CN111711456A - Threshold matrix construction method, system, storage medium, program, and storage system - Google Patents
Threshold matrix construction method, system, storage medium, program, and storage system Download PDFInfo
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- CN111711456A CN111711456A CN202010438776.7A CN202010438776A CN111711456A CN 111711456 A CN111711456 A CN 111711456A CN 202010438776 A CN202010438776 A CN 202010438776A CN 111711456 A CN111711456 A CN 111711456A
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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
- H03M13/13—Linear codes
- H03M13/15—Cyclic codes, i.e. cyclic shifts of codewords produce other codewords, e.g. codes defined by a generator polynomial, Bose-Chaudhuri-Hocquenghem [BCH] codes
- H03M13/151—Cyclic codes, i.e. cyclic shifts of codewords produce other codewords, e.g. codes defined by a generator polynomial, Bose-Chaudhuri-Hocquenghem [BCH] codes using error location or error correction polynomials
- H03M13/1515—Reed-Solomon codes
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- G06F3/00—Input arrangements for transferring data to be processed into a form capable of being handled by the computer; Output arrangements for transferring data from processing unit to output unit, e.g. interface arrangements
- G06F3/06—Digital input from, or digital output to, record carriers, e.g. RAID, emulated record carriers or networked record carriers
- G06F3/0601—Interfaces specially adapted for storage systems
- G06F3/0602—Interfaces specially adapted for storage systems specifically adapted to achieve a particular effect
- G06F3/0614—Improving the reliability of storage systems
- G06F3/0619—Improving the reliability of storage systems in relation to data integrity, e.g. data losses, bit errors
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- G06F3/00—Input arrangements for transferring data to be processed into a form capable of being handled by the computer; Output arrangements for transferring data from processing unit to output unit, e.g. interface arrangements
- G06F3/06—Digital input from, or digital output to, record carriers, e.g. RAID, emulated record carriers or networked record carriers
- G06F3/0601—Interfaces specially adapted for storage systems
- G06F3/0668—Interfaces specially adapted for storage systems adopting a particular infrastructure
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Abstract
The invention belongs to the technical field of data storage, and discloses a threshold matrix construction method, a system, a storage medium, a program and a storage system, which determine threshold matrix parameters (k, n); constructing an initial matrix S0Different column vectors with the dimension of 2k-2 and containing (k-1) 1 and (k-1) 0 are formed into a matrix and are marked as S0(ii) a Construction matrix expansion Se(ii) a Extraction forms S(k，n)From the spreading matrix SeRandomly extracting n rows to form a final threshold matrix S(k，n). The system comprises: a threshold matrix parameter determining module; an initial matrix construction module; a matrix expansion construction module; the threshold array forms a module. Compared with the traditional RS generating matrix supporting any coding scheme, the threshold generating matrix is obtained based on binary domain operation, the complexity of the matrix operation relative to the computation time is low, compared with the array code generating matrix, the generating threshold matrix is flexible,without being limited by the size of the line.
Description
Technical Field
The invention belongs to the technical field of data storage, and particularly relates to a threshold matrix construction method, a threshold matrix construction system, a threshold matrix construction storage medium, a threshold matrix construction program and a threshold matrix construction storage system.
Background
Currently, with the continuous increase of the scale of a storage system, due to economic cost, a large number of systems use thousands or even hundreds of thousands of inexpensive and low-reliability disks to store a large amount of data, so that the probability of disk failure is high, the disks are the most main failure sources in the current distributed storage system, and the disk failure accounts for nearly eighty percent of all failures, which has a great influence on the reliability and data availability of the large storage system. In order to meet the requirement of users on a high-reliability storage system, erasure code redundancy technology is applied to a distributed storage system to improve the reliability of the storage system. The erasure code redundancy technology is to encode original data by a specific encoding method to obtain redundant data, and store the original data and the redundant data in a distributed storage system according to a specific mode. The scale of the distributed storage system is gradually enlarged, and the cost of the coding process of the distributed storage system can be effectively reduced by reducing the calculation complexity of the coding.
Erasure code redundancy techniques in distributed storage systems can be divided into two categories: the first kind of Reed-Solomon (RS, Reed-Solomon) code, the RS code threshold generating matrix is based on finite field operation, (1) the decoding and encoding time of the RS is mostly spent on calculating multiplication on the finite field; (2) the complexity of encoding and decoding of the RS is quadratic. The time complexity is somewhat different for different generator matrices G. The coding time complexity of the vandermonde matrix is O (n)2) The decoding time complexity is higher than O (n)2) The encoding and decoding times of the Cauchy matrix are both O (n)2). The time complexity of encoding and decoding is high, so that the application in a distributed storage system is greatly limited, and the RS code is an MDS (maximum Distance Separable) code, wherein any length in the encoded message is equal to the sub-erasure of the original messageThe codes that can decode the information to obtain the original message are called MDS codes), but because the RS codes are operated based on a finite field, the coding and decoding time complexity is too high, and the practical application is limited. Although the calculation of the encoding and decoding of the array code is rapid, the encoding rule of the array erasure code is that original data blocks are arranged according to an array, check data blocks are generated according to check chains meeting the rule, once the row and column scales of the codes and the strips are determined, the check chains are determined and only correspond to a unique generated matrix, but once the row and column scales of the encoding strips are determined, the unique generated matrix corresponds to the unique generated matrix, the flexibility is lacked in a complex network storage environment, the common array code is an MDS code, but the fault-tolerant capability is limited, the fault-tolerant capability is only 2 or 3 storage nodes, and the requirement of a huge storage system cannot be met.
Through the above analysis, the problems and defects of the prior art are as follows: the erasure code redundancy technology in the existing distributed storage system has high time complexity of coding and decoding, so that the application of the erasure code redundancy technology in the distributed storage system is greatly limited; when the size of the row and column size of the coding strip is determined once, the coding strip corresponds to a unique generating matrix, and the flexibility is lacked in a complex network storage environment.
The difficulty in solving the above problems and defects is: a new code needs to be designed: the method can avoid complex operations in a finite field, can meet MDS properties, and can set fault-tolerant capability as required.
The significance of solving the problems and the defects is as follows: a new coding mode is based on simple operation of a binary domain for coding, can meet the MDS property, can set fault tolerance according to requirements, can recover original data by subdata with any length larger than or equal to K, and cannot recover the original data by subdata with any length smaller than or equal to K-1.
Disclosure of Invention
The invention provides a threshold matrix construction method, a threshold matrix construction system, a storage medium, a program and a storage system, which aim at the problems in the prior art.
The invention is realized in such a way that a threshold matrix construction method comprises the following steps:
firstly, determining threshold matrix parameters (k, n);
second, construct an initial matrix S0Different column vectors with the dimension of 2k-2 and containing (k-1) 1 and (k-1) 0 are formed into a matrix and are marked as S0；
Third, constructing matrix expansion Se；
The fourth step, extracting to form S(k，n)From the spreading matrix SeRandomly extracting n rows to form a final threshold matrix S(k，n)。
Further, the (k, n) threshold matrix: s(k，n)Is a matrix of n × w, and satisfies the following 3 conditions:
(1) all 0 rows cannot exist in S;
(2) the matrix formed by extracting any (more than or equal to k) rows in the S cannot have all 0 columns;
(3) the matrix formed by extracting any (< k) rows in S must have all 0 columns.
Further, the construction matrix is expanded by SeThe method comprises the following steps:
(1) when n is less than or equal to 2k-2, no expansion is needed, Se＝S0；
(2) When n > 2k-2, for S0And (3) expanding: will matrix S0Dividing the rows into k-1 sub-matrices, denoted as sub _ i (i 1.. k-1), and traversing S0When the ith 1 of each column vector is encountered, the column vector is replaced by sub _ i, and when the ith 0 of each column vector is encountered, the column vector is replaced by a full 1 matrix with the same size as the sub _ i to obtain an extended matrix which is marked as Se。
It is another object of the present invention to provide a program storage medium for receiving user input, the stored computer program causing an electronic device to perform the steps comprising:
firstly, determining threshold matrix parameters;
secondly, constructing an initial matrix;
thirdly, constructing matrix expansion;
and fourthly, arbitrarily extracting from the expanded matrix to form a final threshold matrix.
It is a further object of the present invention to provide a computer program product stored on a computer readable medium, comprising a computer readable program for providing a user input interface for implementing said threshold matrix construction method when executed on an electronic device.
Another object of the present invention is to provide a threshold matrix constructing system for implementing the threshold matrix constructing method, wherein the threshold matrix constructing system comprises:
the threshold matrix parameter determining module is used for determining threshold matrix parameters;
an initial matrix construction module for constructing an initial matrix;
the matrix expansion construction module is used for constructing matrix expansion;
and the threshold array forming module is used for arbitrarily extracting from the extended matrix to form a final threshold matrix.
The invention also aims to provide a terminal, and the terminal is provided with the threshold matrix construction system.
The invention also aims to provide a storage system, wherein the storage system is provided with the threshold matrix construction system, a distributed storage system can select a plurality of coding schemes when storing files, and the threshold matrix construction method is a coding generation matrix construction method in a new coding scheme; a method for constructing a generator matrix of a coding scheme applied in a distributed storage system is provided.
By combining all the technical schemes, the invention has the advantages and positive effects that: compared with the traditional RS generating matrix supporting any coding scheme, the threshold generating matrix is obtained based on binary domain operation, the complexity of the matrix operation relative to the calculation time is low, and compared with the array code generating matrix, the threshold generating matrix is flexible and is not limited by the row and column scale. When the invention is used for coding and storing the data file, a plurality of different coding schemes can be selected according to different requirements when the data file is coded and stored, the threshold matrix construction method provides a new generation matrix construction method, and the coding calculation complexity is low.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed to be used in the embodiments of the present application will be briefly described below, and it is obvious that the drawings described below are only some embodiments of the present application, and it is obvious for those skilled in the art that other drawings can be obtained from the drawings without creative efforts.
Fig. 1 is a flowchart of a method for constructing a threshold matrix according to an embodiment of the present invention.
Fig. 2 is a schematic structural diagram of a threshold matrix constructing system according to an embodiment of the present invention;
in the figure: 1. a threshold matrix parameter determining module; 2. an initial matrix construction module; 3. a matrix expansion construction module; 4. the threshold array forms a module.
Fig. 3 is a flowchart of an implementation of a method for constructing a threshold matrix according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
In view of the problems in the prior art, the present invention provides a threshold matrix constructing method, system, storage medium, program, and storage system, and the present invention is described in detail below with reference to the accompanying drawings.
As shown in fig. 1, the method for constructing a threshold matrix provided by the present invention includes the following steps:
s101: determining threshold matrix parameters (k, n);
s102: constructing an initial matrix S0Different column vectors with the dimension of 2k-2 and containing (k-1) 1 and (k-1) 0 are formed into a matrix and are marked as S0；
S103: constructing matrix extension Se;
s104: extraction forms S(k，n)From the spreading matrix SeOptionally extracting n rows to form the finalThreshold matrix S(k，n)。
As shown in fig. 2, the threshold matrix constructing system provided by the present invention includes:
the threshold matrix parameter is fixed by a module 1 for determining the threshold matrix parameter;
an initial matrix constructing module 2, configured to construct an initial matrix;
a matrix expansion constructing module 3, which is used for constructing matrix expansion;
and a threshold array forming module 4, configured to perform arbitrary extraction from the spreading matrix to form a final threshold matrix.
The technical solution of the present invention is further described below with reference to the accompanying drawings.
The invention defines a (k, n) threshold matrix: (k, n) threshold matrix S(k，n)For a matrix of n × w, the following 3 conditions need to be satisfied:
(1) all 0 rows cannot exist in S;
(2) the matrix formed by extracting any (more than or equal to k) rows in the S cannot have all 0 columns;
(3) the matrix formed by extracting any (< k) rows in S must have all 0 columns.
As shown in fig. 3, the method for constructing the threshold matrix provided by the present invention specifically includes the following steps:
step one, determining threshold matrix parameters (k, n).
Step two, constructing an initial matrix S0. Different column vectors with dimension 2k-2 and containing (k-1) 1 and (k-1) 0 are formed into a matrix denoted as S0。
Step three, constructing matrix expansion Se。
(1) When n is less than or equal to 2k-2, no expansion is needed, Se＝S0。
(2) When n > 2k-2, for S0And (3) expanding: will matrix S0Dividing the rows into k-1 sub-matrices, denoted as sub _ i (i 1.. k-1), and traversing S0When the ith 1 of each column vector is encountered, the column vector is replaced by sub _ i, and when the ith 0 of each column vector is encountered, the column vector is replaced by a full 1 matrix with the same size as the sub _ i to obtain an extended matrix which is marked as Se。
Step four, extracting and forming S(k，n). From the spreading matrix SeRandomly extracting n rows to form a final threshold matrix S(k，n)。
The technical solution of the present invention is further described with reference to the following specific examples.
Example 1
The method for constructing the threshold matrix provided by the invention specifically comprises the following steps:
step one, determining threshold matrix parameters (k, n) ═ 2, 4.
Step two, constructing an initial matrix S0. Different column vectors with dimension 2 and respectively containing 1 and 10 form a matrix denoted as S0：
Step three, since 4 is more than 2, for S0Expanding to construct an expanded matrix Se. Will matrix S0Itself as 1 submatrix, denoted as sub _1, traversed S0In each column vector, when element 1 is met, sub _1 is used for replacing, and when element 0 is met, all 1 matrix with the same shape as sub _1 is used for replacing, so that an expansion matrix S is obtainede：
Step four, extracting and forming S(2，4). From the spreading matrix SeArbitrarily extracting 4 rows to form a final threshold matrix S(2，4)：
Example 2
The method for constructing the threshold matrix provided by the invention specifically comprises the following steps:
step one, determining threshold matrix parameters (k, n) ═ 3, 4.
Step two, constructing an initial threshold matrix S0. A matrix is formed by different column vectors with dimension 4 and containing 2 1 and 2 0, and is marked as S0：
Step three, because 4 is less than or equal to 4, S0Without extension, Se＝S0：
And step four, extracting to form S (3, 4). From the spreading matrix SeArbitrarily decimating 4 rows to form a final threshold matrix S (3, 4):
example 3
The method for constructing the threshold matrix provided by the invention specifically comprises the following steps:
step one, determining threshold matrix parameters (k, n) ═ 3, 5.
Step two, constructing an initial threshold matrix S0. A matrix is formed by different column vectors with dimension 4 and respectively containing 2 1 and 2 0, and is marked as S0：
Step three, when 5 is more than 4, for S0Expanding, constructing a matrix expansion Se. Will matrix S0Divide up and down 2 sub-matrices on a line, denoted as sub _ i (i ═ 1, 2), and traverse S0In each column vector, when the ith 1 is encountered, the column vector is replaced by sub _ i, and when the ith 0 is encountered, the column vector is replaced by a full 1 matrix with the same shape as the sub _ i, so that an expansion matrix S is obtainede：
Step four, extracting and forming S(3，5). From SeOptionally extracting 5 rows to form the final S(3，5)：
It should be noted that the embodiments of the present invention can be realized by hardware, software, or a combination of software and hardware. The hardware portion may be implemented using dedicated logic; the software portions may be stored in a memory and executed by a suitable instruction execution system, such as a microprocessor or specially designed hardware. Those skilled in the art will appreciate that the apparatus and methods described above may be implemented using computer executable instructions and/or embodied in processor control code, such code being provided on a carrier medium such as a disk, CD-or DVD-ROM, programmable memory such as read only memory (firmware), or a data carrier such as an optical or electronic signal carrier, for example. The apparatus and its modules of the present invention may be implemented by hardware circuits such as very large scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of hardware circuits and software, e.g., firmware.
The above description is only for the purpose of illustrating the present invention and the appended claims are not to be construed as limiting the scope of the invention, which is intended to cover all modifications, equivalents and improvements that are within the spirit and scope of the invention as defined by the appended claims.
Claims (8)
1. A threshold matrix construction method is characterized by comprising the following steps:
firstly, determining threshold matrix parameters (k, n);
second, construct the initial matrixS0Different column vectors with the dimension of 2k-2 and containing (k-1) 1 and (k-1) 0 are formed into a matrix and are marked as S0；
Third, constructing matrix expansion Se；
The fourth step, extracting to form S(k，n)From the spreading matrix SeRandomly extracting n rows to form a final threshold matrix S(k，n)。
2. The threshold matrix construction method of claim 1, wherein the (k, n) threshold matrix: s(k，n)Is a matrix of n × w, and satisfies the following 3 conditions:
(1) all 0 rows cannot exist in S;
(2) extracting any row which is larger than or equal to k from S to form a matrix which cannot have all 0 columns;
(3) the matrix formed by extracting any < k rows in S must have all 0 columns.
3. The threshold matrix construction method of claim 1, wherein the construction matrix extends by SeThe method comprises the following steps:
(1) when n is less than or equal to 2k-2, no expansion is needed, Se＝S0；
(2) When n > 2k-2, for S0And (3) expanding: will matrix S0Dividing the rows into k-1 sub-matrices, denoted as sub _ i, i 10When the ith 1 of each column vector is encountered, the column vector is replaced by sub _ i, and when the ith 0 of each column vector is encountered, the column vector is replaced by a full 1 matrix with the same size as the sub _ i to obtain an extended matrix which is marked as Se。
4. A program storage medium for receiving user input, the stored computer program causing an electronic device to perform the steps comprising:
firstly, determining threshold matrix parameters;
secondly, constructing an initial matrix;
thirdly, constructing matrix expansion;
and fourthly, arbitrarily extracting from the expanded matrix to form a final threshold matrix.
5. A computer program product stored on a computer readable medium, comprising a computer readable program for providing a user input interface for implementing a method of constructing a threshold matrix as claimed in any one of claims 1 to 3 when executed on an electronic device.
6. A threshold matrix construction system for implementing the threshold matrix construction method of any one of claims 1 to 3, wherein the threshold matrix construction system comprises:
the threshold matrix parameter determining module is used for determining threshold matrix parameters;
an initial matrix construction module for constructing an initial matrix;
the matrix expansion construction module is used for constructing matrix expansion;
and the threshold array forming module is used for arbitrarily extracting from the extended matrix to form a final threshold matrix.
7. A terminal, characterized in that it is equipped with the threshold matrix construction system of claim 6.
8. A storage system carrying the threshold matrix construction system of claim 6.
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