CN110990375A - Method for constructing heterogeneous partial repeat codes based on adjusting matrix - Google Patents
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Abstract
The invention discloses a method for constructing heterogeneous part repeated codes based on an adjusting matrix, which is used for constructing an FRC with heterogeneous node storage capacity and is suitable for the condition that the number n of nodes in a distributed storage system is an odd number, and the repetition rho of a data block in the constructed FRC is equal to 2. Considering that most of actual distributed storage systems have the characteristic of heterogeneity, a method based on an adjusting matrix is introduced to construct heterogeneous FRCs, the constructed FRCs can realize diversity of node storage capacity, and compared with traditional regeneration codes, the constructed FRCs have the advantages of no code repair and low calculation complexity.
Description
Technical Field
The invention belongs to the field of computers, and particularly relates to a construction method of a heterogeneous Repetition Codes (FRC) based on a regulating matrix.
Background
In a distributed storage system, data storage is a problem of multidimensional optimization. Although the regenerated code can optimize the storage consumption and repair bandwidth, the repair process usually involves a large number of finite field operations and has high computational complexity, so that the concept of partial Repetition Codes (FRC) is proposed, which indicates that the FR code can provide accurate and efficient repair and can provide the minimum repair bandwidth. The structure contains two parts of content, one is an external MDS code and the other is an internal repetition code. After the data block is coded by MDS, the output coding block is copied by rho times and then is re-dispersed to each storage node. When a node fault occurs in the system, the data can be directly downloaded from other nodes and stored in the replacement node to complete the repair, no additional operation is needed, and the calculation complexity is reduced to a great extent.
Disclosure of Invention
Aiming at the defects or shortcomings in the prior art, the invention aims to provide a method for constructing a heterogeneous part repeated code based on an adjusting matrix, which meets the requirement of a practical distributed storage system on heterogeneous structure, has heterogeneous node storage capacity and does not need coding operation in a repairing process.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for constructing heterogeneous part repetition codes based on an adjustment matrix is characterized in that the method is used for constructing an FRC with heterogeneous node storage capacity, and is suitable for the condition that the number n of nodes of a distributed storage system is an odd number, and the repetition rho of a data block in the constructed FRC is equal to 2; the method comprises the following specific steps:
step 1: first, a cyclic permutation matrix C is definedn(d-1), the matrix is a binary matrix of n x n orders, wherein n represents the number of nodes, d-1 represents the storage capacity of each node and the number of 1 rows in the matrix, and d satisfies the condition that d>3, d is an odd number;
Cnthe first row of the (d-1) matrix satisfies the following expressionFormula (II):
c(t)＝t+t2+…+t(d-1)/2+tn-(d-1)/2+…+tn-1；
after the first row of the matrix is determined, each subsequent row is sequentially shifted to the right by one bit for n-1 times, and finally C is generatedn(d-1) a matrix;
where C isn(d-1) the matrix is also a correlation matrix, the rows of the correlation matrix correspond to nodes in the distributed storage system, the columns represent stored data blocks, and the correlation matrix and the homogeneous FRCs which are not constructed by the regulation matrix are in one-to-one correspondence;
in order to more intuitively see the storage structure of the internal FRC, a regular graph is further introduced to store the homogeneous FRC, and the regular graph can pass through the incidence matrix Cn(d-1); the vertex n of the regular graph corresponds to the number of nodes in the FRC, the edge of the regular graph represents a data block, and d-1 represents the degree of the node;
step 2: introducing a matrix SnDeregulating C in step 1n(d-1) matrix, SnThe matrix generation method comprises the following steps: adding 0 row and 0 column after the matrix with all 0 elements in the (n-1) order minor diagonal of 1 to generate SnA matrix;
and step 3: the matrix C in the step 1n(d-1) and the matrix S in step 2nPerforming modulo-2 operation to obtain a new matrix P, where P is equal to Cn(d-1)+Sn(mod 2); the matrix P is also a correlation matrix at the same time, the correlation matrix and the heterogeneous FRC constructed by the adjusting matrix are in a one-to-one correspondence relationship, in order to more intuitively embody the storage structure of the internal FRC, the concept of a partial regular graph is further introduced, namely the degree of the nodes in the graph can have various conditions, and for convenience of representation, the degree is marked as PGR (n, d), wherein n represents the number of top points and corresponds to the number of nodes in the FRC, the edges of the graph represent data blocks, and d represents the maximum value of the degree of the nodes;
the obtained matrix P is a 0,1 matrix of n x n order, and after the verification of the algorithm, the condition that d, d-1 and d-2 are 1 appears in different rows of the matrix P, so that the degree of a corresponding partial regular graph has three conditions of d, d-1 and d-2, namely the node storage capacity corresponding to the constructed FRC has three conditions of d, d-1 and d-2;
thus, by adjusting the matrix SnAnd obtaining nodes with different storage capacities, wherein the heterogeneous characteristics of the nodes meet the requirements of an actual distributed storage system.
The FRC with heterogeneous node storage capacity constructed by the method is applied to repairing single-fault nodes.
The constructed FRC has the characteristic of heterogeneous node capacity, the problem of fault node repair is analyzed according to the characteristic of the heterogeneous FRC, and the construction only can consider the problem of single-node fault repair because the construction aims at the FRC with the repetition degree rho of 2, and the following 3 conditions are adopted:
a) if the node with the storage capacity of d fails, the node can be directly repaired by downloading one data block from the other d nodes respectively;
b) if the node with the storage capacity of d-1 fails, the node can be directly repaired by downloading one data block from the other d-1 nodes respectively;
c) if the node with the storage capacity of d-2 fails, the node can be directly repaired by downloading one data block from the other d-2 nodes respectively.
Compared with the prior art, the method for constructing the heterogeneous partial repeat code based on the adjusting matrix has the following technical effects:
1. considering that most of actual distributed storage systems have heterogeneous characteristics, FRC with heterogeneous node storage capacity is introduced, that is, the number of data blocks stored in different nodes is different.
2. When a single node is repaired, the effect of repairing can be achieved only by directly downloading the data blocks from other surviving nodes.
3. The FRC is constructed by adopting the principle based on the matrix and the graph, and only simple XOR operation is involved, so that the calculation complexity is low, no coding operation is performed, and the time is saved.
4. When repairing a failed node, the diversity of the degree of repair can be reflected in the constructed FRC.
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FIG. 1 is a schematic representation of a constructed heterogeneous FRC of the present invention, wherein (a) is C7(4) Matrix, (b) the figure is S7Matrix, (c) the graph is matrix P;
fig. 2 is a schematic diagram of storing a heterogeneous FRC constructed by the present invention in combination with a partial regular graph and then correspondingly storing data blocks on nodes, wherein (a) the graph is a PGR (7,5) partial regular graph, and (b) the graph is a node data node storage distribution graph;
fig. 3 is a schematic diagram of fault node repair.
The present invention will be described in further detail with reference to the accompanying drawings and examples.
Detailed Description
According to the technical scheme of the invention, the embodiment provides a method for constructing heterogeneous part repetition codes based on an adjustment matrix, the method is used for constructing an FRC with heterogeneous node storage capacity and heterogeneous repetition degree, and is suitable for the condition that the number n of nodes of a distributed storage system is an odd number, and the repetition degree rho of a data block in the constructed FRC is equal to 2; the method comprises the following specific steps:
step 1: first, a cyclic permutation matrix C is definedn(d-1), the matrix is a binary matrix of n x n orders, wherein n represents the number of nodes, d-1 represents the storage capacity of each node and the number of 1 rows in the matrix, and d satisfies the condition that d>3, d is an odd number;
Cnthe first row of the (d-1) matrix mathematically satisfies the expression:
c(t)＝t+t2+…+t(d-1)/2+tn-(d-1)/2+…+tn-1；
after the first row of the matrix is determined, each subsequent row is sequentially shifted to the right by one bit for n-1 times, and finally C is generatedn(d-1) a matrix;
where C isn(d-1) the matrix is also a correlation matrix, the rows of the correlation matrix correspond to nodes in the distributed storage system, the columns represent stored data blocks, and the correlation matrix and the homogeneous FRCs which are not constructed by the adjustment matrix are in one-to-one correspondence;
to be more intuitiveThe storage structure of the internal FRC is seen, and a regular graph is further introduced to store the homogeneous FRC, and the regular graph can pass through the incidence matrix Cn(d-1); the vertex n of the regular graph corresponds to the number of nodes in the FRC, the edge of the regular graph represents a data block, and d-1 represents the degree of the node;
step 2: introducing a matrix SnDeregulating C in step 1n(d-1) matrix, SnThe matrix generation method comprises the following steps: adding 0 row and 0 column after the matrix with all 0 elements in the (n-1) order minor diagonal of 1 to generate SnA matrix;
and step 3: the matrix C in the step 1n(d-1) and the matrix S in step 2nPerforming modulo-2 operation to obtain a new matrix P, where P is equal to Cn(d-1)+Sn(mod 2); the matrix P is also a correlation matrix at the same time, the correlation matrix and the heterogeneous FRC constructed by the adjusting matrix are in a one-to-one correspondence relationship, in order to more intuitively embody the storage structure of the internal FRC, the concept of a partial regular graph is further introduced, namely the degree of the nodes in the graph can have various conditions, and for convenience of representation, the degree is marked as PGR (n, d), wherein n represents the number of top points and corresponds to the number of nodes in the FRC, the edges of the graph represent data blocks, and d represents the maximum value of the degree of the nodes;
the obtained matrix P is an n multiplied by n order binary matrix, and after the verification of the algorithm, the conditions of d, d-1 and d-2 1 can occur in different rows of the matrix P, so that the degree of a corresponding partial regular graph has three conditions of d, d-1 and d-2, namely the node storage capacity corresponding to the constructed FRC has three conditions of d, d-1 and d-2; analytically, the adjustment matrix S is obtainednNodes with different storage capacities can be obtained, and the heterogeneous characteristics meet the requirements of an actual distributed storage system.
Research by the applicant shows that the FRC with the heterogeneous node storage capacity constructed by the method can be used for single-node fault repair application.
Since the construction method is directed at the FRC with repetition rate ρ being 2, only the single-node fault repair problem is analyzed here, and the following is discussed in 3 cases:
a) if the node with the storage capacity of d fails, the node can be directly repaired by downloading one data block from the other d nodes respectively;
b) if the node with the storage capacity of d-1 fails, the node can be directly repaired by downloading one data block from the other d-1 nodes respectively;
c) if the node with the storage capacity of d-2 fails, the node can be directly repaired by downloading one data block from the other d-2 nodes respectively.
The following are specific examples given by the inventors.
Example (b):
the present embodiment is a constructive heterogeneous FRC that satisfies the following conditions, where the external one employs MDS coding, and the internal one is a repetition code whose parameters satisfy (n 7, d 5, θ 13, ρ 2), where n denotes the number of nodes, d denotes the maximum storage capacity of the nodes, θ denotes the number of data blocks and may be expressed as [ θ ] {1, 2.
Obtaining a matrix C from a construction method7(4) In which C is7(4) Is a 7 × 7 binary matrix and the first row is denoted c (t) ═ t + t2+t5+t6After the first row is determined, each subsequent row is sequentially shifted to the right by one bit, and finally C is generated7(4) A matrix, as shown in FIG. 1 (a); further using a matrix S according to a construction method7Adjusting matrix C7(4)，S7The matrix is generated by adding a row of 0 and a column of 0 after the matrix with the 6 th-order minor diagonal all being 1 and other elements all being 0, as shown in FIG. 1(b), to obtain S7After the matrix, pass P ═ C7(4)+S7(mod2) to obtain a matrix P, as shown in fig. 1(c), the matrix P, that is, the storage structure of the corresponding FRC node, knows that there are three cases of node storage capacity 5, 4, and 3, and in order to better embody the structure of the partial repetition code, it is represented by a partial regular graph PGR (7,5), and it can be found that there are three cases of degree 5, 4, and 3 of the partial regular graph, as shown in fig. 2(a), and the storage structure of the data block corresponding to each node is as shown in fig. 2 (b).
The single-node fault repair is carried out aiming at the FRC of the embodiment and comprises three conditions:
a) when a node with a capacity of 5 fails, as shown in fig. 3, if U2 fails, the newly born node needs to connect 5 nodes, i.e., U1, U3, U4, U5, and U7, and then download one data block from each of the 5 nodes for repair, i.e., download 5 data blocks, i.e., 1,2,8,12, and 13 for repair;
b) when a node with a capacity of 4 fails, for example, U7 in fig. 3 fails, the new node needs to connect 4 nodes, i.e., U1, U2, U5, and U6, and then download one data block from each of the 4 nodes for repair, i.e., download 4 data blocks, i.e., 5,6,11, and 12, for repair;
c) when a node with a capacity of 3 fails, for example, U1 in fig. 3 fails, the new node needs to connect 3 nodes, i.e., U2, U3, and U7, to repair, and then download one data block from each of the 3 nodes to repair, i.e., download 3 data blocks, i.e., 1,6, and 7, to repair.
This repair method does not have any encoding operation.
Claims (3)
1. A method for constructing heterogeneous part repetition codes based on an adjustment matrix is characterized in that the method is used for constructing an FRC with heterogeneous node storage capacity, and is suitable for the condition that the number n of nodes of a distributed storage system is an odd number, and the repetition rho of a data block in the constructed FRC is equal to 2; the method comprises the following specific steps:
step 1: first, a cyclic permutation matrix C is definedn(d-1), the matrix is a binary matrix of n x n orders, wherein n represents the number of nodes, d-1 represents the storage capacity of each node and the number of 1 rows in the matrix, and d satisfies the condition that d>3, d is an odd number;
Cnthe first row of the (d-1) matrix mathematically satisfies the expression:
c(t)＝t+t2+…+t(d-1)/2+tn-(d-1)/2+…+tn-1；
after the first row of the matrix is determined, each subsequent row is sequentially shifted to the right by one bit for n-1 times, and finally C is generatedn(d-1) a matrix;
where C isn(d-1) the matrix is also a correlation matrix, the rows of which correspond to the distributed storage systemThe column of the node in (1) represents a stored data block, and the incidence matrix and the isomorphic FRC which is not constructed by the regulation matrix are in one-to-one correspondence;
in order to more intuitively see the storage structure of the internal FRC, a regular graph is further introduced to store the homogeneous FRC, and the regular graph can be obtained through a correlation matrix [ theta ] {1, 2.. 13 }; the vertex n of the regular graph corresponds to the number of nodes in the FRC, the edge of the regular graph represents a data block, and d-1 represents the degree of the node;
step 2: introducing a matrix SnDeregulating C in step 1n(d-1) matrix, SnThe matrix generation method comprises the following steps: adding 0 row and 0 column after the matrix with all 0 elements in the (n-1) order minor diagonal of 1 to generate SnA matrix;
and step 3: the matrix C in the step 1n(d-1) and the matrix S in step 2nPerforming modulo-2 operation to obtain a new matrix P, where P is equal to Cn(d-1)+Sn(mod 2); the matrix P is also a correlation matrix at the same time, the correlation matrix and the heterogeneous FRC constructed by the adjusting matrix are in a one-to-one correspondence relationship, in order to more intuitively embody the storage structure of the internal FRC, the concept of a partial regular graph is further introduced, namely the degree of the nodes in the graph can have various conditions, and for convenience of representation, the degree is marked as PGR (n, d), wherein n represents the number of top points and corresponds to the number of nodes in the FRC, the edges of the graph represent data blocks, and d represents the maximum value of the degree of the nodes;
the obtained matrix P is an n multiplied by n order binary matrix, and after the verification of the algorithm, the conditions of d, d-1 and d-2 1 can occur in different rows of the matrix P, so that the degree of a corresponding partial regular graph has three conditions of d, d-1 and d-2, namely the node storage capacity corresponding to the constructed FRC has three conditions of d, d-1 and d-2;
thus, by adjusting the matrix SnAnd obtaining nodes with different storage capacities, wherein the heterogeneous characteristics of the nodes meet the requirements of an actual distributed storage system.
2. The method of claim 1 wherein the FRC with heterogeneous storage capacity of the nodes constructed by the method of claim 1 is used for repairing single failure nodes.
3. The application of claim 2, wherein the problem of failed node repair is analyzed based on the characteristics of heterogeneous FRCs, and because the configuration is for an FRC with a repetition p 2, only single node failure repair problems can be considered, in 3 cases:
a) if the node with the storage capacity of d fails, the node can be directly repaired by downloading one data block from the other d nodes respectively;
b) if the node with the storage capacity of d-1 fails, the node can be directly repaired by downloading one data block from the other d-1 nodes respectively;
c) if the node with the storage capacity of d-2 fails, the node can be directly repaired by downloading one data block from the other d-2 nodes respectively.
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