CN104850468A - Check matrix based erasure code decoding method - Google Patents
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- CN104850468A CN104850468A CN201510290040.9A CN201510290040A CN104850468A CN 104850468 A CN104850468 A CN 104850468A CN 201510290040 A CN201510290040 A CN 201510290040A CN 104850468 A CN104850468 A CN 104850468A
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Abstract
The invention provides a check matrix based erasure code decoding method which is applicable to optional erasure codes on the basis of exclusive or operation. Decoding efficiency is greatly improved by decoding the check matrix. In addition, through an iterative algorithm for structuring a sparse check matrix, decoding efficiency can be further improved. Compared with two conventional implementation methods, the check matrix based erasure code decoding method has the advantages of universality and high efficiency.
Description
Technical field
The present invention relates to a kind of correcting and eleting codes coding/decoding method based on check matrix.
Background technology
Constantly promote the requirement of data reliability along with in large memory system, correcting and eleting codes, as a kind of guarantee high reliability technology of high efficiency, low cost, is widely adopted.By using correcting and eleting codes technology, raw data is together left in (typical apply is as disk array) on multiple memory device with by the checking data generated of encoding, thus when some of them device fails, the data that it is lost can be recovered by the data on other equipment.
Among diversified correcting and eleting codes, a class is had to operate based on XOR (Exclusive-OR), another kind of, be carry out coding and decoding based on the computing in Galois field.At present, the coding based on XOR is more popular, and this is because hardware all directly supports xor operation usually, and make the computing cost of this kind of coding very low, the efficiency of coding and decoding is very high.The common coding based on xor operation has the following: have EVENODD for what recover two disk failure, RDP encodes, and can tolerate three disk failure have STAR and HoVer etc.
Usually, we have two kinds of approach to realize these codings.First method we be referred to as " matrix method ": for any one correcting and eleting codes, as long as provide its " generator matrix " (all correcting and eleting codes have its generator matrix), we just can utilize a series of matrix manipulation to carry out encoding or decoding.The method is a kind of universal method, and for any correcting and eleting codes, we all can realize by the method.Second method we be referred to as special method: for some coding, there are some specifically coding, decoding algorithms.These algorithms design according to coding characteristic inherently, therefore do not have versatility.Specifically, be applicable to a kind of own coding of correcting and eleting codes, decoding algorithm, be not usually suitable for another kind of correcting and eleting codes.
Existing two kinds of methods realizing correcting and eleting codes, i.e., all there is significant shortcoming in matrix method and special method.On the one hand, although matrix method is comparatively general, it has significant deficiency on decoding speed, thus limits the resume speed of disk array, reduces the reliability and availability of storage system.On the other hand, special method still can not reach optimum (as EVENODD and STAR coding) on decoding speed, and the realization of this kind of algorithm is very complicated, is unfavorable for further optimization; In addition, a lot of coding efficiently does not have special implementation, and therefore special method exists significant limitation.In summary, the existing two kinds of methods realizing correcting and eleting codes all can not have versatility and high efficiency simultaneously.
Summary of the invention
The object of the present invention is to provide a kind of correcting and eleting codes coding/decoding method based on check matrix, very large lifting can be brought to decoding efficiency
For solving the problem, the invention provides a kind of correcting and eleting codes coding/decoding method based on check matrix, comprising:
According to the coded system of the encoder matrix of the correcting and eleting codes based on xor operation of disk array, construct the check matrix corresponding to described correcting and eleting codes, described check matrix is 01 matrix;
The fail data of failed disk in disk array is calculated according to described check matrix.
Further, in the above-mentioned methods, calculate the fail data of failed disk in disk array according to described check matrix, comprising:
Mark the fail data L of survival data S and failed disk in disk array;
Check matrix H is divided into two sub-matrix H
land H
s, correspond respectively to described fail data L and survival data S;
Utilize equation
namely the fail data of failed disk in disk array is calculated by check matrix, wherein,
it is 01 group inverse matrices matrix.
Further, in the above-mentioned methods, according to the coded system of the encoder matrix of the correcting and eleting codes based on xor operation of disk array, construct in the check matrix corresponding to described correcting and eleting codes,
The line number of check matrix equals the quantity of the check block in the encoder matrix of correcting and eleting codes, and the columns of check matrix equals the quantity of all proof mass and data block in the encoder matrix of correcting and eleting codes.
Further, in the above-mentioned methods, according to the coded system of the encoder matrix of the correcting and eleting codes based on xor operation of disk array, construct in the check matrix corresponding to described correcting and eleting codes,
A verify calculation formula of the corresponding described encoder matrix of every a line of check matrix, each arranges an element in corresponding encoder matrix, when the element that jth that and if only if row are corresponding appears in i-th verify calculation formula, the value of the element of the i-th row j row of check matrix is 1.
Further, in the above-mentioned methods, according to the coded system of the encoder matrix of the correcting and eleting codes based on xor operation of disk array, construct in the check matrix corresponding to described correcting and eleting codes,
Described check matrix is sparse check matrix.
Further, in the above-mentioned methods, described sparse check matrix is obtained by elementary transformation.
Further, in the above-mentioned methods, described sparse check matrix is obtained by following iterative algorithm structure:
Step S11, arranges variable update, and whether expression one is taken turns check matrix in iteration and be updated, and initial value is set to false;
Step S12, initialization procedure, comprises step S121 ~ step S123:
Step S121, calculates array ones [x], wherein, array ones [x] represent that check matrix xth row comprises 1 quantity;
Step S122, numeration group from [x], wherein from [x] represents that xth row deposits this row and which sum, and initial value is that any other row is not deposited in-1 expression;
Step S123, numeration group visit [x], wherein, visit [x] represents the whether accessed mistake of xth row, and be initially entirely set to false, this row is not accessed;
Step S13, circulation performs following steps S131 ~ step S134, until all row are all accessed:
Step S131, in the row of all not accessed mistakes, choose the row comprising 1 minimum number, suppose it is that x is capable, namely 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 that x is capable and y is capable, namely has the element of how many row not identical, remembers that this value is dis;
Step S1322, if dis<ones [y], then representing needs capable for x that to add to y capable, so by dis assignment to ones [y], then changes the value of from [y] into x, finally the value of update is set as true;
Step S133, if the value of from [x] is not-1, then adds to xth row by from [x] this line;
Step S134, is set as true by visit [x], represents that this row is accessed;
Step S14, if the value of update is true, then return step S11, otherwise algorithm terminates.
Compared with prior art, the present invention is applicable to arbitrarily based on the correcting and eleting codes of xor operation, and the present invention by decoding to check matrix, thus brings very large lifting to decoding efficiency.In addition, by constructing the iterative algorithm of sparse check matrix, decoding efficiency of the present invention can be promoted further.Compared to traditional two kinds of implementation methods, the present invention has versatility and high efficiency simultaneously.
Accompanying drawing explanation
Fig. 1 is the schematic diagram of the coded system of the EVENODD horizontal check of one embodiment of the invention;
Fig. 2 is the schematic diagram of the coded system of the oblique verification 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
For enabling above-mentioned purpose of the present invention, feature and advantage become apparent more, and below in conjunction with the drawings and specific embodiments, the present invention is further detailed explanation.
Before introducing the present invention, first set forth key concept and the conventional implementation of correcting and eleting codes by object lesson, so that set forth concept of the present invention better and show advantage of the present invention.Encode as case using the EVENODD of classics, this coding can be used to realize RAID-6 disk array, can tolerate that two disks lost efficacy simultaneously and do not make loss of data.EVENODD is applicable to the array with p+2 disk, and p must be a prime number here; And in this p+2 disk, have p disk to be used for all the time depositing raw data, and remain two disks and be used for depositing checking data, these checking datas are calculated through coding flow process by raw data.Fig. 1 and Fig. 2 illustrates the coding flow process of the EVENODD being applicable to 7 disks, and the prime number of this coding correspondence is p=5.
In fig. 1 and 2, with the matrix of (p-1) * (p+2), we represent that EVENODD encodes, and wherein a disk is shown in each list of matrix, what each grid represented is on disk one fixed-size piece.First matrix column is numbered 0-6 from left to right, front 5 disk store data, verification deposited by latter two disk.Similarly, the row of matrix is numbered 0-3 from top to bottom, and in matrix, the element representation of the i-th row jth row is C
i,j.
Fig. 1 illustrates the account form of the checking data on disk 5.For each check block on disk 5, it obtains by suing for peace with the data block xor operation of a line in disk 0-4, for example, and C
0,5by formula
calculate and obtain.Correspond in figure, each check block is sued for peace by the data block XOR of same shape and obtains.Because the same element walked crosswise only is used in this part calculating, therefore this verification is commonly called horizontal check.
Fig. 2 illustrates the account form of the checking data on disk 6.We have employed the similar expression way of same Fig. 1, participate in all data blocks of a check block calculating with same shape representation.First we will calculate an intermediate value M, and computing formula is
after calculating M, each check block on disk 6 is then by the value of the data block of shape same in Fig. 2, and the value of M is together sued for peace and obtains.Such as,
this verification is commonly called oblique verification.
If in a computing formula, only have an element to be obliterated data, so this element recovers by other element XORs summation in formula.Namely traditional recovery algorithms make use of this characteristic.Such as, when two data disks lost efficacy simultaneously, first, this coding can utilize the date restoring on two check disks of survival to go out the value of s; Then first find a data block, it directly can be recovered by certain oblique verify calculation formula; Next utilize horizontal check formula, another missing data in same a line can be recovered; The oblique verification of following recycling recovers next data, and iteration like this is until all date restoring are complete.
The invention provides a kind of correcting and eleting codes coding/decoding method based on check matrix, comprising:
Step S1, according to the coded system of the encoder matrix of the correcting and eleting codes based on xor operation of disk array, constructs the check matrix corresponding to described correcting and eleting codes, and described check matrix is 01 matrix, is designated as H;
Step S2, calculates the fail data of failed disk in disk array according to described 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, calculates the fail data of failed disk in disk array, comprising according to described check matrix:
Step S21, marks the fail data L of survival data S and failed disk in disk array;
Step S22, is divided into two sub-matrix H by check matrix H
land H
s, correspond respectively to described fail data L and survival data S, according to the character of check matrix, meet following equation H
ll=H
ss; Check matrix has an important character, namely it with coding after the product of data be always 0, this character determined by its definition mode, and this character is concerning most important decoding step, Fig. 3 illustrates this relation by the example of EVENODD, and concrete decoding scheme will hereafter describe in detail;
Step S23, can be obtained by previous step equation
utilize this equation can be calculated the fail data of failed disk in disk array by check matrix, wherein,
it is 01 group inverse matrices matrix.Concrete, in order to explain decoding process better, we first suppose currently have several disk failure.We still regard a vector as the data in whole band, then the data in failed disk are just counted as unknown number.Now, the equation shown in Fig. 3 is disassembled by we, and first will represent that the vector of all data splits into two vectors, one of them is made up of (being designated as L) fail data entirely, and another is then made up of (being designated as S) survival data; And check matrix H is also divided into two submatrixs, the row corresponding to inefficacy element form and (are designated as H
l), another is made up of element column of surviving and (is designated as H
s).Equation then according to Fig. 3, we can obtain:
in this equation, L is only had to be the data that unknown quantity represents loss.H
ll and H
sthe result of calculation of S is column vector.And two column vector XOR values are that they are equal in 0 explanation, therefore this formula can be write as H
ll=H
ss, we are again by matrix operation, can by the unknown quantity solution in this formula out:
finally, Fig. 4 illustrates the instantiation that is recovered fail data.EVENODD coding in the preceding example that we still adopt, and suppose there is 7 pieces of disks, and wherein No. 0 and No. 2 disks are failure discs, and the data on this disk are fail data.First we split by row check matrix, then the data after coding is divided into survival data and fail data.Now, Fig. 4 illustrate segmentation after the relation of check matrix and coded data.Next, we obtain H
linverse matrix, and calculate the result of equation right-hand member, both be multiplied and namely obtain 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 the coded system of the encoder matrix of the correcting and eleting codes based on xor operation of disk array, construct in the check matrix corresponding to described correcting and eleting codes, the line number of check matrix equals the quantity of the check block in the encoder matrix of correcting and eleting codes, the columns of check matrix equals the quantity of all proof mass and data block in the encoder matrix of correcting and eleting codes, the i.e. quantity of all elements in encoder matrix, a verify calculation formula of the corresponding described encoder matrix of every a line of check matrix, each arranges an element in corresponding encoder matrix, when the element that jth that and if only if row are corresponding appears in i-th verify calculation formula, the value of the element of the i-th row j row of check matrix is 1.Concrete, check matrix is a closely-related matrix with correcting and eleting codes, and it can linear relationship between each field of data after presentation code.In the above example, for representing that the matrix of EVENODD is that 4 row 7 arrange and comprise 28 elements altogether and comprise check block and data block, and 8 elements of last two row are check blocks, and corresponding check matrix of therefore encoding with EVENODD has 8 row 28 to arrange.Specifically, a verify calculation formula of the corresponding described encoder matrix of every a line of check matrix, each arranges an element in corresponding encoder matrix.Each element value of check matrix non-zero namely 1, and when element corresponding to and if only if jth row appears in the calculating formula of i-th verification, the value of the element that the i-th row 1 of check matrix arranges is 1.Fig. 3 gives the sample of the check matrix of the EVENODD coding corresponding with Fig. 1-2.In check matrix shown in this Fig. 3, the verify calculation formula of each element on front four lines is corresponding disk 5, the verify calculation formula of each element on then four lines is corresponding 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 the coded system of the encoder matrix of the correcting and eleting codes based on xor operation of disk array, construct in the check matrix corresponding to described correcting and eleting codes, described check matrix is sparse check matrix, to promote decoding speed further, check matrix complexity in decode procedure is significantly reduced.
In one preferred embodiment of the correcting and eleting codes coding/decoding method based on check matrix of the present invention, described sparse check matrix is obtained by elementary transformation.First, we to observe the check matrix of an encoder matrix not unique.The product of the data after legal check matrix and coding should be 0, if and we construct any one legal check matrix, we carry out Applying Elementary Row Operations to this matrix, and namely the value of a line adds in another row by we, and the new matrix after conversion remains legal check matrix.And according to decoding process described before, we observe, and sparse check matrix has less coding/decoding cost, therefore we can utilize elementary transformation of the present inventionly to realize speed to promote.
In one preferred embodiment of the correcting and eleting codes coding/decoding method based on check matrix of the present invention, described sparse check matrix is obtained by following iterative algorithm structure:
Step S11, arranges variable update, and whether expression one is taken turns check matrix in iteration and be updated, and initial value is set to false;
Step S12, initialization procedure, comprises step S121 ~ step S123:
Step S121, calculates array ones [x], wherein, array ones [x] represent that check matrix xth row comprises 1 quantity;
Step S122, numeration group from [x], wherein from [x] represents that xth row deposits this row and which sum, and initial value is that any other row is not deposited in-1 expression;
Step S123, numeration group visit [x], wherein, visit [x] represents the whether accessed mistake of xth row, and be initially entirely set to false, this row is not accessed;
Step S13, circulation performs following steps S131 ~ step S134, until all row are all accessed:
Step S131, in the row of all not accessed mistakes, choose the row comprising 1 minimum number, suppose it is that x is capable, namely 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 that x is capable and y is capable, namely has the element of how many row not identical, remembers that this value is dis;
Step S1322, if dis<ones [y], then representing needs capable for x that to add to y capable, so by dis assignment to ones [y], then changes the value of from [y] into x, finally the value of update is set as true;
Step S133, if the value of from [x] is not-1, then adds to xth row by from [x] this line;
Step S134, is set as true by visit [x], represents that this row is accessed;
Step S14, if the value of update is true, then return step S11, otherwise algorithm terminates.By above algorithm, recycle Applying Elementary Row Operations to promote the openness of check matrix, some check matrix of encoding can be made more sparse, thus there is coding and decoding speed faster.
The present invention is applicable to arbitrarily based on the correcting and eleting codes of xor operation, and the present invention by decoding to check matrix, thus brings very large lifting to decoding efficiency.In addition, by constructing the iterative algorithm of sparse check matrix, decoding efficiency of the present invention can be promoted further.Compared to traditional two kinds of implementation methods, the present invention has versatility and high efficiency simultaneously.
In this instructions, each embodiment adopts the mode of going forward one by one to describe, and what each embodiment stressed is the difference with other embodiments, between each embodiment identical similar portion mutually see.
Professional can also recognize further, in conjunction with unit and the algorithm steps of each example of embodiment disclosed herein description, can realize with electronic hardware, computer software or the combination of the two, in order to the interchangeability of hardware and software is clearly described, generally describe composition and the step of each example in the above description according to function.These functions perform with hardware or software mode actually, depend on application-specific and the design constraint of technical scheme.Professional and technical personnel can use distinct methods to realize described function to each specifically should being used for, but this realization should not thought and exceeds scope of the present invention.
Obviously, those skilled in the art can carry out various change and modification to invention and not depart from the spirit and scope of the present invention.Like this, if these amendments of the present invention and modification belong within the scope of the claims in the present invention and equivalent technologies thereof, then the present invention is also intended to comprise these change and modification.
Claims (7)
1., based on a correcting and eleting codes coding/decoding method for check matrix, it is characterized in that, comprising:
According to the coded system of the encoder matrix of the correcting and eleting codes based on xor operation of disk array, construct the check matrix corresponding to described correcting and eleting codes, described check matrix is 01 matrix;
The fail data of failed disk in disk array is calculated according to described check matrix.
2., as claimed in claim 1 based on the correcting and eleting codes coding/decoding method of check matrix, it is characterized in that, calculate the fail data of failed disk in disk array according to described check matrix, comprising:
Mark the fail data L of survival data S and failed disk in disk array;
Check matrix H is divided into two sub-matrix H
land H
s, correspond respectively to described fail data L and survival data S;
Utilize equation
namely the fail data of failed disk in disk array is calculated by check matrix, wherein,
it is 01 group inverse matrices matrix.
3., as claimed in claim 2 based on the correcting and eleting codes coding/decoding method of check matrix, it is characterized in that, according to the coded system of the encoder matrix of the correcting and eleting codes based on xor operation of disk array, construct in the check matrix corresponding to described correcting and eleting codes,
The line number of check matrix equals the quantity of the check block in the encoder matrix of correcting and eleting codes, and the columns of check matrix equals the quantity of all proof mass and data block in the encoder matrix of correcting and eleting codes.
4., as claimed in claim 3 based on the correcting and eleting codes coding/decoding method of check matrix, it is characterized in that, according to the coded system of the encoder matrix of the correcting and eleting codes based on xor operation of disk array, construct in the check matrix corresponding to described correcting and eleting codes,
A verify calculation formula of the corresponding described encoder matrix of every a line of check matrix, each arranges an element in corresponding encoder matrix, when the element that jth that and if only if row are corresponding appears in i-th verify calculation formula, the value of the element of the i-th row j row of check matrix is 1.
5., as claimed in claim 4 based on the correcting and eleting codes coding/decoding method of check matrix, it is characterized in that, according to the coded system of the encoder matrix of the correcting and eleting codes based on xor operation of disk array, construct in the check matrix corresponding to described correcting and eleting codes,
Described check matrix is sparse check matrix.
6., as claimed in claim 5 based on the correcting and eleting codes coding/decoding method of check matrix, it is characterized in that, described sparse check matrix is obtained by elementary transformation.
7. as claimed in claim 6 based on the correcting and eleting codes coding/decoding method of check matrix, it is characterized in that, described sparse check matrix is obtained by following iterative algorithm structure:
Step S11, arranges variable update, and it is upgrade that check matrix in iteration is taken turns in expression one, and initial value is set to false;
Step S12, initialization procedure, comprises step S121 ~ step S123:
Step S121, calculates array ones [x], wherein, array ones [x] represent that check matrix xth row comprises 1 quantity;
Step S122, numeration group from [x], wherein from [x] represents that xth row deposits this row and which sum, and initial value is that any other row is not deposited in-1 expression;
Step S123, numeration group visit [x], wherein, visit [x] represents the whether accessed mistake of xth row, and be initially entirely set to false, this row is not accessed;
Step S13, circulation performs following steps S131 ~ step S134, until all row are all accessed:
Step S131, in the row of all not accessed mistakes, choose the row comprising 1 minimum number, suppose it is that x is capable, namely 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 that x is capable and y is capable, namely has the element of how many row not identical, remembers that this value is dis;
Step S1322, if dis<ones [y], then by dis assignment to ones [y], then change the value of from [y] into x, finally the value of update be set as true;
Step S133, if the value of from [x] is not-1, then adds to xth row by from [x] this line;
Step S134, is set as true by visit [x], represents that this row is accessed;
Step S14, if the value of update is true, then return step S11, otherwise algorithm terminates.
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