and redundant elements),which is the theoretical basis used in matrix-based erasure code decoding algorithms.(2)Research on matrix-based erasure code decoding algorithm.In the research of decoding algorithm of erasure code,the advantages and disadvantages of various decoding algorithms are compared by the research of previous decoding algorithms.Based on these advantages and disadvantages and the matrix of erasure codes,a matrix-based erasure code decoding algorithm is proposed.The decoding algorithm is higher in time efficiency than the equation solving method and the pseudo-inverse decoding algorithm,and improves the shortcomings of the pseudo-inverse decoding algorithm.It inherits the advantages of the pseudo-inverse decoding algorithm to recover random missing data blocks,and can be applied in the array erasure code and RS code at the same time.(3)Research on erasure code decoding algorithm based on sparse and global principle.After further analysis of the matrix-based decoding algorithm,the two principle are used to study the decoding algorithm in depth,which are the sparse principle and the global principle.The most sparse principle,as the name suggests,is to find the part with the least number of "1" operations to reduce the amount of computation to improve the efficiency of the algorithm,while the global principle on the other hand ensures the accuracy that the decoding algorithm recovers of missing elements.