CN105721611B - A method of storage code can be divided to generate minimum memory regeneration code by very big distance - Google Patents
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Abstract
The invention discloses a kind of method that there is the very big distance of best repair property storage code can be divided to be converted into minimum memory regeneration code system node, resulting minimum memory regeneration code is suitable for distributed memory system.The very big distance that the conversion method is based on can divide storage code to be non-binary, and conversion process does not change the alphabetical table size of former storage code.If the very big distance that the conversion method is based on can divide the system node of storage code to have optimal access property, the minimum memory regeneration code obtained after conversion has optimal access property.The medicine have the advantages that the storage overhead of (I) system is very small;(II) any one failure node can only consume the smallest bandwidth resources during repairing failure node by best repair;(III) MDS that according to system node there is best I/O to repair property stores code as base code, and I/O expense is also minimum when repairing failure node.
Description
Technical field
The present invention relates to distributed memory system field, in particular to it is a kind of suitable for distributed memory system by system
The coding techniques that there is node the very big distance of best repair property storage code can be divided to be converted into minimum memory regeneration code.
Background technique
For the reliability for improving distributed memory system, redundancy is indispensable.In general, there are two types of increase redundancy
Mechanism: replicate and entangle and delete.Compared with duplication code, correcting and eleting codes can provide more reliabilities in the identical situation of amount of redundancy,
So more advantage.And in all correcting and eleting codes, very big distance can divide (MDS) code such as Reed-Solomon code because in redundancy
Measuring in identical situation, there is maximum entangle to delete error resistance, be widely used in Google Colossus, Microsoft
Multiple distributed cloud storage systems such as Azure.In general, source file is divided into k parts, carried out using one (k+r, k) MDS code
K+r parts of data are obtained after coding, are then stored in respectively in k+r independent storage equipment, these equipment are also referred to as node.
But for large-scale distributed cloud storage system, the reliability of each node is not high, failure phenomenon frequent occurrence, saves
The reliability that point failure will increase a possibility that loss of data, reduce system, and wherein single-unit point failure is up to 98.08%.For
The certain amount of redundancy of maintenance, system can continually carry out node reparation, and common repair mode is the node from other survivals
To repair the failure node, these nodes are also referred to as helping node middle downloading data.In repair process, institute's downloading data
Amount be referred to as and repair bandwidth, reduce expense in real system, repairing bandwidth should minimize.However, tradition MDS stores code
Restorative procedure be connection any k helps node downloading total data, to reconstruct source file, then re-encoding generation is failed
Data in node, corresponding bandwidth of repairing is maximum, this brings great expense to distributed memory system.
Document " Network coding for distributed storage systems, IEEE Trans.on
Information Theory, vol.56, no.9, p.4539-4551, (the distribution based on network code of September 2010
Formula storage system, IEEE information theory transactions, volume 56, the 9th phase, the 4539-4551 pages, in September, 2010) " it has been determined that storage is compiled
The minimum of code repairs bandwidth, and the node for reaching minimum reparation bandwidth, which is referred to as, has best repair property, and all nodes all have
Best repair property is referred to as regeneration code, wherein most important is two classes coding: minimum memory regenerates (MSR) code and minimum is repaired
Bandwidth regenerates (MBR) code.
Specifically, the source file that a size is kN element is divided into k parts by MSR coding, and every part includes N number of element,
The column vector f for being N with lengthiIt indicates, it is equally N with length that 0≤i < k., which obtains r parts of verification data after encoding to initial data,
Column vector fiIt indicates, k≤i < k+r.This k+r parts of data are stored in the distribution that one is included in k+r node respectively to deposit
In storage system.One (k+r, k) MSR code includes (1) MDS property, that is, source file can be reconstructed by connecting any k node, referring to
Attached drawing 1;(2) the reparation bandwidth of best repair property, i.e., one failure node is γ=dN/ (d-k+1), this can pass through connection
D (k≤d≤k+r-1) a help node number is downloaded N/ (d-k+1) a element from each help node and is realized, such as attached drawing 2
It is shown.
In particular, the storage code constructed in above-mentioned document is that function repairs code, i.e., instead of the new of failure node
The data of node storage can be original with failure node data it is different but functionally of equal value;It is, however, required that replacing failure
The data and the duplicate accurate reparation MSR code of the original data of failure node of the new node storage of node, can actually answer
With the complexity of middle reduction system, thus more welcome by real system.In addition, the accurate reparation MSR code being currently known all considers d
The situation of=k+r-1 carrys out maximum reduction and repairs bandwidth.Present invention also contemplates that a kind of this situation.
The code rate k/ (k+r) of MSR code used by actual distributed memory system usually requires that is as large as possible to subtract
Few storage overhead, but MSR code, such as " Repair optimal erasure codes through as only 4 classes at present
hadamard designs,IEEE Trans.on Information Theory,vol.59,no.5,pp.3021-3037,
May 2013 (the best repair correcting and eleting codes based on hadamard design, IEEE information theory transactions, volume 59, the 5th phase, 3021-
Page 3037, in May, 2013) " etc. in construction.In addition, presently, there are some MDS for code rate greater than 1/2 to store code, such as
Document " A framework of constructions of minimal storage regenerating codes with
the optimal access/update property,IEEE Trans.on Information Theory,vol.61,
No.4, pp.1920-1932, April 2015 (tectonic framework with optimal access/more new property MSR code, IEEE
Information theory transactions, volume 61, the 4th phase, the 1920-1932 pages, in April, 2015) " etc. in construction.And this kind of MDS stores code
Can only best repair system node and be unable to best repair check-node.
Summary of the invention
By system node there is the MDS storage code of best repair property to be converted into the purpose of the present invention is to provide a kind of
The method of MSR code.
What above-mentioned purpose of the invention was achieved, it is a kind of to there is the MDS of best repair property to store code system node
The method for being converted into MSR code, comprising the following steps:
(1) select system node that there is the node capacity of best repair property to store code C for (k+r, the k) MDS of N1As
Base code;
(2) r code C is generated1Example, obtain node capacity be rN (k+r, k) MDS store code C2;
(3) using r displacement respectively to C2In the check-node of each example carry out displacement to obtaining node capacity and be
(k+r, the k) MDS of rN stores code C3;
(4) for 0≤j ≠ l < r, by C3The data in data and example l node j on example j node l do two linearly
Unrelated linear combination simultaneously replaces C respectively3The data of middle example j node l and example l node j, so that obtaining node capacity is rN
(k+r, k) MSR code C4。
There is the MDS storage code of best repair property to be converted into the method for MSR code system node of the invention, institute
The base code C stated1It is non-binary.
There is the very big distance of best repair property storage code can be divided to be converted into MSR code system node of the invention
In method, the r displacement is the displacement on { 0,1 ..., r-1 }.
There is the very big distance of best repair property storage code can be divided to be converted into MSR code system node of the invention
In method, base code C is being repaired1With MSR code C4Some memory node when, the help node number that is connected is k+r-1.
There is the very big distance of best repair property storage code can be divided to be converted into MSR code system node of the invention
In method, the code C of centre generation2, C3With the code C after conversion4, system node storage data it is just the same.
There is the very big distance of best repair property storage code can be divided to be converted into MSR code system node of the invention
In method, the MSR code C is repaired4System node j when, restorative procedure with as base code C1The corresponding section of MDS storage code
Restorative procedure identical when point j
There is the very big distance of best repair property storage code can be divided to be converted into MSR code system node of the invention
In method, when repairing the check-node j of the MSR code, rj to rj+r-1 members in the node of remaining k+r-1 are downloaded
Element.
The medicine have the advantages that the storage overhead of (I) system is very small;(II) any one failure node can be by most
Good reparation only consumes the smallest bandwidth resources during repairing failure node;(III) there is best I/ according to system node
O repairs the MDS storage code of property as base code, and I/O expense is also minimum when repairing failure node.
The present invention is described in detail with reference to the accompanying drawing.
Detailed description of the invention
Fig. 1 is using the coding of the distributed memory system of MDS code, storage, reconstruct source file, repairs showing for individual node
It is intended to;
Fig. 2 is the schematic diagram for repairing individual node failure of MSR code in the prior art;
Fig. 3 is the schematic diagram data of MSR code memory node in the prior art;
Fig. 4 is process of the present invention intermediate code C2The schematic diagram data of memory node;
Fig. 5 is process of the present invention intermediate code C3The schematic diagram data of check-node;
Fig. 6 is the MSR code C that the present invention generates4The schematic diagram data of check-node;
Fig. 7 is an example of the MSR code that the present invention generates;
Fig. 8 is that the present invention generates MSR code C4The flow chart of generation.
Specific embodiment
MSR code proposed by the invention has (k+r, the k) that the node capacity of best repair property is N by system node
MDS stores code C1It converts.
It is assumed that using code C1Storage system system node and the data that are stored of check-node be respectively fi', 0≤i < k
And gj', 0≤j < r, wherein fi' it is the column vector that length is N,Ai,iIt is N rank nonsingular square matrix, and system section
The data f of point ii' can be by downloading Si,jfj', 0≤j ≠ i < k and Si,k+lgl', 0≤l < r is recovered, wherein Si,jAnd Si,k+l
It is the matrix of N/r × N.Generation and reparation, the reconstruct of the MSR code then proposed carry out as follows
The generation of MSR code:
1. the file that a size is krN is divided into r one's share of expenses for a joint undertaking file, the size of every one's share of expenses for a joint undertaking file is kN, to every
A subfile is all in accordance with base code C1Coding mode is encoded to obtain r example, these example configuration nodes hold
(k+r, the k) MDS that amount is rN stores code, is denoted as C2, it is stored on system node i and check-node j after remembering subfile l coding
Data are respectively fi (l)WithWherein 0≤l, j < r, 0≤i < k, then fi (l)It can pass through0≤j≠i
< k and0≤s < r is recovered.C2The structure of code is shown in attached drawing 4.
2. generating the displacement on r { 0,1 ..., r-1 }, it is denoted as p0, p1,., pr-1.For in previous step
Matrix Si,jIf (a) to arbitrary 0≤i < k, there are matrix SiSo that Si,j=SiTo 0 all≤j ≠ i < k+r
It all sets up, then this r displacement is arbitrary the displacement on { 0,1 ..., r-1 };(b) otherwise this r displacement needs to meet
pi(j)=pj(i), 0≤i, j < r,
Here plIt will act at data in r checkpoint on example l, 0≤l < r.
Keep code C2The data of middle verification data system node are constant, only adjust its position for verifying data by above-mentioned displacement
It sets and carrys out generated code C3, remember code C3The data being stored on check-node j in example l areWherein 0≤l, j < r,
Code C3The structure of check-node is shown in attached drawing 5.
3. by only modifying code C3In verification data come generate node capacity be rN (k+r, k) MSR code C4,
Remember code C4The data stored on check-node j are
WhereinIt is the column vector that a length is N, passes through code C3In verification data in the following manner
It arrives
Wherein
{θj,l,θl,j}={ 1, a }, 0≤j ≠ l < r, a ∈ Fq\{0,1}。
MSR code C4The structure of check-node is shown in attached drawing 6.
The reparation of MSR code:
1. repairing MSR code C4System node i (0≤i < k) data fiWhen, downloadingWith0≤s<
K, 0≤j, l < r.
If there are matrix S (a) to arbitrary 0≤i < kiSo that Si,j=Si0 all≤j ≠ i < k+r is set up, then
It can basis
With
It obtains0≤j, l < r, further according toIt isDisplacement can further obtain0
≤ j, l < r, to pass through base code C1The restorative procedure of system node i can recover fi。
(b) if not, to 0≤j ≠ l < r, according to
And pl(j)=pj(l) it can be obtained0≤j ≠ l < r, in conjunction with0≤l < r, because
p0, p1,., pr-1It is displacement, they correspond to all0≤j, l < r, to pass through base code C1System node i
Restorative procedure can recover fi。
2. repairing MSR code C4Check-node j (0≤j < r) data fk+jWhen, pass through downloading0≤l ≠ j < r and fi (j), 0≤i < k is available
With
It calculates0≤l < r, i.e. fk+j。
The reconstruct of MSR code:
1.If connecting k system node, source file can be obtained.
2. if k-1 system node of connection and 1 check-node, it is assumed that i is the system node being not attached to, and j is
The check-node being already connected to, wherein 0≤i < k, 0≤j < r, then fiIt can be calculated by following steps:
(a) the data f being connected to from system node is utilizedl (j), 0≤l ≠ i < k and the data being connected to from check-nodeIn conjunction with code C1MDS property, f can be calculatedi (j), can further calculate0≤s < r, so as to
?0≤s<r。
(b) to 0 all≤s ≠ j < r, according to the data having connectedWith it is calculated in step (a)Pass throughIt calculatesI.e.Then utilize the data having connected from system node0≤j ≠ i < k with
And just obtainIn conjunction with code C1MDS property, f can be calculatedi (s), thus obtained the whole on k system node
Data, to reconstruct source file
3.If k-t system node and t check-node are connected, wherein 1 < t < r, it is assumed thatIt is not connected
The system node arrived,It is the check-node being already connected to, wherein 0≤i0< ... < it-1< k, 0≤j0< ... <
jt-1< r.It enables
I={ i0,i1,…it-1, J={ j0,j1,…jt-1}
ThenIt can be calculated by following steps:
(a) to u, s ∈ J and u ≠ s passes through equation group
It calculatesFurther according toI.e. to arbitrary s ∈ J, obtainI.e.u∈J。
If (b) s ∈ J, according to obtained in step (a)U ∈ J and the data being connected to from system node
fi (s), i ∈ { 0,1 ..., k-1 } J, in conjunction with code C1MDS property, system data can be calculatedFrom
And it can calculateI.e.To all l ∈ { 0,1 ..., r-1 } J.
If (c)According to obtained in previous stepAnd the data being connected to from check-nodePass throughIt calculatesI.e.S ∈ J, in conjunction with the data f connected from system nodei (l),i∈{0,
1 ..., k-1 I and code C1MDS property, system data can be calculated
Specific embodiment
Given r=3, enablesWithA system node is respectively indicated with best repair property
Node capacity be N (k+3, k) MDS store code C1An example, 0≤l < 3.And system data fi (l)S can be passed throughi,sfs (l),0≤s < k, 0≤j < 3 are restored.After step 1-3, it is rN that node capacity as shown in Figure 7, which can be obtained,
(k+3, k) MSR code.Here the displacement in step 2 is set as
pi(j)=(i+j) mod3,0≤i, j < 3.
Referring to Fig. 7, if connecting node 2 reconstructs source file to node k+1, from the data that wave marks, can obtain
It arrivesWithThe data marked with underscore And the data f of system nodei (0),fi (1), 2≤i < k in conjunction with
The MDS property of base code calculates fi (0),fi (1), i=0,1.It is further calculated out according to these dataWithFinally from dotted line
It is cut in the data markedWithIt obtains laterWithIn conjunction with the data of system node2≤j < k and base
The MDS property of code can calculate f0 (2),f1 (2), this is arrived, source file reconstruct finishes.Source document is reconstructed by connecting other k node
The case where part, is similar.
Referring to Fig. 7, if repair system node i, 0≤i < k passes through downloading0≤j, l < 3 can calculate0≤j, l < 3, further according to the reparation rule recovery system node i of base code.
Referring to Fig. 7, if repairing check-node 0, downloading0≤j ≠ k < k+3.According toWith the volume of base code
Code rule calculatesI.e.Pass through again
It can calculateI.e. check-node 0 can be repaired.Similar, check-node i can pass through downloading0≤j ≠ k+i < k+3 is repaired.
Referring to Fig. 4, it, which is one, with system node there is the node capacity of best repair property to deposit for (k+r, k) MDS of N
Store up code C1As base code, synthesizes (k+r, the k) MDS that the node capacity that r example of the base code obtains is rN and store code C2Structure
Schematic diagram.
Referring to Fig. 5, it is by the storage code C of Fig. 42, i.e., r storage code C1Example in each example in be stored in school
The data tested on node do a displacement, and (k+r, the k) MDS that obtained node capacity is rN stores code C3Check-node knot
Structure schematic diagram.
Referring to Fig. 6, it gives MDS in Fig. 5 and stores code C3The alteration ruler of middle verification node data, after the modification
Obtain (k+r, k) MSR code C that new node capacity is rN4Check-node structural schematic diagram.
Referring to Fig. 8, it gives the present invention and generates MSR code C4Flow chart.
Claims (4)
1. a kind of method that storage code can be divided to generate minimum memory regeneration code by very big distance, which is characterized in that including following step
It is rapid:
(1) select system node that there is the node capacity of best repair property to store code C for (k+r, the k) MDS of N1As base code;
It is assumed that using code C1The data that are stored of system node i and check-node j of storage system be respectively fi', 0≤i < k and g 'j,
0≤j < r, wherein fi' it is the column vector that length is N,Aj,iIt is N rank nonsingular square matrix, and system node i
Data fi' pass through downloading Si,jf′j, 0≤j ≠ i < k and Si,k+lg′l, 0≤l < r recovers, wherein Si,jAnd Si,k+lIt is N/r × N
Matrix;
(2) r code C is generated1Example, obtain node capacity be rN (k+r, k) MDS store code C2: it is krN a size
File be divided into r one's share of expenses for a joint undertaking file, the size of every one's share of expenses for a joint undertaking file is kN, to each one's share of expenses for a joint undertaking file all in accordance with base code C1Coding mode into
Row coding obtains r example, and (k+r, the k) MDS that these example configuration node capacity are rN stores code, is denoted as C2;Remember subfile l
The data being stored on system node i and check-node j after coding are respectively fi (l)WithWherein 0≤l, j <
R, 0≤i < k, then fi (l)Pass through0≤j ≠ i < k and0≤s < r is recovered;
(3) using r displacement respectively to C2In each example check-node carry out displacement to obtain node capacity be rN (k
+ r, k) MDS storage code C3: the displacement on r { 0,1 ..., r-1 } is generated, p is denoted as0, p1..., pr-1;For in previous step
Matrix Si,jIf (a) to arbitrary 0≤i < k, there are matrix SiSo that Si,j=Si0 all≤j ≠ i < k+r is set up, then
This r displacement is arbitrary the displacement on { 0,1 ..., r-1 };(b) otherwise this r displacement needs to meet
pi(j)=pj(i), 0≤i, j < r,
Here plIt will act at data in r check-node on example l, 0≤l < r;
(4) for 0≤j ≠ l < r, by C3The check number in verification data and example l check-node j on example j check-node l
According to the linear combination for doing two linear independences and respectively instead of C3The verification of middle example j check-node l and example l check-node j
Data, to obtain (k+r, k) MSR code C that node capacity is rN4: by only modifying a yard C3In verification data generate node
Capacity is (k+r, k) MSR code C of rN4, wherein r is the integer more than or equal to 2, and k is the integer more than or equal to 1;Remember code C4Verification
The data stored on node j are
WhereinIt is the column vector that a length is N, passes through code C3In verification data obtain in the following manner
Wherein remember code C3The data being stored on check-node j in example l are
{θj,l,θl,j}={ 1, a }, 0≤j ≠ l < r, a ∈ Fq\{0,1}。
2. a kind of method that storage code can be divided to generate minimum memory regeneration code by very big distance according to claim 1,
It is characterized in that: repairing base code C1With the new code C obtained after conversion4Some memory node when, the help node number that is connected
For k+r-1.
3. a kind of method that storage code can be divided to generate minimum memory regeneration code by very big distance according to claim 1,
It is characterized in that, the base code is the maximum distance separable code of non-binary, and system node is repaired with best repair property, i.e. its
Multiple bandwidth is (k+r-1) N/r.
4. a kind of method that storage code can be divided to generate minimum memory regeneration code by very big distance according to claim 1,
It is characterized in that, the new code C obtained after conversion4In include that all nodes of system node and check-node all have best repair
Matter, i.e., it is (k+r-1) N/r that it, which repairs bandwidth,.
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WO2018209541A1 (en) * | 2017-05-16 | 2018-11-22 | 北京大学深圳研究生院 | Coding structure based on t-design fractional repetition codes, and coding method |
CN108156040A (en) * | 2018-01-30 | 2018-06-12 | 北京交通大学 | A kind of central control node in distribution cloud storage system |
CN108647108B (en) * | 2018-03-21 | 2021-04-13 | 长安大学 | Construction method of minimum bandwidth regeneration code based on cyclic VFRC |
CN108923960A (en) * | 2018-06-20 | 2018-11-30 | 华中科技大学 | A kind of memory node restorative procedure for assisting regeneration code based on agency |
CN109062724B (en) * | 2018-07-21 | 2019-04-05 | 湖北大学 | A kind of correcting and eleting codes conversion method and terminal |
WO2020199162A1 (en) * | 2019-04-03 | 2020-10-08 | 东莞理工学院 | Rack-aware regenerating code for data center |
US11513898B2 (en) | 2019-06-19 | 2022-11-29 | Regents Of The University Of Minnesota | Exact repair regenerating codes for distributed storage systems |
CN110750382B (en) * | 2019-09-18 | 2020-10-30 | 华中科技大学 | Minimum storage regeneration code coding method and system for improving data repair performance |
CN110990188B (en) * | 2019-11-19 | 2023-03-24 | 长安大学 | Construction method of partial repetition code based on Hadamard matrix |
CN112732203B (en) * | 2021-03-31 | 2021-06-22 | 中南大学 | Regeneration code construction method, file reconstruction method and node repair method |
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