CN105227190B - A kind of building method multiplying the LDPC code of cyclic subgroup in group based on finite field - Google Patents
A kind of building method multiplying the LDPC code of cyclic subgroup in group based on finite field Download PDFInfo
- Publication number
- CN105227190B CN105227190B CN201410281293.5A CN201410281293A CN105227190B CN 105227190 B CN105227190 B CN 105227190B CN 201410281293 A CN201410281293 A CN 201410281293A CN 105227190 B CN105227190 B CN 105227190B
- Authority
- CN
- China
- Prior art keywords
- matrix
- cyclic
- row
- ldpc code
- submatrix
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Landscapes
- Error Detection And Correction (AREA)
Abstract
The present invention relates to the channel coding technology field in communication system, specially a kind of building method for multiplying the LDPC code of cyclic subgroup in group based on finite field.The building method can be carried out by five following steps: being determined code parameter, determined that finite field is multiplied the cyclic subgroup of group, the design of basic matrix, the extension of basic matrix are carried out based on subgroup and its piecemeal submatrix is taken to do check matrix, by five above-mentioned steps, the LDPC code that the quasi-cyclic low mistake with larger minimum intersymbol distance is flat on a kind of two element field or polynary domain is constructed.
Description
Technical field
The present invention relates to the channel coding technology field in communication system, specially one kind is multiplied in group based on finite field and is recycled
The building method of the LDPC code of subgroup.
Background technique
LDPC code is a kind of good code close to shannon limit, is found by Gallager within 1962, be found again 1995 and
Return to the sight of people.Subsequently, regarding to the design of this code, construction, decoding, high efficient coding, performance evaluation and it is logical in number
Letter and the hot spot being applied to for research in storage system.
According to the difference of make, LDPC code can be divided into two classes, LDPC code randomly or pseudo-randomly and structure
LDPC code.
Wherein, LDPC code randomly or pseudo-randomly is found to obtain using computer, and searching algorithm is with reference to specific design
Criterion and some Tanner graph structure characteristics, including girth, degree distribution and stopping collection etc..Design the LDPC of good random configuration
Code can be realized outstanding error bit ability, and some researches show that design good code length 10 under Gaussian channel7It is random
LDPC code, away from shannon limit only 0.0045dB.Although the code length of this yard due to it is too long without be applied to display system in,
It is that this suffices to show that the outstanding error performance of random LDPC.At the same time, random due to randomly or pseudo-randomly LDPC code construction
Property so that its check matrix do not have structure on rule and in the realization for encoding and decoding complexity with higher, and
Minimum range of the LDPC code of random configuration by cannot be guaranteed constructed code word, and it is flat to be easy undesirable mistake.
In contrast, constructing the LDPC code of a class formation based on combinatorial theory, which utilizes super flat in finite geometry
Geometrical features such as the intersection in face, parallel or using in finite field plus group or the characteristics of multiply group decompose, masking etc. in conjunction with ranks
Operation produces a kind of LDPC code with more regular texture characteristic.The check matrix of structure LDPC code often has circulation
Or quasi-cyclic design feature, these design features, which make it possible to, can realize line by simple circulating register
Property complexity coding, this in the realization of hardware with random LDPC code coding compared to very big advantage, and it is quasi-cyclic
Structure allows its hardware realization of decoding using quasi-cyclic decoding framework, this is mentioned between the speed and decoding complexity of decoder
Very big compromise is supplied.Compared with long random code, often Lve Xun is well set structure LDPC code with warp in terms of error bit ability
The random LDPC code of meter, but structure LDPC code can guarantee biggish minimum range by constraint condition, and make it have good
Convergence property and extremely low mistake it is flat.
Summary of the invention
(1) technical problems to be solved
The purpose of the present invention is intended to construct a series of structure LDPC using two cyclic subgroups multiplied in finite field in group
The advantages of code, which has both random and traditional structure LDPC code, both ensure that the error bit ability of this yard and design it is good with
Machine LDPC code is suitable, while the quasi- cyclic of this yard also ensures low complex degree advantage of this yard in hardware realization, simultaneously
With the flat characteristic with fast convergence of low mistake.
(2) technical solution
In order to solve the above-mentioned technical problems, the present invention provides a kind of LDPC codes for multiplying cyclic subgroup in group based on finite field
Building method, the method is divided into following steps:
According to the parameter for determining the code of being constructed；
Selection will carry out the finite field gf (q) of code construction, guarantee the code word that basic matrix can construct herein when GF (q) chooses
Maximum length (q-1)2Greater than the code word size L that will be constructed, construction arranges weight MCWith row weight NCMC×NCWhen piecemeal check matrix,
Meet MC+NC≤(q-1)；
Multiply group based on finite field, designs two cyclic subgroups；
Based on described two cyclic subgroups, (q-1) × (q-1), the base of energy unique identification one kind LDPC code are constructed
Matrix W, the element in the basic matrix W belong to the finite field gf (q)；
Operation is extended to the basic matrix W:
When needing to obtain binary quasi-cyclic LDPC code, binary extension is carried out to the basic matrix W: by the basic matrix W
In each non-zero entry be expanded into (q-1) × (q-1) cyclic permutation matrices；Each neutral element in the basic matrix W is expanded
It transforms into as (q-1) × (q-1) null matrix；And then obtain the binary piecemeal check matrix H of (q-1) × (q-1)；From the binary point
Piecemeal submatrix H (γ, ρ) is taken to do check matrix in block check matrix H；The kernel of the matrix H (γ, ρ) forms wanted structure
The LDPC code made；
When needing to obtain polynary quasi-cyclic LDPC code, polynary extension is carried out to the basic matrix W: by the basic matrix W
In each non-zero entry be expanded into (q-1) × (q-1) Generalized Cyclic permutation matrix；By each null element in the basic matrix W
Element is expanded into (q-1) × (q-1) null matrix；And then obtain the polynary piecemeal check matrix H of (q-1) × (q-1)；From described more
Piecemeal submatrix H (γ, ρ) is taken to do check matrix in first piecemeal check matrix H；The kernel of the matrix H (γ, ρ) forms institute
The LDPC code to be constructed.
It is preferably based on the method that described two cyclic subgroups construct the basic matrix W and is divided into following steps:
Described two cyclic subgroups are numbered are as follows: cyclic subgroup 1 and cyclic subgroup 2；
The basic matrix W is configured to the Block Circulant Matrices of c × c, the submatrix of the Block Circulant Matrices is n × n
Circular matrix；
By an element multiplication in all elements and the cyclic subgroup 2 in the cyclic subgroup 1 and subtract one, will
To first row element of the result as a submatrix in the Block Circulant Matrices；
Carry out ring shift right operation: each behavior in the submatrix of the Block Circulant Matrices in addition to the first row is thereon
The ring shift right of a line；The ring shift right of first behavior its last line of the submatrix of the Block Circulant Matrices；
Each of the cyclic subgroup 2 element is multiplied with all elements in the cyclic subgroup 1 respectively, formation
C n ties up row vector, is considered as GF (q) and multiplies c coset in group；
The GF (q) is multiplied into each element in c coset in group and subtracts 1, c n is formed and ties up row vector；
C n dimension row vector is in line, as the first row in certain a line matrix in block form in the basic matrix W
Element；Certain described a line matrix in block form includes c n dimension submatrix；
It is right that the circulation is carried out to each n dimension row vector of the first row in certain a line matrix in block form in the basic matrix W
Operation is moved, obtaining one includes that c n ties up the row matrix in block form for recycling submatrix；
C row matrixs in block form are formed a line the basic matrix W to be formed, wherein each row matrix in block form is above it
Row matrix in block form one block of ring shift right length, i.e. n bit.
(3) beneficial effect
The beneficial effects of the present invention are: the kernel of the constructed check matrix H (γ, ρ) of the present invention gives a code length
For γ (q-1), the advantages of code rate is the quasi-cyclic LDPC code of 1-k/ ρ (q-1), which has both random and traditional structure LDPC code,
Both it ensure that the error bit ability of this yard was suitable with random LDPC code, and the Circulant Block permutation submatrix of the code check matrix
Form ensure that this yard can be realized linear coding and the decoding of quasi- parallel architecture, to reduce this yard of hardware realization complexity
Degree, while the code has biggish minimum intersymbol distance, then the code word constructed has fast convergence, low bit error platform etc. excellent
Point.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
There is attached drawing needed in technical description to be briefly described, it should be apparent that, the accompanying drawings in the following description is only this
Some embodiments of invention for those of ordinary skill in the art without creative efforts, can be with
It obtains other drawings based on these drawings.
Fig. 1 is a kind of building method one implementation for multiplying the LDPC code of cyclic subgroup in group based on finite field according to the present invention
The flow chart of example；
Fig. 2 is a kind of building method one implementation for multiplying the LDPC code of cyclic subgroup in group based on finite field according to the present invention
Two constructed (4080,3079) of example, (8160,7159)
QC-LDPC code utilizes iterative decoding obtained error performance schematic diagram under the conditions of awgn channel.
Specific embodiment
With reference to the accompanying drawings of the specification and embodiment, specific embodiments of the present invention will be described in further detail.With
Lower embodiment is merely to illustrate the present invention, but cannot be used to limit the scope of the invention.
The process for multiplying the LDPC code construction of cyclic subgroup in group based on finite field carries out as follows:
(1) code parameter is determined, and determination will carry out the finite field gf (q) of code construction, based on multiplying following in group in finite field
Ring group determines that one (q-1) × (q-1) basic matrix W, this basic matrix are able to satisfy α power product by the operation in finite field
Line-spacing constraint；Based on finite field gf (q), the extension on two element field or polynary domain is carried out to basic matrix W, obtains (q-1) × (q-
1) piecemeal check matrix H, wherein (q-1) × (q-1) submatrix is cyclic permutation matrices (or Generalized Cyclic permutation matrix) and zero
Matrix；Finally, taking the submatrix of H, final check matrix H (γ, ρ) is obtained, the kernel of this circular matrix provides a code length
For ρ (q-1), code rate is at least quasi- circulation binary (or polynary) LDPC code of (q- γ)/ρ.
(2) wherein, as described in step (1) determine code parameter include according to the requirement of system determine code
The length range of word and the range of code rate, and it is based on this, determine the finite field gf (q) being based in subsequent construction process,
Make the maximum length (q-1) for the code word that basic matrix can construct herein2Greater than the code word size to be constructed, if required
The M constructedc×NcPiecemeal check matrix possesses constant column weight McWith constant row weight Nc, then M is requiredc×Nc≤(q-1)。
(3) wherein, true by the operation in finite field based on cyclic subgroup in group is multiplied in finite field as described in step (1)
Determine the process of basic matrix W, can be carried out according to following step:
Assuming that q-1 is not prime number, it can be decomposed into the product of two relatively prime numbers, q-1=c × n, the then c of primitive element
Power and the integral number power of n times side form two cyclic subgroups, their order is respectively n and c, the friendship of two cyclic subgroups
Collection only contains element 1；
All elements in cyclic subgroup 1 are multiplied with either element in cyclic subgroup 2, form finite field gf (q) and multiply group
A coset, share c coset；
Each element in coset is subtracted 1, lines up the row vector of n dimension, and by its n-1 times circulation of this journey vector sum
The n n dimension row vector of displacement forms a line, and constitutes the cyclic permutation matrices of n dimension；
Aforesaid operations are carried out to each coset, c n dimension cyclic permutation matrices is obtained, is in line, obtains 1
The matrix in block form of × c, each submatrix are that n × cn ties up circular matrix；
Cyclic shift, i.e., each n bit of cyclic shift, by the 1 × c's are carried out by block to the matrix in block form of this 1 × c
Matrix in block form and its c-1 times cyclic shift form a line, and obtain one c × c matrix in block form, and each submatrix is that n dimension circulation is set
Change matrix.
So far, we have obtained (q-1) × (q-1) basic matrix W for the line-spacing constraint that one meets α power product.
(4) wherein, the extension of two element field is carried out to basic matrix W as described in step (1), can be carried out by following operation: to W
In each nonzero element carry out two element field on extension, obtain the binary cycle permutation matrix of (q-1) × (q-1), and replace W
In respective element；Extension on two element field is carried out to each neutral element in W, obtains the null matrix of (q-1) × (q-1), and
The neutral element in W is replaced, thus we obtain one (q-1) × (q-1) piecemeal check matrix H, and each submatrix is (q-1) × (q-
1) cyclic permutation matrices and null matrix.
(5) wherein, the extension in polynary domain is carried out to basic matrix W as described in step (1), can be carried out by following operation: to W
In each nonzero element carry out the extension on polynary domain, obtain the q member Generalized Cyclic permutation matrix of (q-1) × (q-1), and replace
Change the respective element in W；Each neutral element in W is extended, obtains the null matrix of (q-1) × (q-1), and replace in W
Neutral element, thus we obtain (q-1) × (q-1) the piecemeal check matrix H on a q member domain, each submatrix be (q-1) ×
(q-1) Generalized Cyclic permutation matrix and null matrix.
(6) wherein, submatrix H (γ, ρ) is taken to basic matrix piecemeal check matrix H as described in step (1), by following behaviour
Carry out:
About the value of γ and ρ, to make ρ (q-1) close to the length L for the code word of being constructed, and (q- γ)/ρ is less than code
Rate R, and make the order K of check matrix close to (1-R) ρ (q-1)；
Take the γ row ρ column piecemeal submatrix of check matrix as check matrix H (γ, ρ), then the matrix gives a code length
Close or equal to L, code rate is close or equal to the quasi-cyclic LDPC code of R, if being free of zero submatrix, H (γ, ρ) in check matrix
With constant column weight γ row weight ρ, resulting code is regular LDPC code.
With reference to attached drawing 1,2, detailed description multiplies the Algebraic Construction of the LDPC code of cyclic subgroup in group based on finite field.
The construction that present invention construction multiplies the LDPC code of cyclic subgroup in group based on finite field can carry out in accordance with the following steps:
Step 1: determining the parameter of code, mainly determine code length range and code rate required for the channel coding of communication system
Range, and determine therefrom that code construction finite field gf (q), thus can also determine piecemeal check matrix row piecemeal and column point
The value of block.
Step 2: determining that finite field multiplies the cyclic subgroup of group, GF (q) is the finite field determined in step 1, wherein q-1 is not
It is prime number, two relatively prime fac-tors, q-1=c × n can be decomposed into.Enable δ=an, β=ac, then the order of δ and β be respectively
C and n, two following setWith It forms GF (q) and multiplies two cyclic subgroups of group, and have
Step 3: the design of basic matrix is carried out based on subgroup, two subgroups according to obtained in step 2 can be formed as follows
A c × c matrix in block form, each submatrix be one n × n matrix:
Wherein, for 0≤i, the matrix W of each n × n of j < ci,jIt is defined as follows:
The first row of above-mentioned each submatrix is considered asIn an element withIn the products of all elements subtract 1, the circulation of each its lastrow of behavior of submatrix is right
It moves, the ring shift right of first behavior its last line of submatrix.Wherein,In a member
Element withIn all elements product constitute GF (q) a coset for multiplying group.It is same in W
The first row of all submatrixs of a line piecemeal is considered as each element in the c coset for multiplying group to GF (q) and subtracts
One operation.
Based on this, we can see that or provable W have following characteristic:
1) all elements in a row (column) are the different elements in GF (q)；
2) arbitrary two row is different in all a positions (q-1)；
3) one and only one neutral element of every row；
4) all neutral elements are located on leading diagonal.
There is above-mentioned property, can prove that W meets the line-spacing constraint of α power product.
Step 4: the extension of basic matrix, this step is using obtained basic matrix in step 3, and by each non-zero therein
Member is expanded into the cyclic permutation matrices of (q-1) × (q-1), according to the difference of construction dual code and multi-element code, this extended operation
The extension of binary cycle permutation matrix extension and Generalized Multivariate cyclic permutation matrices can be divided into, each neutral element is expanded into
(q-1) × (q-1) null matrix, we obtain the matrix in block form H of following (q-1) × (q-1):
Specific extended operation can carry out as follows:
If we will construct binary LDPC code, by each non-zero entry in W be expanded into (q-1) on two element field ×
(q-1) cyclic permutation matrices, and corresponding element in W is replaced, each null element in W is expanded into (q-1) × (q-1) zero moment
Battle array, and neutral element all in W is replaced, (q-1) × (q-1) the piecemeal check matrix H on a two element field is obtained, submatrix is
(q-1) × (q-1) cyclic permutation matrices and null matrix.
If we will construct multielement LDPC code, by each non-zero entry in W be expanded into (q-1) on polynary domain ×
(q-1) Generalized Cyclic permutation matrix, and corresponding element in W is replaced, each null element in W is expanded into (q-1) × (q-1)
Null matrix, and neutral element all in W is replaced, obtain (q-1) × (q-1) the piecemeal check matrix H on a polynary domain, sub- square
Battle array is the Generalized Cyclic permutation matrix and null matrix of (q-1) × (q-1).
Step 5: taking the piecemeal submatrix of extended matrix to do check matrix, firstly, according to the length for the code word to be constructed
Range and the value range of code rate determine the row piecemeal of piecemeal submatrix and the value γ and ρ of column piecemeal, and determining standard is so that ρ
(q-1) it is close or equal to the code word size L to be constructed, (ρ-γ)/ρ is less than the code rate R of code word, and makes constructed verification
Rank of matrix K is close or equal to (1-R) ρ (q-1)；Then, γ × ρ sub-piecemeal H (γ, ρ) is selected to be used as code from matrix in block form H
Check matrix.
One code length ρ (q-1), code rate are provided by the kernel of check matrix H (γ, ρ)
1-K/ ρ (q-1), minimum intersymbol distance are at least the QC-LDPC code of γ, and the lower bound of minimum range is larger in γ value
When can be relatively tight.If not including complete zero submatrix in H (γ, ρ), then it is γ and ρ that its column overline is again permanent respectively, thus acquired
LDPC code be regular LDPC code.
Applicating example:
Binary LDPC code on GF (q)
1) parameter designing:
Choose q=28As code structural domain.
2) finite field multiplies the determination of cyclic subgroup in group:
Q-1 can be decomposed into 28- 1=255=5 × 51 take c=5, n=51.
3) design of the basic matrix based on subgroup:
According to the construction of above-mentioned basic matrix, we obtain one 255 × 255 basic matrix, and each element in basic matrix is equal
Belong to GF (28)。
4) extension of basic matrix:
Extension on two element field is carried out to acquired basic matrix, obtains 255 × 255 piecemeal check matrix, submatrix is
255 × 255 cyclic permutation matrices and null matrix.
5) take the piecemeal submatrix in extended matrix as check matrix:
γ=4 is taken herein, and zero submatrix on leading diagonal is avoided in ρ=16, obtains one 4 × 16 piecemeal submatrix, son
The cyclic permutation matrices that matrix is 255 × 255, use this piecemeal submatrix as check matrix.The kernel of this matrix provides one
The quasi-cyclic LDPC code of (4080,3079), code rate 0.755, error bit ability curve and corresponding shannon limit such as Fig. 2 institute
Show.
The index of this yard of corresponding basic matrix element primitive element is as follows:
181 136 106 215 197 208 82 70 130 103 174 40 203 202 13 27
254 181 136 106 215 197 208 82 70 130 103 174 40 203 202 13
92 254 181 136 106 215 197 208 82 70 130 103 174 40 203 202
224 92 254 181 136 106 215 197 208 82 70 130 103 174 40 203
γ=4 is taken, the neutral element on leading diagonal is avoided in ρ=32, obtains one 4 × 32 piecemeal submatrix, and submatrix is
255 × 255 cyclic permutation matrices use this piecemeal submatrix as check matrix.The kernel of this matrix provide one (8160,
7159) quasi-cyclic LDPC code, code rate 0.877, error bit ability curve and corresponding shannon limit are as shown in Figure 2.
The index of this yard of corresponding basic matrix primitive element is as follows:
187 91 116 189 14 172 244 129 234 185 24 100 120 224 92 254 181 136 106
75 187 91 116 189 14 172 244 129 234 185 24 100 120 224 92 254 181 136
125 75 187 91 116 189 14 172 244 129 234 185 24 100 120 224 92 254 181
219 125 75 187 91 116 189 14 172 244 129 234 185 24 100 120 224 92 254
215 197 208 82 70 130 103 174 40 203 202 13 27
106 215 197 208 82 70 130 103 174 40 203 202 13
136 106 215 197 208 82 70 130 103 174 40 203 202
181 136 106 215 197 208 82 70 130 103 174 40 203
The above embodiments are only used to illustrate the present invention, rather than limitation of the present invention.Although referring to embodiment to this hair
It is bright to be described in detail, those skilled in the art should understand that, to technical solution of the present invention carry out it is various combination,
Modification or equivalent replacement should all cover and want in right of the invention without departure from the spirit and scope of technical solution of the present invention
It asks in range.
Claims (2)
1. a kind of building method for multiplying the LDPC code of cyclic subgroup in group based on finite field, the method are divided into following steps:
Determine the parameter for the code of being constructed；
Selection will carry out the finite field gf (q) of code construction, guarantee that the code word that basic matrix can construct herein is maximum when GF (q) chooses
Length (q-1)2Greater than the code word size L that will be constructed, construction arranges weight MCWith row weight NCMC×NCWhen piecemeal check matrix, to expire
Sufficient MC+NC≤(q-1)；
Multiply group based on finite field, designs two cyclic subgroups；
Based on described two cyclic subgroups, (q-1) × (q-1), the basic matrix of energy unique identification one kind LDPC code are constructed
Element in W, the basic matrix W belongs to the finite field gf (q)；
Operation is extended to the basic matrix W:
When needing to obtain binary quasi-cyclic LDPC code, binary extension is carried out to the basic matrix W: will be in the basic matrix W
Each non-zero entry is expanded into (q-1) × (q-1) cyclic permutation matrices；Each neutral element in the basic matrix W is extended to
For (q-1) × (q-1) null matrix；And then obtain the binary piecemeal check matrix H of (q-1) × (q-1)；From binary piecemeal school
It tests in matrix H and piecemeal submatrix H (γ, ρ) is taken to do check matrix；What the kernel formation of the matrix H (γ, ρ) to be constructed
LDPC code；
When needing to obtain polynary quasi-cyclic LDPC code, polynary extension is carried out to the basic matrix W: will be in the basic matrix W
Each non-zero entry is expanded into (q-1) × (q-1) Generalized Cyclic permutation matrix；Each neutral element in the basic matrix W is expanded
It transforms into as (q-1) × (q-1) null matrix；And then obtain the polynary piecemeal check matrix H of (q-1) × (q-1)；From described polynary point
Piecemeal submatrix H (γ, ρ) is taken to do check matrix in block check matrix H；The kernel of the matrix H (γ, ρ) forms wanted structure
The LDPC code made.
2. a kind of building method for multiplying the LDPC code of cyclic subgroup in group based on finite field according to claim 1, special
Sign is that the method for constructing the basic matrix W based on described two cyclic subgroups is divided into following steps:
Described two cyclic subgroups are numbered are as follows: cyclic subgroup 1 and cyclic subgroup 2；
The basic matrix W is configured to the Block Circulant Matrices of c × c, the submatrix of the Block Circulant Matrices is following for n × n
Ring matrix；
By an element multiplication in all elements and the cyclic subgroup 2 in the cyclic subgroup 1 and subtract one, by what is obtained
As a result the first row element as a submatrix in the Block Circulant Matrices；
Carry out ring shift right operation: by all elements in the cyclic subgroup 1 and an element phase in the cyclic subgroup 2
Result composition finite field gf (q) multiplied multiplies a coset in group；The first row will be removed in the submatrix of the Block Circulant Matrices
Ring shift right of every a line as its lastrow in addition；First behavior of the submatrix of the Block Circulant Matrices its last
Capable ring shift right；
Each of the cyclic subgroup 2 element is multiplied with all elements in the cyclic subgroup 1 respectively, c n of formation
Row vector is tieed up, GF (q) is considered as and multiplies c coset in group；
The GF (q) is multiplied into each element in c coset in group and subtracts 1, c n is formed and ties up row vector；
C n dimension row vector is in line, the member as the first row in certain a line matrix in block form in the basic matrix W
Element；Certain described a line matrix in block form includes c n dimension submatrix；
The ring shift right behaviour is carried out to each n dimension row vector of the first row in certain a line matrix in block form in the basic matrix W
Make, obtaining one includes that c n ties up the row matrix in block form for recycling submatrix；
The c row matrixs in block form are formed a line to form basic matrix W, wherein each row matrix in block form is the row point above it
The length of one block of block matrix ring shift right, i.e. n bit.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201410281293.5A CN105227190B (en) | 2014-06-20 | 2014-06-20 | A kind of building method multiplying the LDPC code of cyclic subgroup in group based on finite field |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201410281293.5A CN105227190B (en) | 2014-06-20 | 2014-06-20 | A kind of building method multiplying the LDPC code of cyclic subgroup in group based on finite field |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN105227190A CN105227190A (en) | 2016-01-06 |
| CN105227190B true CN105227190B (en) | 2019-05-14 |
Family
ID=54995932
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201410281293.5A Active CN105227190B (en) | 2014-06-20 | 2014-06-20 | A kind of building method multiplying the LDPC code of cyclic subgroup in group based on finite field |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN105227190B (en) |
Families Citing this family (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105915231B (en) * | 2016-04-07 | 2019-03-26 | 西安电子科技大学 | The long constraint convolutional code building method of superposition is repeated based on multiplying property |
| US10447303B2 (en) * | 2017-12-20 | 2019-10-15 | Qualcomm Incorporated | Low-density parity check (LDPC) incremental parity-check matrix rotation |
| CN111198673B (en) * | 2018-11-19 | 2022-07-12 | 北京智谱微科技有限责任公司 | Word length adjusting method, device, equipment and storage medium |
Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101247202A (en) * | 2006-10-18 | 2008-08-20 | 北京凌讯华业科技有限公司 | Method for generating ldpc code for a LDPC based TDS-OFDM system |
-
2014
- 2014-06-20 CN CN201410281293.5A patent/CN105227190B/en active Active
Patent Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101247202A (en) * | 2006-10-18 | 2008-08-20 | 北京凌讯华业科技有限公司 | Method for generating ldpc code for a LDPC based TDS-OFDM system |
Non-Patent Citations (4)
| Title |
|---|
| A Unified Approach to the Construction of Binary and Nonbinary Quasi-Cyclic LDPC Codes Based on Finite Fields;Shumei Song 等;《IEEE TRANSACTIONS ON COMMUNICATIONS》;20090131;第57卷(第1期);第84-93页 |
| Construction of Quasi-Cyclic LDPC Codes for AWGN and Binary Erasure Channels A Finite Field Approach;Lan Lan 等;《IEEE TRANSACTIONS ON INFORMATION THEORY》;20070731;第53卷(第7期);第2429-2458页 |
| 光通信中一种基于有限域循环子群的QC-LDPC码构造方法;袁建国 等;《半导体光电》;20131231;第36卷(第6期);第1017-1019、1026页 |
| 光通信系统中基于伽罗华域乘群的QC-LDPC码的一种新颖构造方法;袁建国 等;《光电子·激光》;20120731;第23卷(第7期);第1304-1308页 |
Also Published As
| Publication number | Publication date |
|---|---|
| CN105227190A (en) | 2016-01-06 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN105207680B (en) | A kind of building method of the quasi-cyclic LDPC code based on finite field primitive element | |
| Jin et al. | New MDS self-dual codes from generalized Reed—Solomon codes | |
| Jin et al. | A construction of new quantum MDS codes | |
| CN105227190B (en) | A kind of building method multiplying the LDPC code of cyclic subgroup in group based on finite field | |
| CN104168030A (en) | LDPC code construction method based on two generators of primitive domain cyclic group | |
| CN103795424B (en) | A kind of communication means based on QC LDPC | |
| CN102932007A (en) | Highly parallel encoder and method for encoding QC-LDPC (quasi-cyclic low-density parity-check) codes for deep space communication | |
| Meyerovitch et al. | On independence and entropy for high-dimensional isotropic subshifts | |
| Zhang | Type‐II quasi‐cyclic low‐density parity‐check codes from Sidon sequences | |
| Li et al. | A new computational approach for determining rate regions and optimal codes for coded networks | |
| Shi et al. | Optimal p-ary codes from one-weight and two-weight codes over | |
| Han et al. | CONSTRUCTION OF SELF-DUAL CODES OVER F 2+ uF 2 | |
| CN105207681B (en) | It is a kind of to multiply the LDPC code building method that cyclic subgroup in group generates member based on finite field | |
| CN103259544A (en) | Quasi-cyclic LDPC serial encoder in DTMB of shared storage mechanism | |
| CN102857238A (en) | LDPC (Low Density Parity Check) encoder and encoding method based on summation array in deep space communication | |
| Kruglik et al. | On one generalization of LRC codes with availability | |
| Venkaiah et al. | Quasi-cyclic codes over F13 and enumeration of defining polynomials | |
| CN105306072A (en) | LDPC construction method based on primitive field cyclic group generation element set | |
| CN108494411B (en) | Construction method of multi-system LDPC code check matrix | |
| Baldi et al. | On the generator matrix of array LDPC codes | |
| Jahangir et al. | Design of novel quaternary encoders and decoders | |
| Cheng et al. | On the girth of the bipartite graph D (k, q) | |
| CN104202059B (en) | Deterministic design method for structuring QC-LDPC (quasi-cyclic low-density parity check) codes 12 in girth | |
| CN103268214A (en) | Quasi-cyclic matrix high-speed multiplier in deep space communication based on lookup table | |
| Pilipchuk et al. | Decoding multicomponent codes based on rank subcodes |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |