CN1564465A - Regular (3.d) low density parity code coding method - Google Patents

Abstract

The method designs structure of sparse parity check matrix H. given information sequence d, based on H cT=[HpHd] [p d]=Hpp+ Hdd=0, solving check bit sequence p, thus, solving decoding word sequence c=[p/d]. Ring shifting right first row of parity check matrix H creates each low below. Information bit matrix Hd is constituted by arranging a group of orthogonal Q- matrix properly. Structure of Q- matrix is non-diagonal unit square matrix. Sub matrix Q1 is searched out by empress algorithm. Q1 is expressed in vector. Value of each element in Q- vector expresses number of row of nonzero element in this column of the Q- matrix.

Description

A kind of rule (3, d c) low density parity check code encoding method

Technical field

The present invention relates to a kind of rule (3, d _c) low density parity check code encoding method.Low-density checksum (LDPC) sign indicating number is the new sign indicating number class that information theory field of channel coding in recent years occurs.Because LDPC sign indicating number iterative decoding algorithm has the premium properties near shannon limit, and its decoding complex degree makes it have huge use value in field of channel coding far below Turbo code.Studies show that the LDPC sign indicating number will be applied in the error control protection of a plurality of communications fields such as high speed fibre Netcom letter, broadband radio multi-media communication, IPv6 internet communication, space communication, Computer Storage and transmission system.

Background technology

LDPC sign indicating number and iterative decoding algorithm thereof 1963 are invented by Gallager, Gallager has only provided (20,3,4) construction algorithm of the sparse parity matrix of LDPC sign indicating number ad hoc structure, do not provide the building method of the sparse parity matrix of arbitrary structures, do not propose the encoder design method yet.The LDPC sign indicating number had not been subject to people's attention at that time, and up to the nineties later stage, Spielman et al. and MacKay et al. have been discovered and developed the LDPC sign indicating number once again, and appearing again and prosperity of LDPC sign indicating number just arranged.Nearest to the improvement of LDPC code structure design and the realization of decoding algorithm hardware, and to the effort that it is further exploited potentialities its simplification aspect is done, the LDPC sign indicating number can both matched in excellence or beauty with Turbo code aspect performance and the complexity, even surmount Turbo code.At present, abroad the patented technology of existing Turbo code is multinomial, and does not still have the patented technology appearance of relevant LDPC sign indicating number both at home and abroad.

Since the LDPC sign indicating number was appeared again, the LDPC sign indicating number that good LDPC sign indicating number, particularly block length is very long was mainly produced by computer search.The storage of large-scale sparse parity matrix and quick generating algorithm, and the design problem of low complex degree LDPC code coder are to hinder the bottleneck problem that the LDPC sign indicating number moves towards application always.The present invention propose a kind of practicality rule (3, d _c) (wherein every row of 3 expression parity matrixs have only three 1, d to LDPC Exploit of Designing Encoder method _cFor greater than 3 positive integer, it represents that every row has d _cIndividual 1), for the realization of the encoder low complex degree of LDPC sign indicating number provides a selection scheme, so that quicken the process that the LDPC sign indicating number move towards application.

Summary of the invention

The objective of the invention is to propose the attainable rule of a kind of low complex degree (3, d _c) LDPC sign indicating number encryption algorithm.The LDPC sign indicating number is defined as the kernel of sparse parity check matrix H, and Hc is promptly arranged ^T=0, c is a code word.Rule (3, d _c) the H matrix of LDPC sign indicating number correspondence, every row have only three 1, and every row has d _cIndividual 1.Designing the encoder key is the structure of design H matrix, and the superiority and inferiority of H matrix structure can produce the influence of three aspects, the one, and the performance of iterative decoding, the 2nd, the complexity of decoder, the 3rd, the complexity of encoder.The present invention solves the formation of H matrix emphatically.

Technical scheme of the present invention: rule (3, d _c) low density parity check code encoding method, mainly be the structure of the sparse parity check matrix H of design, to an information sequence d who gives, according to ${\mathrm{Hc}}^T=\left[\begin{array}{cc}{H}^p& H^d\end{array}\right]\left[\begin{array}{c}p\\ d\end{array}\right]=H^{p}p+H^{d}d=0$ Find the solution check digit sequence p, find the solution codeword sequence c=[pd thus], the present invention is decomposed into the check digit matrix H with matrix H ^pWith information bit matrix H ^d, H ^pMatrix can produce following each row successively by its first row ring shift right; H ^dMatrix is made of through suitably arranging one group of quadrature Q-matrix, the structure of Q-matrix is non-to the angular unit square formation, its every row, every row, every diagonal all have only one 1, make submatrix by the Q-matrix, and the permutation and combination of Q-matrix is constructed various forms of sparse parity check matrix H.

Described coding method, the structure of one group quadrature Q-matrix are every row, every row, every diagonal all has only n * n rank of one 1 non-to the angular unit square formation, is to go out a submatrix Q with queen's algorithm search ₁, represent Q with vector form ₁, the corresponding relation of Q-vector and Q-matrix is: the residing line number in position of the nonzero element of these row of value representation matrix of each element of vector, by sequential counting from top to bottom; To vector Q ₁Cyclic shift 2t-2 time, t represents H ^dEach row of matrix contains the number of Q-matrix, obtains one group of orthogonal matrix Q ₁, Q ₂..., Q _2t-1

Described coding method, its H ^dOrthogonal matrix Q in the matrix ₁, Q ₂..., Q _2t-1Arrange as follows:

$H^d=\left[\begin{array}{cccc}{Q}_1& Q_1& \·\·\·& Q_1\\ Q_1& Q_2& \·\·\·& Q_{t-1}\\ Q_1& Q_t& \·\·\·& Q_{2t-2}\end{array}\right],$

Wherein first row and first row are placed Q ₁Matrix, all the other 2t-2 Q-matrix Q ₂..., Q _2t-1Be successively placed on remaining position.

Described coding method, the check digit matrix H ^pBe made of four matrixs in block form, wherein diagonal matrix two two equates, is respectively H ₁ ^pAnd H ₂ ^p, promptly $H^p=\left[\begin{array}{cc}{H}_1^p& H_2^p\\ H_2^p& H_1^p\end{array}\right],H^p=\left[\begin{array}{cc}{H}_1^p& H_2^p\\ H_2^p& H_1^p\end{array}\right]$ Middle matrix H ₁ ^pStructure be biconjugate angle lower triangular matrix, matrix H ₂ ^pStructure be that the unit diagonal matrix adds upper right corner element and gets 1, structure is respectively:

$H_1^p=\left[\begin{array}{ccccccc}1& 0& 0& \·\·\·& & & 0\\ 1& 1& 0& & & & \\ 0& 1& 1& & & & \\ & & & \·& & & \\ & & & & \·& & \\ & & & & & \·& \\ 0& & & & & 1& 1\end{array}\right],H_2^p=\left[\begin{array}{ccccccc}1& 0& & & & 0& 1\\ 0& 1& & & & & \\ & & 1& & & & \\ & & & \·& & & \\ & & & & \·& & \\ & & & & & \·& 0\\ 0& & & & & 0& 1\end{array}\right]$

Described coding method, the H with 8 * 8 ^pMatrix is that example is represented:

In fact H ^pThe dimension of matrix can be any positive integer M, each row of matrix produces next line by one of lastrow ring shift right successively, promptly first one of the row ring shift right produces second row, second one of the row ring shift right produces the third line, go down successively, the building method of first row is to sort according to the following rules in three 1 position: first, the Position, last position all get 1, and all the other positions get 0.

Advantage of the present invention: the present invention can generate the variable sparse parity check matrix H of dimension fast, the line number M and the columns N of the variable H of the being exactly matrix of dimension can change as required, thereby energy adaptively modifying code length and code check are encoded, make the storage of the sparse parity matrix of ultra-large type only take very little memory space, only need Q vector of storage.

Embodiment

1. encoder algorithm design:

The basic design of encoder algorithm is the check digit matrix H that the sparse parity check matrix H of LDPC sign indicating number is decomposed into system form ^pWith information bit matrix H ^d, H=[H is promptly arranged ^pH ^d], code word c is decomposed into check digit p and information bit d, c=[pd is promptly arranged]; Respectively so that the mode that realizes is constructed H ^pAnd H ^d, like this to wanting information encoded sequence d={d _i, i=1,2 ..., N} can utilize (1) formula to obtain check digit sequence p={p _i, i=1,2 ..., M}, thus obtain codeword sequence c={c _i, i=1,2 ..., N}.

${\mathrm{Hc}}^T=\left[\begin{array}{cc}{H}^p& H^d\end{array}\right]\left[\begin{array}{c}p\\ d\end{array}\right]=H^{p}p+H^{d}d=0---\left(1\right)$

2.H ^pThe structure of matrix:

H ^pConstitute as (2) formula by four submatrixs:

$H^p=\left[\begin{array}{cc}{H}_1^p& H_2^p\\ H_2^p& H_1^p\end{array}\right]---\left(2\right)$

H wherein ₁ ^pBe configured to biconjugate dihedral formula.H ₂ ^pBe configured to triangular form, its feature is to be 1 at the upper right corner of unit diagonal matrix element.Promptly have:

$H_1^p=\left[\begin{array}{ccccccc}1& 0& 0& \·\·\·& & & 0\\ 1& 1& 0& & & & \\ 0& 1& 1& & & & \\ & & & \·& & & \\ & & & & \·& & \\ & & & & & \·& \\ 0& & & & & 1& 1\end{array}\right],H_2^p=\left[\begin{array}{ccccccc}1& 0& & & & 0& 1\\ 0& 1& & & & & \\ & & 1& & & & \\ & & & \·& & & \\ & & & & \·& & \\ & & & & & \·& 0\\ 0& & & & & 0& 1\end{array}\right]---\left(3\right)$

For example construct 8 * 8 H ^pMatrix has following form (for ease of the H with 8 * 8 is described ^pMatrix is example, in fact H ^pThe dimension of matrix is exactly the line number M of H matrix, and M is any positive integer):

H ^pThe characteristics of 9 matrixes are that every row and every row all have only three 1, and line number and columns all are even numbers.It can be produced by the mode of cyclic shift, constructs first row, to its ring shift right, obtains second row, and the ring shift right lastrow obtains next line successively, and delegation to the last so goes on doing.The building method of first row is to sort according to the following rules in three 1 position: get 1, for first The position gets 1, and last position gets 1, and all the other positions get 0.

3.H ^dThe structure of matrix:

Definition: if every row, every row and every diagonal of n * n rank square formation (n is any positive integer) all have only one 1, then this matrix is called the Q-matrix.The Q-matrix is non-to the angular unit square formation, and it is equivalent to " queen's problem ".Being described as of " queen's problem ": n ²The square that individual square is lined up the capable n row of n is called " n unit chessboard ".If any two queenes are positioned at same delegation or same row or same diagonal on the n unit chessboard, then claim them for running foul of each other.N the layout that queen does not attack mutually that makes on the n unit chessboard found out in requirement.At present, " queen's problem " had fast search algorithm.

With the Q-matrix as H ^dThe submatrix of matrix carries out suitable arrangement to 2t-1 Q-matrix, finally constitutes H ^dMatrix.

Go out a submatrix Q by queen's algorithm search ₁, represent Q with vector form ₁The corresponding relation of Q-vector and Q-matrix is which row the position of the every row nonzero element of each element value representing matrix of vector is in, by sequential counting from top to bottom.For example, establish n=5, can search for one 5 * 5 matrix, as: $Q_1=\left[\begin{array}{ccccc}1& 0& 0& 0& 0\\ 0& 0& 0& 1& 0\\ 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 1\\ 0& 0& 1& 0& 0\end{array}\right],$ The Q-vector that contains 5 elements of its correspondence is (1,3,5,2,4), and wherein the element that first row first is listed as in the 1 expression Q-matrix is that the element of the third line secondary series in 1, the 3 expression Q-matrix is 1, knows the implication of other element in the Q-vector thus by inference.With Q-vector ring shift left 4 times, can obtain 4 vectors (3,5,2,4,1), (5,2,4,1,3), (2,4,1,3,5) and (4,1,3,5,2), corresponding 5 the Q-matrixes of these 5 vectors are respectively:

$Q_1=\left[\begin{array}{ccccc}1& 0& 0& 0& 0\\ 0& 0& 0& 1& 0\\ 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 1\\ 0& 0& 1& 0& 0\end{array}\right],$ $Q_2=\left[\begin{array}{ccccc}0& 0& 1& 0& 0\\ 1& 0& 0& 0& 0\\ 0& 0& 0& 1& 0\\ 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 1\end{array}\right],$ $Q_3=\left[\begin{array}{ccccc}0& 0& 0& 0& 1\\ 0& 0& 1& 0& 0\\ 1& 0& 0& 0& 0\\ 0& 0& 0& 1& 0\\ 0& 1& 0& 0& 0\end{array}\right],$ $Q_4=\left[\begin{array}{ccccc}0& 1& 0& 0& 0\\ 0& 0& 0& 0& 1\\ 0& 0& 1& 0& 0\\ 1& 0& 0& 0& 0\\ 0& 0& 0& 1& 0\end{array}\right],$ $Q_5=\left[\begin{array}{ccccc}0& 0& 0& 1& 0\\ 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 1\\ 0& 0& 1& 0& 0\\ 1& 0& 0& 0& 0\end{array}\right]$

If represent H with t ^dEach row of matrix contains the number of Q-matrix, when n is very big, as gets n=250, can search a Q ₁＝[230 56 202 88 170 26 29 184 161 214 13206 140 220 112 52 210 242 43 64 174 176 75 97 147 132 17 185 24457 250 10 212 113 166 55 163 130 96 34 115 188 114 45 201 249 21535 241 67 221 36 138 178 95 150 162 217 108 120 44 74 179 203 86143 98 228 141 68 19 247 101 175 38 18 92 84 157 6 16 192 139 58248 90 133 181 223 160 82 196 234 50 225 7 226 240 40 28 76 2278 12 25 72 5 198 77 79 169 51 66 235 14 167 236 1 122 145 135 8085 231 216 91 60 211 151 195 31 243 197 123 186 118 89 124 208 8170 146 136 33 193 53 27 237 100 32 20 171 111 189 134 183 149 1872 71 46 39 137 172 24 110 199 144 94 200 62 103 204 177 213 148238 117 156 42 48 105 246 153 93 219 59 30 104 4 69 232 164 21 107152 159 205 37 218 168 23 106 87 222 102 9 173 125 3 109 155 54128 41 49 154 63 73 129 180 182 19 111 165 209 15 229],Q₁Cyclic shift 2t-2 time obtains one group of orthogonal matrix Q ₁, Q ₂..., Q _2t-1, with this group matrix construction H ^d:

$H^d=\left[\begin{array}{cccc}{Q}_1& Q_1& \·\·\·& Q_1\\ Q_1& Q_2& \·\·\·& Q_{t-1}\\ Q_1& Q_t& \·\·\·& Q_{2t-2}\end{array}\right]---\left(5\right)$

4.H obtaining of the formation of matrix and code word:

(2) formula and the merging of (5) formula are obtained the H matrix:

(6) Shi Dai as (1) formula, and is launched:

$\left[\begin{array}{cc}{H}_1^p& H_2^p\\ H_2^p& H_1^p\end{array}\right]\left[\begin{array}{c}{p}_1\\ p_2\end{array}\right]+\left[\begin{array}{cccc}{Q}_1& Q_1& \·\·\·& Q_1\\ Q_1& Q_2& \·\·\·& Q_{t-1}\\ Q_1& Q_t& \·\·\·& Q_{2t-2}\end{array}\right]\left[\begin{array}{c}{d}_1\\ M\\ d_t\end{array}\right]=0---\left(7\right),$

The given information encoded bit vector d=[d that wants ₁d ₂D _t], can obtain check digit vector p=[p by (7) formula ₁p ₂], finally obtain code word vector C=[p ₁p ₂d ₁d ₂D _t].

As submatrix, combination also can directly be constructed various forms of sparse parity check matrix H to the Q-arranged with Q-matrix of the present invention.

Core of the present invention is the constituted mode of submatrix Q-matrix, can have multiple mode to constitute the H matrix with the Q-matrix as submatrix.Therefore, every serves as the coding method that the basis constitutes the H matrix with Q-matrix of the present invention, all belongs to protection scope of the present invention.

Claims (5)

1. A rule (3, d _c) low density parity check code encoding method, mainly be the structure of the sparse parity check matrix H of design, to an information sequence d who gives, according to ${\mathrm{Hc}}^T=\left[\begin{array}{cc}{H}^p& H^d\end{array}\right]\left[\begin{array}{c}p\\ d\end{array}\right]=H^{p}p+H^{d}d=0$ Find the solution check digit sequence p, find the solution codeword sequence c=[pd thus], it is characterized in that matrix H is decomposed into the check digit matrix H ^pWith information bit matrix H ^d, H ^pMatrix can produce following each row successively by its first row ring shift right; H ^dMatrix is made of through suitably arranging one group of quadrature Q-matrix, the structure of Q-matrix is non-to the angular unit square formation, its every row, every row, every diagonal all have only one 1, make submatrix by the Q-matrix, and the permutation and combination of Q-matrix is constructed various forms of sparse parity check matrix H.
2. 2. according to the described coding method of claim 1, it is characterized in that one group of quadrature Q-matrix, their structure is every row, every row, every diagonal all has only n * n rank of one 1 non-to the angular unit square formation, is to go out a submatrix Q with queen's algorithm search ₁, represent Q with vector form ₁, the corresponding relation of Q-vector and Q-matrix is: the residing line number in position of the nonzero element of these row of value representation matrix of each element of vector, by sequential counting from top to bottom; To vector Q ₁Cyclic shift 2t-2 time, t represents H ^dEach row of matrix contains the number of Q-matrix, obtains one group of orthogonal matrix Q ₁, Q ₂..., Q _2t-1
3. 3. according to claim 1 or 2 described coding methods, it is characterized in that H ^dOrthogonal matrix Q in the matrix ₁, Q ₂..., Q _2t-1Arrange as follows:

   $H^d=\left[\begin{array}{cccc}{Q}_1& Q_1& ...& Q_1\\ Q_1& Q_2& ...& Q_{t-1}\\ Q_1& Q_t& ...& Q_{2t-2}\end{array}\right],$

   Wherein first row and first row are placed Q ₁Matrix, all the other are 2 years old _T-2Individual Q (3, d _c)-matrix Q ₂..., Q _2t-1Be successively placed on remaining position.
4. 4. according to claim 1 or 2 described coding methods, it is characterized in that the check digit matrix H ^pBe made of four matrixs in block form, wherein diagonal matrix two two equates, is respectively H ₁ ^pAnd H ₂ ^p, promptly $H^p=\left[\begin{array}{cc}{H}_1^p& H_2^p\\ H_2^p& H_1^p\end{array}\right],$ $H^p=\left[\begin{array}{cc}{H}_1^p& H_2^p\\ H_2^p& H_1^p\end{array}\right]$ Middle matrix H ₁ ^pStructure be biconjugate angle lower triangular matrix, matrix H ₂ ^pStructure be that the unit diagonal matrix adds upper right corner element and gets 1, structure is respectively: $H_1^p=\left[\begin{array}{ccccccc}1& 0& 0& ...& & & 0\\ 1& 1& 0& & & & \\ 0& 1& 1& & & & \\ & & & .& & & \\ & & & & .& & \\ & & & & & .& \\ 0& & & & & 1& 1\end{array}\right],$ $H_2^p=\left[\begin{array}{ccccccc}1& 0& & & & 0& 1\\ 0& 1& & & & & 0\\ & & 1& & & & \\ & & & .& & & \\ & & & & .& & \\ & & & & & .& 0\\ 0& & & & & 0& 1\end{array}\right]$ 。
5. 5. according to the described coding method of claim 4, it is characterized in that: H with 8 * 8 ^pMatrix is that example is represented:

   In fact H ^pMatrix is a square formation, and its dimension is exactly the line number M of H matrix, matrix H ^pEach row produce next line by one of lastrow ring shift right successively, promptly first one of the row ring shift right produces second row, second one of the ring shift right of row produces the third line, goes down successively, and the building method of first row is to sort according to the following rules in three 1 position: first, the Position, last position all get 1, and all the other positions get 0.