CN108134610A - The building method of special construction protograph QC-LDPC codes based on pascal's triangle - Google Patents
The building method of special construction protograph QC-LDPC codes based on pascal's triangle Download PDFInfo
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
- H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
- H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
- H03M13/11—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits using multiple parity bits
- H03M13/1102—Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
- H03M13/1148—Structural properties of the code parity-check or generator matrix
- H03M13/116—Quasi-cyclic LDPC [QC-LDPC] codes, i.e. the parity-check matrix being composed of permutation or circulant sub-matrices
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Abstract
The present invention relates to the building methods of the special construction protograph QC LDPC codes based on pascal's triangle, belong to channel coding studying technological domain.This method constructs basic matrix using pascal's triangle, specifically includes following steps：Build the weight matrix of protograph, i.e. basic matrix Hbase；It is rotated counterclockwise using pascal's triangle structure, obtains s-matrix；Element in s-matrix is filled into the weight matrix H of protograph by rulebaseObtain the basic matrix H of protograph；Check matrix is obtained with null matrix and unit matrix extension protograph basic matrix H, the iteratively faster encryption algorithm of the code word is given according to the structure of H.This basic matrix has accurate double diagonal arrangements, avoids Fourth Ring and can realize fast coding, reduce the complexity of coding, iterative decoding has excellent performance no manifest error flat bed.
Description
Technical field
The invention belongs to channel coding studying technological domains, are related to a kind of special construction protograph based on pascal's triangle
The building method of QC-LDPC codes.
Background technology
With the development of science and technology, the information-based main trend for becoming current era development.In this information-based tide, lead to
Letter technology plays the effect to become more and more important.The key problem of Communication System Design is that how to ensure the rate of information throughput
While reduce information transmission error as far as possible.Information age continues to develop, Novel Communication business and information service constantly into
Innovation is gone, user further promotes the development of the communication technology, also push to the requirements at the higher level of communication quality and transmission rate
The fast development of channel coding technology.Quasi-circulating low-density parity check (quasi-cyclic low-density
Parity-check, QC-LDPC) code, cause concern due to it has the decoding performance for approaching shannon limit.QC-LDPC codes are
One subclass of LDPC code, 2016, LDPC code was chosen as the encoding scheme of 5G, and LDPC code is made to have shone vigor again.
Due to the check matrix of LDPC code have it is openness, LDPC code decoding when it is easy to implement.But LDPC code
Generator matrix does not have usually openness, and the position of nonzero element is random alignment in matrix and density is larger, and encoder needs
All nonzero elements of generator matrix are stored, this causes the encoder complexity of LDPC code higher.To solve these problems, both at home and abroad
Many scholars propose it is a variety of can fast coding method.It is existing construction LDPC code method be generally divided into random configuration and
Structured configurations.Random configuration method searches the position of nonzero element in matrix according to specific design criteria and Tanner figures
It puts, more representational two：Gallager is constructed and Mackay constructions.2001, Hu Xiaoyu etc. were in order to as much as possible
Girth in increase Tanner figures proposes progressive edge and increases (PEG) algorithm, it is contemplated that the degree of communication of check matrix has also been proposed
ACE structured approaches.Although random configuration can flexibly choose code check and code length, and can obtain good error performance.But
Since it is obtained by computer search, cataloged procedure is more complicated, and is unfavorable for the realization of hardware.In order to reduce
, there are structured configurations in the complexity of coding and decoding.This kind of building method utilizes the side such as Combinational Mathematics, finite aggregate and graph theory
Method constructs the check matrix with cycle or quasi- cyclic.Woods in 2003 relax et al. based in galois field multiply group,
The thought of group and subgroup is added to propose the building method of a large amount of structuring QC-LDPC codes, and in euclidean geometry and projective geometry
On the basis of propose the building methods of a few type of structured QC-LDPC codes；The QC-LDPC codes that these method constructs come out have certain
Quasi- cycle characteristics, therefore, there is preferable convergence rate and good error-correcting performance in decoding, while can save a large amount of
Memory space, convenient for hardware realization, but be constrained to specific Algebraic Structure and cause the selection of code length and code check not clever enough
It is living., there is combination construction method in encoder complexity and code parameters selection in order to balance, combination construction method be utilized algebraical sum with
The advantages of machine structured approach, basic thought are in the case where keeping code part minor structure, then to minor structure in particular constraints
Under the conditions of random permutation, be finally completed construction.Combination construction method is mainly used for constructing quasi-cyclic low-density parity check codes at present,
It is protograph LDPC (Protograph that combination construction method, which is mainly used for constructing one of quasi-cyclic LDPC code, example, at present
LDPC construction).Protograph LDPC code causes both at home and abroad because having the advantages that high-speed coding, low decoding platform, low decoding threshold
Some scholars' note that it was put forward earliest by J.Thorpe in 2003, but the code of its construction has higher mistake to put down
Layer.Divsalar D propose the LDPC code of the low rate with protograph structure, realize with low error floor and decoding
The advantages of thresholding is close to shannon limit.It is excellent according to the high-speed coding of protograph QC-LDPC codes, low bit error platform and low decoding threshold etc.
Point does in-depth study to it and is of great importance.
The extended method of LDPC code based on protograph is computer random search method and PEG (progressive mostly
Edge growth, PEG) method.But computer random search method search time is longer, and PEG algorithm coding complexities are too high.
It is at least partly based on the method construct protograph QC-LDPC codes of Combinational Mathematics and respectively has limitation.Protograph QC- based on the ordered series of numbers that spreads out greatly
LDPC code fills basic matrix using the ordered series of numbers that spreads out greatly, but the codeword coding complexity constructed is higher, is unfavorable for hardware realization.It is based on
The QC-LDPC codes of BIBD and protograph, code length are constrained, it is impossible to flexibly selection.
Invention content
In view of this, the purpose of the present invention is to provide a kind of special construction protograph QC-LDPC based on pascal's triangle
The building method of code reduces the interference of signal in the channel by the good QC-LDPC codes of structural behavior, improves the reliable of transmission
Property.
In order to achieve the above objectives, the present invention provides following technical solution：
The building method of special construction protograph QC-LDPC codes based on pascal's triangle, this method comprise the following steps：
S1：Construct the weight basic matrix of protograph；
S2：The basic matrix obtained using pascal's triangle filling weight basic matrix；
S3：Basic matrix is extended to obtain the check matrix of protograph QC-LDPC codes, the coding for analyzing check matrix is answered
Miscellaneous degree；
S4：Ask for the effect code vector of the check matrix of QC-LDPC codes；
S5：The iterative decoding performance of check matrix is verified.
Further, step S2 is specifically comprised the following steps：
S21：Assuming that the weight basic matrix of protograph is Hbase；
S22：Using pascal's triangle structure to Hbase45 degree of rotation counterclockwise is carried out, and deletes postrotational the first row and the
The element of one row, the element value in other positions be one's own profession, element and this row of previous column, lastrow the sum of element, obtain
Obtain s-matrix；
S23：By the element in s-matrix according to HbaseMatrix column is filled, suitable by matrix in first row filling element
Sequence is filled, and the lower target row number of next line filling element is identical with the row number of previous column row filling element subscript, secondary series first trip
The subscript of filling element is bigger by 1 than the subscript of the last one element of first row last column, and thus completing filling obtains basic matrix.
Further, step 3 is specially：
S31：Basic matrix is extended with null matrix and unit matrix to obtain the check matrix H of QC-LDPC codes；
S32：It verifies in the check matrix H of QC-LDPC codes without the becate that length is 4, it is assumed that the position at Fourth Ring in check matrix H
(a, c) is set to, (a, d), (b, c), (b, d), corresponding Fourth Ring sequence is expressed as (pa,c,pa,d,pb,c,pb,d), and it is full
Foot
(pa,c-pa,d)+(pb,c-pb,d)≠0modp
Then without the becate that length is 4 in check matrix H.
Further, step S4 is specifically comprised the following steps：
S41：If effect code vector c=[s1 s2 … sk p1 p2 p3], wherein [s1 s2 … sk] it is the letter that length is k
Breath vector, [p1 p2 p3] for code verification vector, according to the standard principle formula of encryption algorithm
HcT=0
It is calculated；
S42：The form of system of linear equations, and abbreviation are rewritten as to the standard principle formula of encryption algorithm：
Wherein,1≤j≤k, sjRepresent j-th of letter
Breath vector, H1,jRepresent j-th of element of the first row in check matrix H, H2,jRepresent j-th of element of the second row in check matrix H,
H3,jRepresent j-th of element of the third line in check matrix H, X1=Φ1+Φ2, X2=Φ3+Φ4, Φ1、Φ2、Φ3、Φ4Respectively by
Basic matrix is obtained by 1,2,3,4 cyclic shift；
S43：Effect code vector is obtained by the elimination
Wherein, I is unit vector.
Further, step S5 is specially：
S51：It is modulated using the binary phase shift keying under additive white noise Gaussian channel, builds simulated environment；
S52：It is 50 times, spreading factor N=200 to set maximum iteration, code check 0.5；
S53：According to the iterative decoding performance of simulation results show check matrix.
The beneficial effects of the present invention are：It is proposed that a kind of construction code length can the present invention is based on the pascal's triangle in Combinational Mathematics
Flexibly selection and can fast coding protograph QC-LDPC codes, this basic matrix has accurate pair of diagonal arrangements, overcomes double diagonal line
Low code weight problem, avoids Fourth Ring and can realize fast coding, reduce the complexity of coding, be conducive to hardware caused by structure
It realizes, iterative decoding has excellent performance no manifest error flat bed, and decoding performance is good.Suitable for the neck of digital video broadcasting
Domain.
Description of the drawings
In order to make the purpose of the present invention, technical solution and advantageous effect clearer, the present invention provides drawings described below and carries out
Explanation：
Fig. 1 is flow chart of the present invention；
Fig. 2 is a protograph of the embodiment of the present invention；
Fig. 3 is the schematic diagram after protograph of the embodiment of the present invention replicates 3 times；
Fig. 4 is the derivation figure of protograph of the embodiment of the present invention；
Fig. 5 is the structure chart of pascal's triangle of the embodiment of the present invention；
Fig. 6 is the protograph of construction of the embodiment of the present invention；
Fig. 7 is protograph QC-LDPC codes proposed by the present invention and the decoding performance comparison diagram of other patterns.
Specific embodiment
Below in conjunction with attached drawing, the preferred embodiment of the present invention is described in detail.
The present invention is the building method of the special construction protograph QC-LDPC codes based on pascal's triangle, specifically comprising as follows
Step：
Step 1：Construct the weight basic matrix of protograph；
Step 2：The basic matrix obtained using pascal's triangle filling；
Step 3：Basic matrix is extended to obtain check matrix；
Step 4：Verify that the building method without becate, analyzes its encoder complexity；
Step 5：Verify its iterative decoding performance；
The protograph of the present embodiment construction is as shown in Figure 1；
Protograph defines：One simple protograph G=(B, C, E), the set of comprising variable node (bit node, BN)
B, the set C of check-node (check nodes, CN) and the set E on side.Each edge e ∈ E one variable node of connection:be∈V
With a check-node:ce∈C.Allow have heavy side in protograph.A simple protograph as shown in Figure 1, the figure contain 4
Variable node (b0,b1,b2,b3), 3 check-node (c0,c1,c2) and 8 sides.
Shown in the basic matrix such as formula (1) that protograph LDPC code can be obtained by the protograph of Fig. 1：
By to Fig. 1 replicate-replace obtaining widened protograph as shown in Figures 2 and 3：
Fig. 2 replicates protograph n times (taking N=3), and shown in check matrix such as formula (2), wherein I is the unit of 3 × 3 sizes
Matrix, 0 is the null matrix of 3 × 3 sizes.
Fig. 3 is derived from shown in the basic matrix such as formula (3) of figure.
Wherein, Mi,jFor 3 × 3 cyclic permutation matrices (0<i<3,0<j<4), 0 is 3 × 3 null matrix.In permutation matrix
Hcopy-permuteIn, shifting two is recycled to the right for lastrow element per row element, so we are it is only necessary to know that each permutation matrix
Mi,jThe first row.This property is equally applicable to the situation of high-order derivation.
Pascal's triangle is referred to as arithmetical triangle again, after its every a line can regard 11 power mistake one as,
According to result obtained by the operation rule that ten not-carrys is met to be added by from left to right be ranked sequentially gained, pascal's triangle has been at present
It is used in the applications such as flip football, Path selection.The structure of pascal's triangle is simple, as shown in figure 4, being a kind of ripe by everybody institute
The triangle number table known.
Figure 4, it is seen that pascal's triangle has such a notable feature：Often go in addition to two elements of initial and end
Except, the element in other positions is equal to the sum of two numbers being positioned above.If make pascal's triangle along direction counterclockwise
45 degree of rotation can obtain such as the matrix of formula (4).
The matrix S obtained after pascal's triangle rotation is in addition to the first row and the first column element, the element value in other positions
Be one's own profession, element and this row of previous column, lastrow the sum of element, this feature phase with the above-mentioned pascal's triangle being previously mentioned
It is corresponding.If this structure type of pascal's triangle is applied in the check matrix of QC-LDPC codes, storage verification square is only needed
The first row and the first column element of battle array, the element in other positions can be obtained by simple additional calculation, be conducive in this way
Save a large amount of memory space.
Below by specific embodiment, the present invention is described in detail：
Realize the present invention the special construction protograph QC-LDPC codes based on pascal's triangle building method, it including with
Lower step：
Step 1 is：Build the weight matrix of protograph, i.e. basic matrix Hbase。
Shown in the basic matrix such as formula (5) that protograph can be obtained from Fig. 5：
Cannot exist when extending fundamental matrix and weigh side, and matrix HbaseComprising element 0,1,2, wherein element 2 is protograph
Heavy side.In order to eliminate weight side, Modulo-two operation has been carried out to it in extension.
By HbaseIn the null matrix 0 that is substituted for of element " 0 ", element " r " is substituted for a permutation matrixes of r (r is not equal to 0)
Mould 2 adds.The permutation matrix P used hereini,jThe ring shift right position q of unit matrix for N × Ni,jIt is secondary to obtain, q thereini,j
Element of the value in the matrix P (matrix that matrix S removal the first row first rows are formed) obtained based on pascal's triangle.
Step 2 is：It is rotated counterclockwise using pascal's triangle structure, obtains s-matrix；By the element in s-matrix by rule
Then it is filled into the weight matrix H of protographbaseObtain the basic matrix of protograph；With null matrix and unit matrix extension protograph base
Matrix is obtained shown in the check matrix H such as formula (6) of protograph QC-LDPC codes that the present invention constructs.
P3,3Unit matrix ring shift right q for N × N3,3Position obtains, and Fourth Ring is not present in ultimately constructed H out.Extension
The dimension of check matrix H afterwards is 3N × 6N (N is not less than the maximum value in P matrixes).
Step 3 is：Prove the check matrix of protograph QC-LDPC codes of the invention constructed without becate.
Becate present in Tanner figures can seriously affect the performance of LDPC code.The repetition superposition of information is precisely due to becate
And generate, information is sent out from a certain node, and origin node is returned to by the transmission in becate.Then becate can lead to each section
The autonomous behavior of loss of learning statistics that point receives, in turn results in the increase of bit error rate.And LDPC code cannot in decoding
Caused by the appearance of Fast Convergent, i.e. error floor is also due to becate.So herein in the verification of design protograph LDPC code
During matrix, the becate that length is 4 is eliminated.
In check matrix H, if four ring positions are respectively (a, c), (a, d), (b, c), (b, d), then its corresponding Fourth Ring
Sequence is expressed as (pa,c,pa,d,pb,c,pb,d).Theorem by the necessary and sufficient condition that Fourth Ring is not present, can obtain：
(pa,c-pa,d)+(pb,c-pb,d)≠0modp (7)
For the element in the matrix form (4) with pascal's triangle structure, if a>b,c>D, then：
pa,c-pa,d=pa,c-pa,c-1+pa,c-1-pa,c-2+pa,c-2+…+pa,d+1+pa,d+1-pa,d=
pa-1,c+pa-1,c-1+…+pa-1,d+1≥pb,c+pb,c-1+…+pb,d+1＞ pb,c-pb,d (8)
(pa,c-pa,d)+(pb,c-pb,d) ＞ 0 (9)
Obviously, (7) formula all sets up arbitrary element in P, therefore the protograph QC- based on pascal's triangle that the present invention constructs
There is no the becates that length is four in the check matrix of LDPC code.
Step 4 is：Analyze the encoder complexity of the QC-LDPC codes of construction.The present invention construct based on pascal's triangle structure
The LDPC code of protograph is referred to as YH-YMT-QC-LDPC codes, have can fast coding characteristic.In order to verify its quick braiding
Code characteristic, if code vector c=[s1 s2 … sk p1 p2 p3], wherein, [s1 s2 … sk] be code information bit vector, [p1
p2 p3] be code verification bit vector.According to the standard principle Hc of encryption algorithmT=0 can obtain
Each element of protograph basic matrix is extended to Φ, basic matrix obtains Φ by 1,2,3,4 cyclic shift1、
Φ2、Φ3、Φ4。
Above formula is rewritten into the form of system of linear equations：
Wherein,1≤j≤k, sjRepresent j-th of letter
Breath vector, H1,jRepresent j-th of element of the first row in check matrix H, H2,jRepresent j-th of element of the second row in check matrix H,
H3,jRepresent j-th of element of the third line in check matrix H, X1=Φ1+Φ2, X2=Φ3+Φ4。
Can be by (11) formula abbreviation
Code vector can must be verified by the elimination
Formula (13)~formula (15) is the iteratively faster encryption algorithm of YH-YMT-QC-LDPC codes proposed by the present invention, when
When knowing information code vector sum check matrix, can code vector be obtained by formula (13)~formula (15)：C=[s1 s2 … sk p1 p2
p3].By above verification, it can show that YH-YMT-QC-LDPC codes proposed by the present invention have fast coding characteristic, only pass through
Code vector can be obtained in system of linear equations.And its approximate Double diagonal structure significantly reduces encoder complexity.
Step 5 is further：Error bit ability is analyzed
The performance of irregular YH-YMT-QC-LDPC codes that the present invention is constructed will be analyzed by testing below, emulate ring
Border is modulated using the binary phase shift keying (BPSK) under additive white noise Gauss (AWGN) channel, confidence spread (BP)
Iterative decoding, maximum iteration take 50 times.Based on protograph as shown in fig. 6, spreading factor is selected as N=200, due to basic matrix
The code check of corresponding pattern is 0.5, and for code check still for 0.5, ultimately constructed code length is 1200 based on pascal's triangle after extension
Protograph QC-LDPC code abbreviation YH-YMT-QC-LDPC (1200,600).From figure 7 it can be seen that in BER=10-6When, the present invention
YH-YMT-QC-LDPC (1200,600) codes constructed are encoded only than identical code length based on PEG-QC-LDPC (1200,600) code
Gain improves about 0.2dB, and the net coding gain based on mackay-QC-LDPC (1224,612) code longer than code length improves about
0.6dB, standard QC-LDPC (1752,878) code net coding gain based on GPS system longer than code length improve a 0.3dB left sides
The right side, and work as BER close to 10-7When inerrancy flat bed phenomenon.
Finally illustrate, preferred embodiment above is only to illustrate the technical solution of invention and unrestricted, although passing through
Above preferred embodiment is described in detail the present invention, however, those skilled in the art should understand that, can be in shape
Various changes are made in formula and to it in details, without departing from claims of the present invention limited range.
Claims (5)
1. the building method of the special construction protograph QC-LDPC codes based on pascal's triangle, it is characterised in that：This method includes such as
Lower step：
S1：Construct the weight basic matrix of protograph；
S2：The basic matrix obtained using pascal's triangle filling weight basic matrix；
S3：Basic matrix is extended to obtain the check matrix of protograph QC-LDPC codes, the coding for analyzing check matrix is complicated
Degree；
S4：Ask for the effect code vector of the check matrix of QC-LDPC codes；
S5：The iterative decoding performance of check matrix is verified.
2. the building method of the special construction protograph QC-LDPC codes according to claim 1 based on pascal's triangle, special
Sign is：Step S2 is specifically comprised the following steps：
S21：Assuming that the weight basic matrix of protograph is Hbase；
S22：Using pascal's triangle structure to HbaseCarry out 45 degree of rotation, and delete postrotational the first row and first row counterclockwise
Element, the element value in other positions be one's own profession, element and this row of previous column, lastrow the sum of element, acquisition S squares
Battle array；
S23：By the element in s-matrix according to HbaseMatrix column is filled, and in first row filling element, is filled out by sequence of matrices
It fills, the lower target row number of next line filling element is identical with the row number of previous column row filling element subscript, secondary series first trip filling
The subscript of element is bigger by 1 than the subscript of the last one element of first row last column, thus completes filling and obtains basic matrix.
3. the building method of the special construction protograph QC-LDPC codes according to claim 2 based on pascal's triangle, special
Sign is：Step 3 is specially：
S31：Basic matrix is extended with null matrix and unit matrix to obtain the check matrix H of QC-LDPC codes；
S32：It verifies in the check matrix H of QC-LDPC codes without the becate that length is 4, it is assumed that the position at Fourth Ring is in check matrix H
(a, c), (a, d), (b, c), (b, d), corresponding Fourth Ring sequence are expressed as (pa,c,pa,d,pb,c,pb,d), and meet
(pa,c-pa,d)+(pb,c-pb,d)≠0modp
Then without the becate that length is 4 in check matrix H.
4. the building method of the special construction protograph QC-LDPC codes according to claim 3 based on pascal's triangle, special
Sign is：Step S4 is specifically comprised the following steps：
S41：If effect code vector c=[s1 s2…sk p1 p2 p3], wherein [s1 s2…sk] it is the information vector that length is k,
[p1 p2 p3] for code verification vector, according to the standard principle formula of encryption algorithm
HcT=0
It is calculated；
S42：The form of system of linear equations, and abbreviation are rewritten as to the standard principle formula of encryption algorithm：
Wherein,1≤j≤k, sjRepresent j-th of information to
Amount, H1,jRepresent j-th of element of the first row in check matrix H, H2,jRepresent j-th of element of the second row in check matrix H, H3,jTable
Show j-th of element of the third line, X in check matrix H1=Φ1+Φ2, X2=Φ3+Φ4, Φ1、Φ2、Φ3、Φ4Respectively by basic matrix
It is obtained by 1,2,3,4 cyclic shift；
S43：Effect code vector is obtained by the elimination
Wherein, I is unit vector.
5. the building method of the special construction protograph QC-LDPC codes according to claim 4 based on pascal's triangle, special
Sign is：Step S5 is specially：
S51：It is modulated using the binary phase shift keying under additive white noise Gaussian channel, builds simulated environment；
S52：It is 50 times, spreading factor N=200 to set maximum iteration, code check 0.5；
S53：According to the iterative decoding performance of simulation results show check matrix.
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| CN109450453A (en) * | 2018-11-29 | 2019-03-08 | 中国科学院计算技术研究所 | A method of construction PTG-LDPC code |
| CN109802689A (en) * | 2019-03-13 | 2019-05-24 | 重庆邮电大学 | A kind of QC-LDPC code constructing method that the girth based on Hoey sequence is 8 |
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| CN111934692A (en) * | 2020-08-20 | 2020-11-13 | 西安电子科技大学 | Quantum LDPC code construction method based on BIBD variable code rate |
| CN113055026A (en) * | 2021-03-16 | 2021-06-29 | 重庆邮电大学 | Construction method of LDPC code check matrix based on original pattern suitable for deep space communication |
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