CN108199720B - Node repairing method and system for reducing storage overhead and improving repairing efficiency - Google Patents

Node repairing method and system for reducing storage overhead and improving repairing efficiency Download PDF

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CN108199720B
CN108199720B CN201711362733.XA CN201711362733A CN108199720B CN 108199720 B CN108199720 B CN 108199720B CN 201711362733 A CN201711362733 A CN 201711362733A CN 108199720 B CN108199720 B CN 108199720B
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代明军
王霞
王晖
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Shenzhen University
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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/11—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits using multiple parity bits
    • H03M13/1102—Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
    • H03M13/1148—Structural properties of the code parity-check or generator matrix
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
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    • H04L67/01—Protocols
    • H04L67/10—Protocols in which an application is distributed across nodes in the network
    • H04L67/1097—Protocols in which an application is distributed across nodes in the network for distributed storage of data in networks, e.g. transport arrangements for network file system [NFS], storage area networks [SAN] or network attached storage [NAS]

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Abstract

The invention is suitable for the field of distributed storage technology improvement, and provides a node repairing method for reducing storage overhead and improving repairing efficiency, wherein the node repairing method comprises the following steps: grouping system nodes on a piggyback coding framework for (n, k) codes and defining system vectors and coding matrixes; s2, substituting the defined coding matrix into the coding structure to obtain a corresponding coding mode; and S3, repairing the damaged node in the distributed storage system through zigzag decoding according to the encoding mode. According to the special coding mode, the designed code not only meets the MDS property, but also has smaller storage cost. In the actual operation process, through zigzag decoding, the decoding complexity can be effectively reduced, and meanwhile, the node repairing efficiency is improved.

Description

Node repairing method and system for reducing storage overhead and improving repairing efficiency
Technical Field
The invention belongs to the field of distributed storage technology improvement, and particularly relates to a node repairing method and system for reducing storage overhead and improving repairing efficiency.
Background
In a large distributed storage system, we can store and analyze large-scale data, however, during daily operations, there are various failures of nodes in the system, such as: data loss due to disk damage or wire breakage. Therefore, it is important to ensure the reliability and availability of the nodes in the system.
1. In a conventional distributed storage system, a repetition strategy is often adopted for storing data. I.e., by replicating multiple copies of data and storing on nodes in the system. When data is damaged and data recovery is needed, the data stored in the corresponding node only needs to be found, and recovery can be achieved.
2. In recent years, related scholars propose an erasure code-based redundancy strategy, which reduces storage overhead by increasing redundancy and simultaneously ensures the reliability of data when nodes are repaired. The coding mode is as follows: the original data is equally divided into k original data packets, then the k original data packets are mapped into n (n is larger than or equal to k) coded data packets, and the k original data packets can be recovered by taking any k coded data packets. The most typical Reed-solomon codes (RS codes) have been widely used in modern digital communication, distributed storage systems.
The storage mode of the duplicate copy: although this ensures a high degree of data reliability. However, a large amount of redundant data is generated, which increases the burden of the server, and the utilization rate of the nodes is not high, which easily causes waste of resources. In addition, as data grows explosively, storage overhead increases exponentially.
The conventional (n, k) code generally has the disadvantages of high complexity of encoding or decoding, large storage overhead and the like, and in the node repairing process, all data in the selected repairing node generally needs to be read and downloaded.
For example, in a conventional (8, 4) code, assuming that two encoded data packets are stored in each node, if any one of the 8 nodes is damaged, any 4 nodes in the remaining nodes are required to repair the damaged node. During the repair process, 8 encoded packets need to be read and downloaded.
In the actual operation process, the decoding mode not only increases the burden of network bandwidth and is easy to damage a disk, but also excessively occupies I/O port resources of the system in the repair process. Resulting in poor scalability.
Disclosure of Invention
The present invention aims to provide a node repair method and system for reducing storage overhead and improving repair efficiency, and aims to solve the above technical problems.
The invention is realized in this way, a node repairing method for reducing storage overhead and improving repairing efficiency, the node repairing method includes the following steps:
s1, grouping system nodes on the piggyback coding framework by the (n, k) codes, defining system vectors and coding matrixes, and defining the system vectors: a ═ a1 a2…ak}T，b＝{b1 b2…bk}T，c＝{c1 c2…ck}T，d＝{d1 d2…dk}T(ii) a When r-1 is an odd number, the coding matrix P is:
Figure BDA0001509975110000021
when r-1 is an even number, the coding matrix P is:
Figure BDA0001509975110000031
when r-1 is odd or even, the encoding matrix Q is:
Figure BDA0001509975110000032
s2, substituting the defined coding matrix into the coding structure to obtain a corresponding coding mode;
s3, repairing the damaged node through zigzag decoding according to the encoding mode;
wherein k denotes the number of system nodes, r denotes the number of parity nodes, n-k + r, n denotes the total number of nodes, T denotes the transpose of the vector,
Figure BDA0001509975110000033
indicating rounding up.
The further technical scheme of the invention is as follows: in step S1, a storage cost is generated by shifting when the coding matrix is established, where the storage cost is related to the number of parity check nodes and system nodes, and the larger r is, the larger k is, the larger the storage cost is, where the storage cost is:
Figure BDA0001509975110000034
the further technical scheme of the invention is as follows: in the step S1, r is more than or equal to 2, and k/r is an integer; the storage overhead is reduced in the coding matrix P by arranging the elements of the row vector of the same row in a forward and a backward direction.
The further technical scheme of the invention is as follows: the damaged node repair in the step S3 includes system node repair and parity node repair; when the system node is repaired, the fault node
Figure BDA0001509975110000035
When the system node is repaired, mx (k + | S) is needed1|) repairing the failed node by the number of packets; the fault node h belongs to SrWhen the system node is repaired, mx (k + | S) is neededrAnd l + r-2) data packets repair the failed node, wherein m is any positive integer.
The further technical scheme of the invention is as follows: when the parity check Node is repaired, the (n, k) code meets the CP-BZD property, if the first parity check Node (Node k +1) is damaged, k nodes are required to be selected from the rest n-1 nodes, each Node stores 2m data packets, and 2mk data packets are required for repairing the first parity check Node; if other parity check nodes L are repaired, wherein the L belongs to { k +2, …, k + r }, the repair is related to the values of r and m, when r is 2, data packets with the storage sequence being odd number and the last data packet stored in each system node are downloaded from each system node, and the 3 rd, 5 th and 2m-1 th data packets of the node k +1 need to be read and downloaded to repair the damaged node; when r is more than or equal to 3, downloading the data packet (q) with the odd storage sequence from each system nodeiF, i ═ 1, …, k, and the last packet stored in each system node, and reading f1，f2E { k +1, …, k + r } \ L, where m is any positive integer and f denotes other parity nodes excluding the failed node.
Another object of the present invention is to provide a node repairing system that reduces storage overhead and improves repairing efficiency, the node repairing system including:
a defining module, configured to group system nodes for (n, k) codes on a piggyback coding framework and define system vectors and coding matrices, defining the system vectors: a ═ a1 a2…ak}T，b＝{b1 b2…bk}T，c＝{c1 c2…ck}T，d＝{d1d2…dk}T(ii) a When r-1 is an odd number, the coding matrix P is:
Figure BDA0001509975110000051
when r-1 is an even number, the coding matrix P is:
Figure BDA0001509975110000052
when r-1 is odd or even, the encoding matrix Q is:
Figure BDA0001509975110000053
the coding mode acquisition module is used for substituting the defined coding matrix into a coding structure to acquire a corresponding coding mode;
the node repairing module is used for repairing the damaged node through zigzag decoding according to the coding mode;
wherein k denotes the number of system nodes, r denotes the number of parity nodes, n-k + r, n denotes the total number of nodes, T denotes the transpose of the vector,
Figure BDA0001509975110000054
indicating rounding up.
The further technical scheme of the invention is as follows: generating storage overhead through displacement when the coding matrix is established in the definition module, wherein the storage overhead is related to the number of parity check nodes and system nodes, the larger r is, the larger k is, the larger the storage overhead is, and the storage overhead is, wherein the storage overhead is:
Figure BDA0001509975110000055
the further technical scheme of the invention is as follows: r in the definition module is more than or equal to 2, and k/r is an integer; the storage overhead is reduced in the coding matrix P by arranging the elements of the row vector of the same row in a forward and a backward direction.
The further technical scheme of the invention is as follows: the damaged node repair in the node repair module comprises system node repair and parity check node repair; when the system node is repaired, the fault node
Figure BDA0001509975110000061
When the system node is repaired, mx (k + | S) is needed1|) repairing the failed node by the number of packets; when a fault node h belongs to Sr, the node of the system needs to be repaired by mx (k + | S)rAnd l + r-2) data packets repair the failed node, wherein m is any positive integer.
The further technical scheme of the invention is as follows: when the parity check Node is repaired, the (n, k) code meets the CP-BZD property, if the first parity check Node (Node k +1) is damaged, k nodes are required to be selected from the rest n-1 nodes, each Node stores 2m data packets, and 2mk data packets are required for repairing the first parity check Node; if other parity check nodes L are repaired, wherein the L belongs to { k +2, …, k + r }, the repair is related to the values of r and m, when r is 2, data packets with the storage sequence being odd number and the last data packet stored in each system node are downloaded from each system node, and the 3 rd, 5 th and 2m-1 th data packets of the node k +1 need to be read and downloaded to repair the damaged node; when r is more than or equal to 3, downloading the data packet (q) with the odd storage sequence from each system nodeiF, i ═ 1, …, k, and the last packet stored in each system node, and reading f1，f2E { k +1, …, k + r } \ L, where m is any positive integer and f denotes other parity nodes excluding the failed node.
The invention has the beneficial effects that: in a distributed storage system, according to a special coding mode, the designed code meets MDS properties and has relatively low storage cost. In the actual operation process, through zigzag decoding, the decoding complexity can be effectively reduced, and meanwhile, the node repairing efficiency is improved.
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Fig. 1 is a flowchart of a node repair method for reducing storage overhead and improving repair efficiency according to an embodiment of the present invention.
Fig. 2 is a first diagram of 84 codes according to an embodiment of the present invention.
Fig. 3 is a second schematic diagram of 84 codes according to an embodiment of the present invention.
Fig. 4 is a block diagram of a node repair system for reducing storage overhead and improving repair efficiency according to an embodiment of the present invention.
Detailed Description
As shown in fig. 1, the node repair method for reducing storage overhead and improving repair efficiency provided by the present invention is detailed as follows:
step S1, grouping the system nodes by the (n, k) codes on the piggyback coding framework and defining the system vectors and the coding matrix, and using zigzag decoding on the piggyback coding framework, thereby reducing the decoding complexity and improving the repair efficiency of the failed nodes, which is an improvement on the node repair scheme proposed by k.v. rashmi et al; the proposed (n, k) code has CP-BZD properties. The CP-BZD property means that (n, k) codes can be zigzag decoded in the binary domain, which can tolerate up to n-k nodes failing simultaneously. We divide the original information s into k packets of length L bits, denoted s respectively1，…，sk。siIs denoted as si，jAnd s isi，jE {0, 1}, where Si，jAlso called information bits. The k packets are encoded into n packets (n > k), denoted c, according to an (n, k) code1，…，cn. In addition, we have ci＝siWhere i is 1, …, k. The first k node packets are referred to as system nodes and the remaining n-k data packets are referred to as parity nodes.
zigzag decoding only involves back-substitution operation in binary domain, the decoding step is similar to Z, and has low complexity in the decoding process, and the zigzag decoding method is widely applied in binary domain. It can be considered as a recovery bit. This bit is then subtracted from the other parity data packets. This process is repeated until all of the information bits are decoded.
For any (n, k) code, k represents the number of system nodes, and the data packets stored in the system nodes are called original data packets. r (r ═ n-k) represents the number of parity check nodes, data packets stored in the parity check nodes are called check data packets, wherein original data packets and check data packets are collectively called data packets, each node can store a plurality of data packets, and r is required to be more than or equal to 2, and k/r is an integer. The system nodes are divided into r groups denoted as S1……SrWherein
Figure BDA0001509975110000081
Figure BDA0001509975110000082
We define the system vector: a ═ a1 a2…ak}T，b＝{b1 b2…bk}T
c＝{c1 c2…ck}T，d＝{d1 d2…dk}T
T represents the transpose of the vector, and each set of system components is independent of each other.
When r-1 is an odd number, the coding matrix P is:
Figure BDA0001509975110000091
when r-1 is an even number, the coding matrix P is:
Figure BDA0001509975110000092
whether r-1 is odd or even, there are
Figure BDA0001509975110000093
Where k denotes the number of system nodes, r denotes the number of parity nodes, n-k + r, n denotes the total number of nodes, T denotes the transpose of the vector,
Figure BDA0001509975110000094
indicating rounding up.
In the invention
Figure BDA0001509975110000095
Indicating rounding up, each element in the coding matrices P and Q indicates the number of bits shifted in the corresponding original packet when constituting the check packet. Where 0 indicates that the shift is 0 bits, k indicates that the shift is k bits, and-1 indicates that the corresponding original packet does not participate in the operation.
Step S2, substituting the defined coding matrix into the coding structure to obtain the corresponding coding mode; the number of packets stored in each node is denoted by 2m, where m is an arbitrary positive integer, and when m is 2, a general encoding scheme is shown in table 1.
Figure BDA0001509975110000096
Figure BDA0001509975110000101
TABLE 1
Wherein: vr＝Pr+qr。
The storage overhead refers to the storage redundancy generated by the shift of the coding matrix, and in the present invention, the storage overhead is determined by the largest element in the P matrix. Storage overhead:
Figure BDA0001509975110000103
therefore, the storage overhead of the coding mode is related to the number of parity check nodes and system nodes, the larger r is, the larger k is, and the larger k is.
The invention can greatly reduce the decoding complexity by zigzag decoding, and simultaneously reduces the average downloading amount of data by downloading the data packet stored in the specific node, thereby effectively improving the node repairing efficiency. Further, when the packets stored in each node can be extended to 2m, the encoding rule is consistent with table 1, and only the packets stored in parity node k +1 need to be changed, and the j ∈ {2, 4, … 2m-2} packets stored in parity nodes k +2 through k + r are all added to the j +1 th packet of parity node k + 1. As shown in table 1, when m is 2, j is 2, and the 3 rd packet stored in the parity node k +1 is
Figure BDA0001509975110000102
Step S3, repairing the damaged node through zigzag decoding according to the encoding mode; the piggyback-based coding framework can reduce the data download amount by reading and downloading the data packets stored in a specific node when a single node fails, thereby improving the average repair efficiency of the node. In addition, in the present invention, when the packet stored in each node can be extended to 2m, the encoding rule is consistent with table 1, it is the packet stored in parity node k +1 that needs to be changed, and it is necessary to add the jth e {2, 4, … 2m-2} packets stored in parity nodes k +2 to k + r to the jth +1 packet of parity node k + 1.
Repairing the system node:
1. fault node
Figure BDA0001509975110000111
Without loss of generality, we assume h e S1As shown in Table 1, we first download k packets from the distributed storage system, where the k packets include { b }1，…，bh-1，bh+1，…，bk，p1a, so we can decode bhObtaining the system vector b ═ b1 b2…bk}TAnd due to ahCan be downloaded by a data package ai}i∈S1H, and P2b+q2a is obtained, i.e. k + S1A can be obtained from one data packeth，bh. By downloading { d1，…，dh-1，dh+1，…，dk，p1d, d can be obtained by decodinghAnd finally chCan be composed of P2d+q2c and { ci}i∈S1Decoding shows that only 2 x (k + | S) is needed in the repair process1|)) data packets can recover the failed system node h. When m is any positive integer, m × (k + | S) is needed to repair system nodes1|)) a number of packets can repair the failed node.
2. The fault node h belongs to SrAs shown in Table 1, we first download k packets from the distributed storage system, where the k packets include { b }1，…，bh-1，bh+1，…，bk，p1a, so we can decode bhThen downloading V from parity check node k + rra+Prb, simultaneously reading and downloading the parity check node k +2 to the second data packet { p } stored in the parity check node k + rib+qia } i is equal to {2, …, r-1}, and a can be obtained by decodinghRepair of ah，bhThe number of data packets needing to be read and downloaded in the whole process is k + | SrL + r-2, can repair c as shown in Table 1h，dhWhen m is any positive integer, m × (k + | S) is required for repairing the system noderAnd | r-2) data packets can repair the fault node.
Repairing the parity check node;
if the first parity check Node (Node k +1) is damaged, since the (n, k) code of the present invention satisfies the CP-BZD property, k nodes need to be arbitrarily selected from the remaining n-1 nodes, and since each Node stores 2m packets, 2mk packets are required to recover the first parity check Node.
Repairing other parity check nodes L, wherein L is formed by { k +2, …, k + r }, the repair efficiency is related to the values of r and m, and when r is 2, data packets { q, the storage sequence of which is odd number, need to be downloaded from each system nodeiAnd {1, …, k } and the last data packet stored in each system node, and furthermore, the 3 rd, 5 th, and 2m-1 st data packets of the node k +1 need to be read and downloaded, so that the damaged node can be repaired. When r is more than or equal to 3, we need to download the data packet q with odd storage sequence from each system nodeiF, i ═ 1, …, k, and the last packet stored in each system node, and reading f1，f2E { k +1, …, k + r } \ L, packets with even order are stored. I.e., all information bits of the failed node can be recovered, and f represents the other parity nodes excluding the failed node.
As shown in fig. 2-3. Suppose we want to recover the information bits from c3 and c 4. The order in which the information bits are recovered is indicated by the numbers in the corresponding brackets. First, the leftmost information bit in c4 is s21We can obtain it directly because they do not involve any computation with other information bits. They can be considered the first recovery bits and are indexed by 1 within the parenthesis, respectively. Then we will s21Replace with the first bit of c3 and resume s11. It is the second recovery bit and is therefore indexed by 2 within the parenthesis. Similarly, by mixing s11Substituting the second bit of c4 can recover s22It is the third recovery bit and is therefore indexed 4 within the parenthesis. The decoding process is repeated until all information bits are recovered.
For the (8, 4) code, k is 4, r is 8-4 is 4, and m is 1, and two packets are stored in each node.
We first divide the system nodes into 4 groups, S1＝{Node1}，S2＝{Node2}，S3＝{Node3}，S4＝{Node4}
Defining a system vector: a ═ a1，a2，a3，a4}T；b＝{b1，b2，b3，b4}T
The coding matrix is:
Figure BDA0001509975110000131
Figure BDA0001509975110000132
wherein, 0, 1, 2, 3 respectively indicate that the shift of the original component is 0 bit, 1 bit, 2 bits, 3 bits, -1 indicates that the original component corresponding to the bit does not participate in the encoding operation.
The corresponding encoding scheme is shown in table 2:
Figure BDA0001509975110000133
Figure BDA0001509975110000141
TABLE 2
In the present invention, zigzag decoding is adopted, and as shown in fig. 2, a data packet is divided into a system Node and a parity check Node, wherein Node1, Node2, Node3 and Node4 are system nodes, Node5, Node6, Node7 and Node8 are parity check nodes, and each bit in the parity check nodes is obtained by adding corresponding bits of the system Node through shifting. Since the code satisfies the CP-BZD property, the original data can be restored by taking any 4 packets. Without loss of generality, we recover the original data from Node1, Node2, Node5, Node6, small labels indicate the decoding order of bits, in Node6, S3，1Without addition to other bits, we can directly conclude that we label it as 1, meaning the first decoded bit, S3，1Substituted into Node5, since the first bit of Node5 is S1，1+S2，1+S3，1+S4，1Thus we can getTo S4，1Denoted by 2, and S4，1Substituting into Node6, S can be obtained according to XOR3，2And according to the method, iteration is carried out in sequence, and finally all original information can be recovered.
And (3) node repairing:
1. if Node1 is damaged, we can repair packet b1 by taking coded packets b2, b3, b4, and p1b, and repair a1 by taking coded packet p2b + q2 a. In the repair scheme, the Node1 can be repaired by only 5 data packets, and compared with the traditional MDS code repair (the failed Node can be repaired by 8 data packets), the repair efficiency is improved by 37.5%. In the same way as described above,
the repair of Node2, Node3 also only needs 5 data packets;
2. if Node4 is damaged, we can decode b4, p1b by taking coded data packet, b1, b2, b3, p1b4a+(p4b+q4a)，p3b+q3a，p2b+q2a can repair a4, namely 7 coding data packets can repair Node4, and compared with the traditional MDS code, the repair efficiency is improved by 12.5%.
3. If Node5, Node6, Node7, Node8 are damaged, 8 coded data packets are needed.
As shown in fig. 4, another object of the present invention is to provide a node repair system that reduces storage overhead and improves repair efficiency, the node repair system including:
a defining module, configured to group system nodes for (n, k) codes on a piggyback coding framework and define system vectors and coding matrices, defining the system vectors: a ═ a1 a2…ak}T，b＝{b1 b2…bk}T，c＝{c1 c2…ck}T，d＝{d1d2…dk}T(ii) a When r-1 is an odd number, the coding matrix P is:
Figure BDA0001509975110000151
when r-1 is an even number, the coding matrix P is:
Figure BDA0001509975110000152
when r-1 is odd or even, the encoding matrix Q is:
Figure BDA0001509975110000161
the coding mode acquisition module is used for substituting the defined coding matrix into a coding structure to acquire a corresponding coding mode;
the node repairing module is used for repairing the damaged node through zigzag decoding according to the coding mode;
wherein k denotes the number of system nodes, r denotes the number of parity nodes, n-k + r, n denotes the total number of nodes, T denotes the transpose of the vector,
Figure BDA0001509975110000162
indicating rounding up.
Generating storage overhead through displacement when the coding matrix is established in the definition module, wherein the storage overhead is related to the number of parity check nodes and system nodes, the larger r is, the larger k is, the larger the storage overhead is, and the storage overhead is, wherein the storage overhead is:
Figure BDA0001509975110000163
r in the definition module is more than or equal to 2, and k/r is an integer; the storage overhead is reduced in the coding matrix P by arranging the elements of the row vector of the same row in a forward and a backward direction.
The damaged node repair in the node repair module comprises system node repair and parity check node repair; when the system node is repaired, the fault node
Figure BDA0001509975110000164
When the system node is repaired, mx (k + | S) is needed1|) repairing the failed node by the number of packets; the fault node h belongs to SrWhen the system node is repaired, mx (k + | S) is neededrAnd l + r-2) data packets repair the failed node, wherein m is any positive integer.
When the parity check Node is repaired, the (n, k) code meets the CP-BZD property, if the first parity check Node (Node k +1) is damaged, k nodes are required to be selected from the rest n-1 nodes, each Node stores 2m data packets, and 2mk data packets are required for repairing the first parity check Node; if other parity check nodes L are repaired, wherein the L belongs to { k +2, …, k + r }, the repair is related to the values of r and m, when r is 2, data packets with the storage sequence being odd number and the last data packet stored in each system node are downloaded from each system node, and the 3 rd, 5 th and 2m-1 th data packets of the node k +1 need to be read and downloaded to repair the damaged node; when r is more than or equal to 3, downloading the data packet (q) with the odd storage sequence from each system nodeiF, i ═ 1, …, k, and the last packet stored in each system node, and reading f1，f2E { k +1, …, k + r } \ L, where m is any positive integer and f denotes other parity nodes excluding the failed node.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.

Claims (10)

1. A node repairing method for reducing storage overhead and improving repairing efficiency is characterized by comprising the following steps:
s1, grouping system nodes on the piggyback coding framework by the (n, k) codes, defining system vectors and coding matrixes, and defining the system vectors: a ═ a1 a2…ak}T，b＝{b1 b2…bk}T，c＝{c1 c2…ck}T，d＝{d1 d2…dk}T(ii) a When r-1 is an odd number, the coding matrix P is:
Figure FDA0002808053800000011
when r-1 is an even number, the coding matrix P is:
Figure FDA0002808053800000012
when r-1 is odd or even, the encoding matrix Q is:
Figure FDA0002808053800000013
s2, substituting the defined coding matrix into the coding structure to obtain a corresponding coding mode;
s3, repairing the damaged node through zigzag decoding according to the encoding mode;
where k denotes the number of system nodes, r denotes the number of parity nodes, n-k + r, n denotes the total number of nodes, T denotes the transpose of the vector,
Figure FDA0002808053800000014
represents rounding up; the storage overhead is reduced in the coding matrix P by arranging the elements of the row vector of the same row in a forward and a backward direction.
2. The node repairing method according to claim 1, wherein the storage overhead generated by shifting during the building of the coding matrix in step S1 is related to the number of parity check nodes and system nodes, and the larger r is, the larger k is, the larger the storage overhead is, wherein the storage overhead is:
Figure FDA0002808053800000021
3. the node repairing method for reducing storage overhead and improving repairing efficiency according to claim 2, wherein r is greater than or equal to 2 in step S1, and k/r is an integer; the storage overhead is reduced in the coding matrix P by arranging the elements of the row vector of the same row in a forward and a backward direction.
4. The node repairing method for reducing storage overhead and improving repair efficiency according to claim 3, wherein the damaged node repair in step S3 includes system node repair and parity node repair; when the system node is repaired, the fault node
Figure FDA0002808053800000022
When the system node is repaired, mx (k + | S) is needed1|) repairing the failed node by the number of packets; the fault node h belongs to SrWhen the system node is repaired, mx (k + | S) is neededrAnd l + r-2) data packets repair the failed node, wherein m is any positive integer.
5. The Node repairing method for reducing storage overhead and improving repair efficiency according to claim 3, wherein, when repairing the parity check Node, the (n, k) code satisfies the CP-BZD property, if the first parity check Node (Node k +1) is damaged, k nodes are required to be selected from the remaining n-1 nodes, each Node stores 2m data packets, and 2mk data packets are required for repairing the first parity check Node; if other parity check nodes L are repaired, wherein the L belongs to { k +2, …, k + r }, the repair is related to the values of r and m, when r is 2, data packets with the storage sequence being odd number and the last data packet stored in each system node are downloaded from each system node, and the 3 rd, 5 th and 2m-1 th data packets of the node k +1 need to be read and downloaded to repair the damaged node; when r is more than or equal to 3, downloading the number with the odd storage sequence from each system nodeData packet qiF, i ═ 1, …, k, and the last packet stored in each system node, and reading f1，f2E { k +1, …, k + r } \ L, where m is any positive integer and f denotes other parity nodes excluding the failed node.
6. A node repair system that reduces storage overhead and improves repair efficiency, the node repair system comprising:
a defining module, configured to group system nodes for (n, k) codes on a piggyback coding framework and define system vectors and coding matrices, defining the system vectors: a ═ a1 a2…ak}T，b＝{b1 b2…bk}T，c＝{c1 c2…ck}T，d＝{d1 d2…dk}T(ii) a When r-1 is an odd number, the coding matrix P is:
Figure FDA0002808053800000031
when r-1 is an even number, the coding matrix P is:
Figure FDA0002808053800000032
when r-1 is odd or even, the encoding matrix Q is:
Figure FDA0002808053800000033
the coding mode acquisition module is used for substituting the defined coding matrix into a coding structure to acquire a corresponding coding mode;
the node repairing module is used for repairing the damaged node through zigzag decoding according to the coding mode;
wherein k denotes the number of system nodes, r denotes the number of parity nodes, n-k + r, n denotes the total number of nodes, T denotes the transpose of the vector,
Figure FDA0002808053800000041
represents rounding up; the storage overhead is reduced in the coding matrix P by arranging the elements of the row vector of the same row in a forward and a backward direction.
7. The node repairing system of claim 6, wherein the defining module generates the storage overhead through shifting when establishing the coding matrix, the storage overhead is related to the number of parity check nodes and system nodes, the larger r is, the larger k is, the larger the storage overhead is, and the storage overhead is:
Figure FDA0002808053800000042
8. the node repairing system capable of reducing storage overhead and improving repairing efficiency according to claim 7, wherein r is greater than or equal to 2 in the defining module, and k/r is an integer; the storage overhead is reduced in the coding matrix P by arranging the elements of the row vector of the same row in a forward and a backward direction.
9. The node repair system that reduces storage overhead and improves repair efficiency according to claim 8, wherein the repair of the damaged node in the node repair module comprises a system node repair and a parity node repair; when the system node is repaired, the fault node
Figure FDA0002808053800000043
When the system node is repaired, mx (k + | S) is needed1|) repairing the failed node by the number of packets; the fault node h belongs to SrWhen, it takes mx (k) to repair the system node+|SrAnd l + r-2) data packets repair the failed node, wherein m is any positive integer.
10. The Node repair system of claim 9, wherein when repairing the parity check Node, the (n, k) code satisfies CP-BZD property, and if the first parity check Node (Node k +1) is damaged, k nodes are selected from the remaining n-1 nodes, each Node stores 2m packets, and 2mk packets are required to repair the first parity check Node; if other parity check nodes L are repaired, wherein the L belongs to { k +2, …, k + r }, the repair is related to the values of r and m, when r is 2, data packets with the storage sequence being odd number and the last data packet stored in each system node are downloaded from each system node, and the 3 rd, 5 th and 2m-1 th data packets of the node k +1 need to be read and downloaded to repair the damaged node; when r is more than or equal to 3, downloading the data packet (q) with the odd storage sequence from each system nodeiF, i ═ 1, …, k, and the last packet stored in each system node, and reading f1，f2E { k +1, …, k + r } \ L, where m is any positive integer and f denotes other parity nodes excluding the failed node.
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