CN104850468B - Correcting and eleting codes coding/decoding method based on check matrix - Google Patents
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- CN104850468B CN104850468B CN201510290040.9A CN201510290040A CN104850468B CN 104850468 B CN104850468 B CN 104850468B CN 201510290040 A CN201510290040 A CN 201510290040A CN 104850468 B CN104850468 B CN 104850468B
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Abstract
The present invention provides a kind of correcting and eleting codes coding/decoding method based on check matrix, the present invention is suitable for the arbitrarily correcting and eleting codes based on xor operation, and the present invention is by decoding check matrix, so as to bring very big lifting to decoding efficiency.In addition, the iterative algorithm by constructing sparse check matrix, can further lift decoding efficiency of the invention.Compared to two kinds of traditional implementation methods, the present invention has versatility and high efficiency at the same time.
Description
Technical field
The present invention relates to a kind of correcting and eleting codes coding/decoding method based on check matrix.
Background technology
As the requirement in large memory system to data reliability is constantly lifted, correcting and eleting codes are as a kind of high efficiency, low cost
Guarantee high reliability technology, be widely adopted.By using correcting and eleting codes technology, initial data and the verification by encoding generation
Data are together stored in multiple storage devices (typical case such as disk array), so that when some of device fails
When, the data lost in it can be recovered with the data in other equipment.
Among diversified correcting and eleting codes, have one kind based on exclusive or (Exclusive-OR) operate, it is another kind of then
It is that coding and decoding is carried out based on the computing in finite field.For at present, the coding based on exclusive or is more popular, this is because
Hardware usually all directly supports xor operation so that the computing cost of this kind of coding is very low, and the efficiency of coding and decoding is very high.
The common coding based on xor operation has the following：For the EVENODD that has of two disk failures of recovery, RDP is encoded, and
Can tolerate three disk failures has STAR and HoVer etc..
In general, we have two kinds of approach to realize these codings.We term it " matrix method " for first method：For
Any one correcting and eleting codes, as long as providing its " generator matrix " (all correcting and eleting codes have its generator matrix), we just can utilize
A series of matrix manipulations are encoded or decoded.This method is a kind of universal method, and for any correcting and eleting codes, we are available should
Method is realized.We term it special method for second method：For some codings, there are some specific coding, decodings
Algorithm.These algorithms are designed according to coding characteristic inherently, therefore and do not have a versatility.Specifically, fit
For a kind of own coding of correcting and eleting codes, decoding algorithm, another correcting and eleting codes are generally unsuitable for.
Existing two kinds of methods for realizing correcting and eleting codes, i.e. matrix method and special method, there are it is notable the shortcomings that.One side
Face, although matrix method is more general, it has significant deficiency on decoding speed, so as to limit the recovery of disk array
Speed, reduces the reliability and availability of storage system.On the other hand, special method still cannot reach most on decoding speed
Excellent (such as EVENODD and STAR coding), and this kind of algorithm is realized extremely complex, is unfavorable for further optimizing；It is in addition, very much
It is efficient to encode and do not have dedicated implementation, therefore there are significant limitation for special method.In summary, it is existing
Versatility and high efficiency cannot be had at the same time by realizing the two methods of correcting and eleting codes.
The content of the invention
, can be to decoding efficiency band it is an object of the invention to provide a kind of correcting and eleting codes coding/decoding method based on check matrix
Carry out very big lifting
To solve the above problems, the present invention provides a kind of correcting and eleting codes coding/decoding method based on check matrix, including：
According to the coding mode of the encoder matrix of the correcting and eleting codes based on xor operation of disk array, construct corresponding to institute
The check matrix of correcting and eleting codes is stated, the check matrix is 01 matrix；
The fail data of failed disk in disk array is calculated according to the check matrix.
Further, in the above-mentioned methods, the failure of failed disk in disk array is calculated according to the check matrix
Data, including：
Mark the survival data S and fail data L of failed disk in disk array；
Check matrix H is divided into two sub- matrix HsLAnd HS, correspond respectively to the fail data L and survival data S；
Utilize equationThe fail data of failed disk in disk array can be calculated by check matrix,
Wherein,For 01 group inverse matrices matrix.
Further, in the above-mentioned methods, according to the encoder matrix of the correcting and eleting codes based on xor operation of disk array
Coding mode, constructs in the check matrix corresponding to the correcting and eleting codes,
The line number of check matrix is equal to the quantity of the check block in the encoder matrix of correcting and eleting codes, and the columns of check matrix is equal to
All quantity for examining block and data block in the encoder matrix of correcting and eleting codes.
Further, in the above-mentioned methods, according to the encoder matrix of the correcting and eleting codes based on xor operation of disk array
Coding mode, constructs in the check matrix corresponding to the correcting and eleting codes,
Every a line of check matrix corresponds to a verification calculation formula of the encoder matrix, each corresponding encoder matrix of row
In an element, when jth arranges corresponding element and appears in i-th of verification calculating formula, the i-th of check matrix
The value of the element of row j row is 1.
Further, in the above-mentioned methods, according to the encoder matrix of the correcting and eleting codes based on xor operation of disk array
Coding mode, constructs in the check matrix corresponding to the correcting and eleting codes,
The check matrix is sparse check matrix.
Further, in the above-mentioned methods, the sparse check matrix is obtained by elementary transformation.
Further, in the above-mentioned methods, the sparse check matrix constructs to obtain by following iterative algorithm：
Step S11, sets variable update, represents whether check matrix is updated in a wheel iteration, and initial value is arranged to
false；
Step S12, initialization procedure, including step S121~step S123：
Step S121, calculates array ones [x], wherein, array ones [x] represents check matrix xth row is included 1
Quantity；
Step S122, numeration group from [x], wherein from [x] represent xth row store the row and which the sum of, initially
It is worth and represents not storing any other row for -1；
Step S123, numeration group visit [x], wherein, visit [x] represents whether xth row is accessed, and is initially set to entirely
False, the row are not accessed；
Step S13, circulation perform following steps S131~step S134, until all rows are accessed：
Step S131, in all rows not being accessed, chooses the row for including 1 minimum number, it is assumed that be x rows, i.e.,
The value of ones [x] is minimum；
Step S132, enumerates every other row, if line number is y, performs following steps S1321~S1322：
Step S1321, calculates the Hamming distance of x rows and y rows, i.e. the element of how many row differs, and it is dis to remember the value；
Step S1322, if dis<Ones [y], then it represents that need x rows adding to y rows, dis is then assigned to ones
[y], is then changed to x by the value of from [y], the value of update finally is set as true；
Step S133, if the value of from [x] is not -1, by from [x], this line adds to xth row；
Step S134, is set as true by visit [x], represents that the row has been accessed；
Step S14, if the value of update is true, return to step S11, otherwise algorithm terminate.
Compared with prior art, the present invention is suitable for the arbitrarily correcting and eleting codes based on xor operation, and the present invention passes through to verification
Matrix is decoded, so as to bring very big lifting to decoding efficiency.In addition, calculated by the iteration for constructing sparse check matrix
Method, can further lift the decoding efficiency of the present invention.Compared to two kinds of traditional implementation methods, the present invention has versatility at the same time
And high efficiency.
Brief description of the drawings
Fig. 1 is the schematic diagram of the coding mode of the EVENODD horizontal checks of one embodiment of the invention；
Fig. 2 is the schematic diagram of the coding mode of the oblique verifications of EVENODD of one embodiment of the invention；
Fig. 3 is the check matrix sample figure of the EVENODD of one embodiment of the invention；
Fig. 4 is the check matrix decoding process schematic diagram of one embodiment of the invention.
Embodiment
In order to make the foregoing objectives, features and advantages of the present invention clearer and more comprehensible, it is below in conjunction with the accompanying drawings and specific real
Applying mode, the present invention is described in further detail.
Before the present invention is introduced, specific example is first passed through to illustrate the basic conception of correcting and eleting codes and conventional implementation,
In order to preferably illustrate the advantage of idea of the invention and the displaying present invention.Using classical EVENODD codings as case,
The coding can be used to realize RAID-6 disk arrays, can tolerate two disks while failure is without making loss of data.
EVENODD is suitable for the array with p+2 disk, and p must be a prime number here；And in this p+2 disk, there is p
A disk is used to store initial data all the time, and remaining two disks are used to store verification data, these verification datas are by original
Obtained by the encoded workflow management of beginning data.Fig. 1 and Fig. 2 illustrates the encoding stream of the EVENODD suitable for 7 disks
Journey, the corresponding prime number of the coding are p=5.
In fig. 1 and 2, we represent that EVENODD is encoded with the matrix of (p-1) * (p+2), wherein matrix
Each row represent a disk, and what each grid represented is one fixed-size piece on disk.First by matrix column from a left side
It is 0-6 to right numbering, preceding 5 disks store data, the storage verification of latter two disk.Similarly, the row of matrix is compiled from top to bottom
Number it is 0-3, and the element representation that the i-th row jth arranges in matrix is Ci,j。
Fig. 1 illustrates the calculation of the verification data on disk 5.For each check block on disk 5, it is by magnetic
Data block in disk 0-4 with a line is summed and obtained with xor operation, for example, C0,5It is by formulaCalculate and obtain.Correspond in figure, each check block is by the data of same shape
Block is summed and obtained with exclusive or.Since the element of same row is only used in the calculating of this part, which is commonly known as laterally
Verification.
Fig. 2 illustrates the calculation of the verification data on disk 6.We employ the similar expression ways of same Fig. 1, use
Same shape representation participates in all data blocks that a check block calculates.We first have to calculate a median M, calculate public
Formula isAfter calculating M, each check block on disk 6 is then by same shape in Fig. 2
Data block value, and the value of M together sums and obtains.For example,The verification
Commonly known as oblique verification.
If in a calculation formula, an only element is to lose data, then the element can pass through other in formula
Element exclusive or is summed and is recovered.Traditional recovery algorithms make use of the characteristic.For example, when two data disks lose at the same time
During effect, first, which can go out the value of S using the data recovery on two check disks of survival；Then a data are first found
Block, it can directly be recovered by some oblique verification calculation formula；Next travsverse check formula is utilized, same a line can be recovered
In another missing data；Next oblique verification is recycled to recover next data, such iteration is until all data are extensive
Finish again.
The present invention provides a kind of correcting and eleting codes coding/decoding method based on check matrix, including：
Step S1, according to the coding mode of the encoder matrix of the correcting and eleting codes based on xor operation of disk array, constructs
Corresponding to the check matrix of the correcting and eleting codes, the check matrix is 01 matrix, is denoted as H；
Step S2, the fail data of failed disk in disk array is calculated according to the check matrix.
In one preferred embodiment of the correcting and eleting codes coding/decoding method based on check matrix of the present invention, step S2, according to institute
The fail data that check matrix calculates failed disk in disk array is stated, including：
Step S21, marks the survival data S and fail data L of failed disk in disk array；
Step S22, two sub- matrix Hs are divided into by check matrix HLAnd HS, correspond respectively to the fail data L and deposit
Live data S, according to the property of check matrix, meets following equation HLL=HS·S；Check matrix has an important properties,
I.e. it and the product of the data after coding are always 0, this property is determined by its definition mode, and the property is to decoding
Most important for step, Fig. 3 illustrates this relation by the example of EVENODD, and specific decoding scheme will be
Describe in detail below；
Step S23, can be obtained by previous step equationMagnetic can be calculated by check matrix using the equation
The fail data of failed disk in disk array, wherein,For 01 group inverse matrices matrix.Specifically, in order to preferably explain
Decoding process, we first assume currently there are several disk failures.We still the data in whole band regard as one to
Amount, then the data in failed disk are just counted as unknown number.Now, we are disassembled the equation shown in Fig. 3, first will
Represent that the vector of all data splits into two vectors, one of them is formed by fail data entirely and (be denoted as L), another is then by surviving
Data form (being denoted as S)；And check matrix H is also partitioned into two submatrixs, one is made of the row corresponding to failure element
(it is denoted as HL), another is made of survival element column and (is denoted as HS).The then equation according to Fig. 3, we can obtain：In this equation, only L is the data that unknown quantity represents to lose.HLL and HSThe calculating of S
Result is column vector.And two column vector exclusive or values illustrate that they are equal for 0, therefore the formula can be write as HLL=HS·
S, we by matrix operation, can come out the unknown quantity solution in the formula again：Finally, Fig. 4 is illustrated
The instantiation of one recovery fail data.EVENODD codings in the preceding example that we still use, and suppose there is 7 blocks of magnetic
Disk, wherein No. 0 and No. 2 disks are failure discs, the data on the disk are fail data.We are first to check matrix by row
Split, the data after coding are then divided into survival data and fail data.At this time, Fig. 4 is verified after illustrating segmentation
The relation of matrix and coded data.Next, we obtain HLInverse matrix, and calculate equation right end as a result, by two
Person, which is multiplied, obtains fail data.
In one preferred embodiment of the correcting and eleting codes coding/decoding method based on check matrix of the present invention, step S1, according to magnetic
The coding mode of the encoder matrix of the correcting and eleting codes based on xor operation of disk array, constructs the verification corresponding to the correcting and eleting codes
In matrix, the line number of check matrix is equal to the quantity of the check block in the encoder matrix of correcting and eleting codes, and the columns of check matrix is equal to
All quantity for examining block and data block in the encoder matrix of correcting and eleting codes, i.e., the quantity of all elements in encoder matrix, verifies square
Every a line of battle array corresponds to a verification calculation formula of the encoder matrix, and each row correspond to an element in encoder matrix,
When jth arranges corresponding element and appears in i-th of verification calculating formula, the element of the i-th row j row of check matrix
It is worth for 1.Specifically, check matrix is a matrix closely related with correcting and eleting codes, it can be with each of the data after presentation code
Linear relationship between a field.In the above example, 28 elements are included altogether for representing that the matrix of EVENODD arranges for 4 rows 7
Including check block and data block, and 8 elements of most next two columns are check blocks, thus with the corresponding verification of EVENODD codings
Matrix has 8 rows 28 to arrange.Specifically, every a line of check matrix corresponds to a verification calculation formula of the encoder matrix, often
An element in the corresponding encoder matrix of one row.Each element value non-zero i.e. 1 of check matrix, and arrange and correspond to and if only if jth
Element appear in check matrix when in the calculating formula of i-th of verification the i-th row 1 row element value be 1.Fig. 3 gives
The sample of the check matrix of EVENODD codings corresponding with Fig. 1-2.In check matrix shown in the Fig. 3, preceding four row corresponds to
The verification calculation formula of each element on disk 5, then four rows corresponded to the verification calculation formula of each element on disk 6.
In one preferred embodiment of the correcting and eleting codes coding/decoding method based on check matrix of the present invention, step S1, according to magnetic
The coding mode of the encoder matrix of the correcting and eleting codes based on xor operation of disk array, constructs the verification corresponding to the correcting and eleting codes
In matrix, the check matrix is sparse check matrix, further to lift decoding speed, makes check matrix in decoding process
Complexity significantly reduces.
In one preferred embodiment of the correcting and eleting codes coding/decoding method based on check matrix of the present invention, the sparse verification
Matrix is obtained by elementary transformation.First, it is observed that the check matrix of an encoder matrix is not unique.One legal
Check matrix should be 0 with the product of data after coding, and if we construct any one legal check matrix, we are right
The matrix carries out Applying Elementary Row Operations, i.e., we add to the value of a line in another row, and the new matrix after conversion is still legal
Check matrix.And according to the decoding process of the foregoing description, it is observed that sparse check matrix has coding/solution of smaller
Code cost, therefore we can using elementary transformation come be lifted the present invention realize speed.
In one preferred embodiment of the correcting and eleting codes coding/decoding method based on check matrix of the present invention, the sparse verification
Matrix constructs to obtain by following iterative algorithm：
Step S11, sets variable update, represents whether check matrix is updated in a wheel iteration, and initial value is arranged to
false；
Step S12, initialization procedure, including step S121~step S123：
Step S121, calculates array ones [x], wherein, array ones [x] represents check matrix xth row is included 1
Quantity；
Step S122, numeration group from [x], wherein from [x] represent xth row store the row and which the sum of, initially
It is worth and represents not storing any other row for -1；
Step S123, numeration group visit [x], wherein, visit [x] represents whether xth row is accessed, and is initially set to entirely
False, the row are not accessed；
Step S13, circulation perform following steps S131~step S134, until all rows are accessed：
Step S131, in all rows not being accessed, chooses the row for including 1 minimum number, it is assumed that be x rows, i.e.,
The value of ones [x] is minimum；
Step S132, enumerates every other row, if line number is y, performs following steps S1321~S1322：
Step S1321, calculates the Hamming distance of x rows and y rows, i.e. the element of how many row differs, and it is dis to remember the value；
Step S1322, if dis<Ones [y], then it represents that need x rows adding to y rows, dis is then assigned to ones
[y], is then changed to x by the value of from [y], the value of update finally is set as true；
Step S133, if the value of from [x] is not -1, by from [x], this line adds to xth row；
Step S134, is set as true by visit [x], represents that the row has been accessed；
Step S14, if the value of update is true, return to step S11, otherwise algorithm terminate.By algorithm above, instead
The openness of check matrix is lifted using Applying Elementary Row Operations again, the check matrix of some codings can be made more sparse, so that
With faster coding and decoding speed.
The present invention is suitable for the arbitrarily correcting and eleting codes based on xor operation, of the invention by being decoded to check matrix, from
And very big lifting is brought to decoding efficiency.In addition, the iterative algorithm by constructing sparse check matrix, can further be lifted
The decoding efficiency of the present invention.Compared to two kinds of traditional implementation methods, the present invention has versatility and high efficiency at the same time.
Each embodiment is described by the way of progressive in this specification, what each embodiment stressed be and other
The difference of embodiment, between each embodiment identical similar portion mutually referring to.
Professional further appreciates that, with reference to each exemplary unit of the embodiments described herein description
And algorithm steps, can be realized with electronic hardware, computer software or the combination of the two, in order to clearly demonstrate hardware and
The interchangeability of software, generally describes each exemplary composition and step according to function in the above description.These
Function is performed with hardware or software mode actually, application-specific and design constraint depending on technical solution.Specialty
Technical staff can realize described function to each specific application using distinct methods, but this realization should not
Think beyond the scope of this invention.
Obviously, those skilled in the art can carry out invention spirit of the various modification and variations without departing from the present invention
And scope.If in this way, these modifications and changes of the present invention belong to the claims in the present invention and its equivalent technologies scope it
Interior, then the present invention is also intended to including these modification and variations.
Claims (5)
- A kind of 1. correcting and eleting codes coding/decoding method based on check matrix, it is characterised in that including：According to the coding mode of the encoder matrix of the correcting and eleting codes based on xor operation of disk array, construct and entangled corresponding to described The check matrix of code is deleted, the check matrix is 01 matrix；The fail data of failed disk in disk array is calculated according to the check matrix；The check matrix is sparse check matrix, and the sparse check matrix constructs to obtain by following iterative algorithm：Step S11, sets variable update, represents that check matrix is renewal in a wheel iteration, initial value is arranged to false；Step S12, initialization procedure, including step S121~step S123：Step S121, calculates array ones [x], wherein, array ones [x] represents 1 number that check matrix xth row is included Amount；Step S122, numeration group from [x], wherein from [x] represent xth row store the xth row and which the sum of, initially It is worth and represents not storing any other row for -1；Step S123, numeration group visit [x], wherein, visit [x] represents whether xth row is accessed, and is initially set to entirely False, the xth row are not accessed；Step S13, circulation perform following steps S131~step S134, until all rows are accessed：Step S131, in all rows not being accessed, chooses and includes the row of 1 minimum number, it is assumed that and be x rows, i.e. ones [x] Value it is minimum；Step S132, enumerates every other row, if line number is y, performs following steps S1321~S1322：Step S1321, calculates the Hamming distance of x rows and y rows, i.e. the element of how many row differs, and remembers the x rows and y rows Hamming distance is dis；Step S1322, if dis<Ones [y], then be assigned to ones [y] by dis, the value of from [y] then is changed to x, finally The value of update is set as true；Step S133, if the value of from [x] is not -1, by from [x], this line adds to xth row；Step S134, true is set as by visit [x], represents that the xth row has been accessed；Step S14, if the value of update is true, return to step S11, otherwise algorithm terminate.
- 2. the correcting and eleting codes coding/decoding method based on check matrix as claimed in claim 1, it is characterised in that according to the verification square Battle array calculates the fail data of failed disk in disk array, including：Mark the survival data S and fail data L of failed disk in disk array；Check matrix H is divided into two sub- matrix HsLAnd HS, correspond respectively to the fail data L and survival data S；Utilize equationThe fail data of failed disk in disk array can be calculated by check matrix, wherein,For 01 group inverse matrices matrix.
- 3. the correcting and eleting codes coding/decoding method based on check matrix as claimed in claim 2, it is characterised in that according to disk array The coding mode of the encoder matrix of correcting and eleting codes based on xor operation, constructs in the check matrix corresponding to the correcting and eleting codes,The line number of check matrix is equal to the quantity of the check block in the encoder matrix of correcting and eleting codes, and the columns of check matrix, which is equal to entangle, to be deleted The total quantity of all check blocks and data block in the encoder matrix of code.
- 4. the correcting and eleting codes coding/decoding method based on check matrix as claimed in claim 3, it is characterised in that according to disk array The coding mode of the encoder matrix of correcting and eleting codes based on xor operation, constructs in the check matrix corresponding to the correcting and eleting codes,Every a line of check matrix corresponds to a verification calculation formula of the encoder matrix, and each row are corresponded in encoder matrix One element, when jth arranges corresponding element and appears in i-th of verification calculating formula, the i-th row j of check matrix The value of the element of row is 1.
- 5. the correcting and eleting codes coding/decoding method based on check matrix as claimed in claim 1, it is characterised in that the sparse verification square Battle array is obtained by elementary transformation.
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