CN102386932B - LDPC code constitution method - Google Patents

Abstract

The invention discloses a constitution method for two LDPC codes with different check matrix structures. The method comprises the steps as follows: firstly, the structure of the rarefaction check matrix H1 of the first LDPC code is confirmed; secondly, the parallel degree P and parameter n of an LDPC code encoder are selected according to the P and n search parameter combination (wrow, wco1 and k2); thirdly, according to the searched combination (wrow, wco1 and k2), a mother board matrix C is constructed; fourthly; a matrix Hi and j replaces the corresponding elements of the motherboard matrix C so as to obtain the check matrix H1of the first LDPC code; and fifthly, and the second check matrix H2 is obtained through ordering the rows and the lines of the H1. According to the invention, the first LDPC code with linear coding complexity and low required memory capacity can be constructed through simple search; the second LDPC code can be obtained through ordering the lines and the rows of the rarefaction check matrix of the first LDPC code; the first LDPC code with the same coed rate but different code lengths can be gained through simple replacing; and the design difficulty is greatly reduced.

Description

The building method of LDPC code

Technical field

The present invention relates to the communications field, particularly the building method of LDPC code.

Background technology

Communication system adopts channel coding technology to guarantee the reliability of in noisy communication channel, communicating by letter usually.Such as, in satellite communication system,, there is a large amount of noise sources in the impact due to geographical and environmental factor.These communication channels have its theoretic maximum communication capacity (namely famous shannon limit), and this capacity can use the bit rate (bps) under specific signal to noise ratio (SNR) condition to represent.Therefore, the design of forward error correction (FEC) is exactly in order to pursue the maximum bit rate near shannon limit.Wherein a kind of coding near shannon limit is exactly low-density checksum (LDPC) code.

The LDPC code is a kind of linear block codes, it can obtain the performance near shannon limit in a large amount of transfer of data and memory channel, be widely used in various wireless communication systems, such as second generation satellite digital video broadcast standard (DVB-S2), China's military satellite communication system and global microwave H access H interoperability technology (WiMax) etc., it is up to a hundred million that the flank speed of supporting at present will reach, and will realize the data rate of hundreds of million future.

Why traditional LDPC code is not widely used, and is because there are a plurality of defects in it, and one of them defect is exactly that the coding techniques of LDPC code is very complicated.If use the generator matrix of LDPC code to encode to information, need non-sparse check matrix of storage, and for the performance of pursuing the LDPC code requires the code length long enough, this just causes this sparse check matrix can be very large, to storage, brings very large problem.Following defect is arranged aspect design of encoder: one, the check matrix of traditional LDPC code has stochastic behaviour, need to store a non-sparse check matrix during decoding, and require the code length long enough for the performance of pursuing the LDPC code, this just causes this sparse check matrix can be very large, to storage, brings very large problem; Two, have contradiction between the decoder throughput of traditional LDPC code and implementation complexity, if use serial decoding, throughput must be very low, if use complete parallel or part parallel decoding, the read-write of memory is controlled and must be become quite loaded down with trivial details.

Summary of the invention

, in order to overcome the deficiencies in the prior art, the object of the present invention is to provide the building method of the LDPC code of simplicity of design.

Purpose of the present invention is achieved through the following technical solutions:

The building method of LDPC code comprises the following steps:

(1) determine the sparse check matrix H of first kind LDPC code ¹Structure, H ¹Size is mP * nP, has following form:

$H^1=\left[H_{\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="HDA0000104845430000012.png"\; state="\{\{state\}\}">s</figure-callout>}}^1\right|H_p^1]=\left[\begin{array}{cccccc}{H}_{\mathrm{1,1}}& L& H_{1,k}& H_{1,k+1}& L& H_{1,n}\\ H_{\mathrm{2,1}}& L& H_{2,k}& H_{2,k+1}& L& H_{2,n}\\ M& O& M& M& O& M\\ H_{m,1}& L& H_{m,k}& H_{m,k+1}& L& H_{m,n}\end{array}\right]$

H in formula _{I, j}Be the matrix of P * P for size, the row of each matrix is heavy is fixed value 1 or 0, by unit matrix I or null matrix, through cyclic shift, is obtained; 1≤i≤m wherein, 1≤j≤n;

In formula

Corresponding informance bit part, size is mP * kP, wherein k=n-m;

Have following structure:

${\mathrm{<figure-callout\; id="1"\; label="H\; p"\; filenames="HDA0000104845430000012.png"\; state="\{\{state\}\}">H</figure-callout>}}_p^{}=\left[\begin{array}{ccccccc}I& 0& 0& L& 0& 0& a\\ I& I& 0& L& 0& 0& 0\\ 0& I& I& L& 0& 0& 0\\ L& L& O& O& L& L& L\\ 0& 0& 0& L& I& 0& 0\\ 0& 0& 0& L& I& I& 0\\ 0& 0& 0& L& 0& I& I\end{array}\right];$

Wherein

The matrix that upper right corner a represents has following structure:

$a=\left[\begin{array}{ccccc}0& 0& \mathrm{\&Lambda;}& \mathrm{\&Lambda;}& 0\\ 1& 0& O& O& M\\ 0& 1& O& O& M\\ M& O& O& 0& 0\\ 0& \mathrm{\&Lambda;}& 0& 1& 0\end{array}\right];$

(2) select degree of parallelism P and the parameter n of ldpc code decoder according to the demand of designed communication system, the code length of LDPC code is nP, and wherein the value of parameter n is the common multiple of designed all code check denominators of communication system; According to P and n search parameter combination (w _row, w _col, k ₂); W wherein _rowFor

Row heavy, w _colFor

Column weight, k ₂=(m _Wrow-3k)/(w _col-3);

(3) according to the parameter combinations (w that searches _row, w _col, k ₂), structure motherboard Matrix C, described mother matrix Matrix C is defined as: use matrix H _{I, j}In the first row, the row mark of 1 position replaces In H _{I, j}, use 0 matrix that replaces full null matrix to obtain;

(4), according to the motherboard Matrix C of structure, use the submatrix H corresponding with each nonzero element in the motherboard Matrix C _{I, j}Substitute the nonzero element in the mother matrix Matrix C, use the neutral element in full null matrix replacement mother matrix Matrix C, obtain In conjunction with

Obtain the check matrix of first kind LDPC code word

The submatrix H that wherein nonzero element is corresponding with it _{I, j}Corresponding relation as follows: the value of nonzero element is submatrix H _{I, j}The first row in the row mark of 1 position.

Can also construct the step of the method for the Equations of The Second Kind LDPC code that is associated with described first kind LDPC code after completing steps (4):

(5) to H ¹The row of matrix sorts in the following order:

1，P+1，...，(m-1)P+1，2，P+2，...，(m-1)P+2，P，2P，...，mP；

After being resequenced

Submatrix in formula

Size is mP * kP,

Size is mP * mP, wherein k=n-m;

Then with submatrix

Row arrange in the following order,

1，P+1，...，(m-1)P+1，2，P+2，...，(m-1)P+2，P，2P，...，mP，

Namely obtain the sparse check matrix H of Equations of The Second Kind LDPC code ²

The submatrix of step (4) structure

Also meet following restrictive condition:

(a) the heavy w of row _rowIdentical, span is [3,40];

(b) value of column weight has at most two, and wherein less one is fixed value 3, and shared columns is designated as k ₁P, another one is designated as w _col, shared columns is designated as k ₂P, wherein k ₁+ k ₂=k;

(c) value of column weight is according to arranging from left to right from big to small, corresponding to information bit from the highest significant bit to minimum effective bit;

(d) with

The check matrix H that forms ¹Ring length is not 4 ring.

Parameter combinations (the w that the described basis of step (3) searches _row, w _col, k ₂), structure motherboard Matrix C specifically comprises the following steps:

(3-1) design k ₂Individual column weight is w _colRow, be specially:

(3-1-1) produce at random w _colNumbers different between individual [1, m] are listed as the rower at non-zero element place, 1≤i≤k as i in the motherboard Matrix C ₂If the heavy w that equaled of the row that rower is corresponding _row, will equal the heavy rower of row and be adjusted into the heavy minimum rower of row in nonoptional rower in prostatitis;

(3-1-2) produce at random w _colThe nonzero element that number between individual [1, P] is listed as i in the motherboard Matrix C: described w _colNumber meets: the value of (1) adjacent two row nonzero elements is different; (2) this w _colThe value of any row corresponding row in individual value in any two values and the i-1 row that produce before is not identical;

(3-2) the design column weight is the k of 3 motherboard Matrix C ₁=k-k ₂Row are specially:

(3-2-1) produce at random the rower of numbers different between 3 [1, m] as i row non-zero element place in the motherboard Matrix C, k ₂+ 1≤i≤k; If the heavy w that equaled of the row that rower is corresponding _row, will equal the heavy rower of row and be adjusted into the heavy minimum rower of row in nonoptional rower in prostatitis;

(3-2-2) produce at random the nonzero element of 3 numbers between [1, P] as i row in C: described 3 numbers meet: the value of (1) adjacent two row nonzero elements is different; (2) in these 3 values, the value of any row corresponding row in any two values and the i-1 row that produce before is not identical;

The k that (3-3) step (3-1) is produced ₂The k that row and step (3-2) produce ₁The row amalgamation forms the motherboard Matrix C together.

The described search parameter combination of step (2) (w _row, w _col, k ₂), detailed process is:

At w _row(max (3,3k/m)≤w _row≤ 40) and w _col(3≤w _col≤ m) search in scope, search and meet k ₂=(mw _row-3k)/(w _col-3), and k ₂Combination (w for nonnegative integer _row, w _col, k ₂) be rational combination.

Completing steps (4) is also constructed the identical but process of the LDPC code check matrix that code length is different of the code check of the first kind LDPC code that obtains from step (4) afterwards: use size as P ' * P ' (P '＞P) matrix H " _{I, j}Nonzero element in the mother matrix Matrix C that replacement step (3) obtains, use full null matrix replacement wherein the neutral element of size as P ' * P ', obtains matrix

Associate(d) matrix again

Obtain sparse check matrix $H^{}$ ${}^{1\&prime;\&prime;}=\left[H_s^{1\&prime;\&prime;}\right|{\mathrm{<figure-callout\; id="1"\; label="H\; p"\; filenames="HDA0000104845430000012.png"\; state="\{\{state\}\}">H</figure-callout>}}_p^{}].$

Compared with prior art, the present invention has the following advantages and technique effect:

(1) simplicity of design of the present invention, only need to carry out simply searching for just can construct to have uniform enconding complexity and the low first kind LDPC code of required storage;

The sparse check matrix of the first kind LDPC code that (2) will construct can obtain the check matrix of Equations of The Second Kind LDPC code through the sequence of simple row and column, these two kinds of LDPC code close relation, in actual applications, if the coder of known a kind of yard, can carry out simple sequence to check digit at the input of the output of encoder and decoder and can obtain the coder of another kind of code, greatly simplify design difficulty;

(3) in first kind LDPC code construction process, just can construct a plurality of code checks by simple replacement identical, the first kind LDPC code that code length is different, simplified design difficulty greatly.

Description of drawings

Fig. 1 is the structure flow chart of two class LDPC code check matrixes.

Fig. 2 is the cycle characteristics schematic diagram of the sparse check matrix of Equations of The Second Kind LDPC code.

Embodiment

, below in conjunction with embodiment and accompanying drawing, the present invention is described in further detail, but embodiments of the present invention are not limited to this.

Embodiment

As shown in Figure 1, the building method of LDPC code of the present invention comprises the following steps:

(1) determine the sparse check matrix H of first kind LDPC code ¹Structure, H ¹Size is mP * nP, has following form:

$H^1=\left[H_{\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="HDA0000104845430000012.png"\; state="\{\{state\}\}">s</figure-callout>}}^1\right|H_p^1]=\left[\begin{array}{cccccc}{H}_{\mathrm{1,1}}& L& H_{1,k}& H_{1,k+1}& L& H_{1,n}\\ H_{\mathrm{2,1}}& L& H_{2,k}& H_{2,k+1}& L& H_{2,n}\\ M& O& M& M& O& M\\ H_{m,1}& L& H_{m,k}& H_{m,k+1}& L& H_{m,n}\end{array}\right]$

H in formula _{I, j}Be the matrix of P * P for size, the row of each matrix is heavy is fixed value 1 or 0, is to be obtained through cyclic shift by unit matrix I or null matrix; 1≤i≤m wherein, 1≤j≤n;

In formula

Corresponding informance bit part, size is mP * kP, wherein k=n-m;

Have following structure:

${\mathrm{<figure-callout\; id="1"\; label="H\; p"\; filenames="HDA0000104845430000012.png"\; state="\{\{state\}\}">H</figure-callout>}}_p^{}=\left[\begin{array}{ccccccc}I& 0& 0& L& 0& 0& a\\ I& I& 0& L& 0& 0& 0\\ 0& I& I& L& 0& 0& 0\\ L& L& O& O& L& L& L\\ 0& 0& 0& L& I& 0& 0\\ 0& 0& 0& L& I& I& 0\\ 0& 0& 0& L& 0& I& I\end{array}\right]$

Wherein

The matrix that upper right corner a represents has following structure:

$a=\left[\begin{array}{ccccc}0& 0& \mathrm{\&Lambda;}& \mathrm{\&Lambda;}& 0\\ 1& 0& O& O& M\\ 0& 1& O& O& M\\ M& O& O& 0& 0\\ 0& \mathrm{\&Lambda;}& 0& 1& 0\end{array}\right]$

The characteristics of matrix have guaranteed that LDPC code coding has linear complexity,

The characteristics of matrix have guaranteed that the LDPC CODEC has lower memory space.

(2) select degree of parallelism P and the parameter n of ldpc code decoder according to the demand of designed communication system, the code length of LDPC code is nP; Such as: when the data rate of design system is had relatively high expectations, should select larger P; While requiring compatible various code rate, the n of selection should be the common multiple of all code check denominators, and guarantee m and k are integer like this.For example, the compatible code check 1/3,1/2,2/3,3/4 of system requirements, 4/5,7/8 o'clock, n should be all code check denominators { integral multiples of the least common multiple 120 of 3,2,3,4,5,8}.

For the check matrix that makes structure simple and practical, can be right

Do following restriction:

(a)

The heavy w of row _rowIdentical, span is [3,40];

(b)

The value of column weight have at most two, wherein less one is fixed value 3, shared columns is designated as k ₁P, another one is designated as w _col, shared columns is designated as k ₂P, wherein k ₁+ k ₂=k;

(c) value of column weight, according to arranging from left to right from big to small, arrives minimum effective bit (LSB, Least Significant Bits) corresponding to information bit from the highest significant bit (MSB, Most Significant Bits);

(d) with

The check matrix H that forms after combination ¹Ring length is not 4 ring (being called for short ring 4), can resolve into two conditions: (1)

Do not encircle 4, (2) Any row in two non-zero submatrices H of arbitrary neighborhood _{I, j}And H _{I+1, j}Not identical.According to

Characteristics as can be known, like this With

H after combination ¹Just can not form ring length and be 4 ring.

Search procedure is specially:

(b) knows according to condition, w _colHunting zone be 3≤w _col≤ m, and by matrix

In 1 number fixing as can be known:

(3k ₁+w _colk ₂)P＝mPw _row(1)

Again due to w _col〉=3, k ₁+ k ₂=k, therefore:

k ₂＝(mw _row-3k)/(w _col-3)(2)

w _row≥3k/m (3)

In summary, w _rowHunting zone be max (3,3k/m)≤w _row≤ 40.

To w _row(max (3,3k/m)≤w _row≤ 40) and w _col(3≤w _col≤ m) search in the scope of appointment, search and meet formula (2) and be the combination (w of nonnegative integer _row, w _col, k ₂) be exactly reasonably combination.

(3) according to the parameter combinations (w that searches _row, w _col, k ₂), structure motherboard Matrix C, described mother matrix Matrix C is defined as: use matrix H _{I, j}In the first row, the row mark of 1 position substitutes

In H _{I, j}The matrix that (full null matrix replaces with 0) obtains, for example, matrix H _{I, j}The first row in 1 be positioned at the 3rd row, use 3 to replace In H _{I, j}

Specifically comprising the following steps of structure motherboard Matrix C:

(3-1) design k ₂Individual column weight is w _colRow, be specially:

(3-1-1) produce at random w _colNumbers different between individual [1, m] are listed as the rower at non-zero element place, 1≤i≤k as i in C ₂If the heavy w that equaled of the row that rower is corresponding _row, will equal the heavy rower of row and be adjusted into the heavy minimum rower of row in nonoptional rower in prostatitis;

(3-1-2) produce at random w _colThe nonzero element that number between individual [1, P] is listed as i in C: described w _colNumber meets: the value of (1) adjacent two row nonzero elements is different; (2) this w _colThe value of any row corresponding row in individual value in any two values and the i-1 row that produce before is not identical; If do not meet wherein one, need to adjust this w _colThe position of number., if through the value that does not still satisfy condition after the several times adjustment, need to restart the search procedure of (3-1-2).Still do not find suitable value if pass through again several times (3-1-2) process, return to (3-1-1) and again search for until satisfy condition;

(3-2) the design column weight is the k of 3 C ₁=k-k ₂Row are specially:

(3-2-1) produce at random the rower of numbers different between 3 [1, m] as i row non-zero element place in C, k ₂+ 2≤i≤k; If the heavy w that equaled of the row that rower is corresponding _row, will equal the heavy rower of row and be adjusted into the heavy minimum rower of row in nonoptional rower in prostatitis;

(3-2-2) produce at random the nonzero element of 3 numbers between [1, P] as i row in C: described 3 numbers meet: the value of (1) adjacent two row nonzero elements is different; (2) in these 3 values, the value of any row corresponding row in any two values and the i-1 row that produce before is not identical;

The k that (3-3) step (3-1) is produced ₂The k that row and step (3-2) produce ₁The row amalgamation forms the motherboard Matrix C together.

(4), according to the motherboard Matrix C of structure, use the submatrix H corresponding with each element value in the motherboard Matrix C _{I, j}The element (0 element uses full null matrix to replace) that substitutes in the mother matrix Matrix C obtains

And then obtain The submatrix H that wherein nonzero element is corresponding with it _{I, j}Corresponding relation as follows: the value of nonzero element is submatrix H _{I, j}The first row in the row mark of 1 position, for example nonzero element is 3, its corresponding submatrix H _{I, j}The first row in 1 be positioned at the 3rd row.

By top search condition as can be known,, if the motherboard Matrix C meets the search condition that parameter is P, necessarily meeting the structural environment of the motherboard matrix of P '＞P, is therefore the submatrix H of P ' * P ' with size _{I, j}Replace the element in C can obtain the submatrix that parameter is P ' time

The LDPC code code check that construct this moment is identical with code word code check before, and just code length is different, and detailed process is:

Use the matrix H of size as P ' * P ' " _{I, j}Nonzero element in the mother matrix Matrix C that replacement step (3) obtains, use full null matrix replacement wherein the neutral element of size as P ' * P ', obtains matrix

Associate(d) matrix again

Obtain sparse check matrix

According to H ¹" encode;

H wherein " _{I, j}Be the matrix of P ' * P ' for size, P '＞P, the row of each matrix is heavy is fixed value 1 or 0, is to be obtained through cyclic shift by unit matrix I or null matrix.

If input information bits s=[s ₁, s ₂, L, s _kP], the check bit p=[p that calculates ₁, p ₂, L, p _mP], the coding method of first kind LDPC code is as follows:

Step 1: utilize input message vector s, calculate intermediate object program x=[x ₁, x ₂, L, x _mP]:

$x=s{\left(H_s^1\right)}^T---\left(4\right)$

Step 2: utilize x computation of parity bits p, adopt following formula:

$p_i=\left\{\begin{array}{cc}{x}_i& ,i=1\\ x_i\&CirclePlus;p_{(m-1)P+i-1}& ,i<i\&le;P\\ x_i\&CirclePlus;p_{i-P}& ,i>P\end{array}\right.---\left(5\right)$

Wherein

Addition in expression GF (2).

At first obtain first check bit p during coding ₁=x ₁, then obtain successively $p_{P+1}=x_{P+1}\&CirclePlus;{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA0000104845430000012.png"\; state="\{\{state\}\}">p</figure-callout>}}_1,$ $p_{2P+1}=x_{2P+1}\&CirclePlus;p_{P+1},......,p_{(m-1)P+1}=x_{(m-1)P+1}\&CirclePlus;p_{(m-2)\mathrm{<figure-callout\; id="1"\; label="P\; +"\; filenames="HDA0000104845430000012.png"\; state="\{\{state\}\}">P</figure-callout>}+1},{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA0000104845430000012.png"\; state="\{\{state\}\}">p</figure-callout>}}_2=x_2\&CirclePlus;p_{(m-1)\mathrm{<figure-callout\; id="1"\; label="P\; +"\; filenames="HDA0000104845430000012.png"\; state="\{\{state\}\}">P</figure-callout>}+1},......,$ $p_{\mathrm{mP}}=x_{\mathrm{mP}}\&CirclePlus;p_{(m-1)P}.$

Code word c=[c after coding ₁, c ₂, L, c _nP]=[s|p].

If need to construct the sparse check matrix H of the Equations of The Second Kind LDPC code that is associated with first kind LDPC code ², can be undertaken by following steps:

To H ¹The row of matrix sorts in the following order:

1，P+1，...，(m-1) P+ 1，2，P+2，...，(m-1)P+2，P，2P，...，mP；

After being resequenced Submatrix in formula

Size is mP * kP, Size is mP * mP, wherein k=n-m;

Then with submatrix

Row arrange in the following order:

1，P+1，...，(m-1) P+ 1，2，P+2，...，(m-1)P+2，P，2P，...，mP

Can obtain the sparse check matrix H of Equations of The Second Kind LDPC code ²

Equations of The Second Kind LDPC code is that non-canonical repeats accumulated codes (IRA), the sparse check matrix H of such LDPC code ²Following feature is arranged:

${\mathrm{<figure-callout\; id="2"\; label="H"\; filenames="HDA0000104845430000012.png"\; state="\{\{state\}\}">H</figure-callout>}}^2=\left[H_s^2\right|H_p^2]$

Wherein

Triangle battle array under notch cuttype:

The characteristics of matrix have guaranteed that LDPC code coding has linear complexity,

The characteristics of matrix have guaranteed that the LDPC CODEC has lower memory space.

Matrix has structure as follows

$H_s^2=[A_1{\mathrm{<figure-callout\; id="2"\; label="A"\; filenames="HDA0000104845430000012.png"\; state="\{\{state\}\}">A</figure-callout>}}_2..A_k]$

Each A wherein _i(1≤i≤k) inner column weight is all identical, and size is mP * P, and is circular matrix, has cycle characteristics shown in Figure 2, and the black box that has same numeral in figure represents that the element on the check matrix correspondence position is 1, and colourless square corresponds to 0.As seen from Figure 2, the line number at the square place of same numeral can be determined by the line number of the square of same label in any row, the square line number difference of two row same numerals that face mutually is fixed as m=2mod (mP), and (mod is modulo operation, P=16 wherein), therefore each A in this case _i1 line number during only needs storage one is listed as, then by calculating the line number of other row.Generally storing the line number at 1 place in the 1st row, is also initial verification address.

The coding of Equations of The Second Kind LDPC code (being the IRA code) divides following two steps to carry out:

Step 1: utilize input message vector s, calculate intermediate object program x=[x ₁, x ₂, L, x _mP]:

$x=s{\left(H_s^2\right)}^T---\left(6\right)$

Step 2: utilize x computation of parity bits p, adopt following formula:

$p_i=\left\{\begin{array}{cc}{x}_i,& i=1\\ x_i\&CirclePlus;p_{i-1},& 1<i\&le;\mathrm{mP}\end{array}\right.,$

Wherein Addition in expression GF (2).

At first obtain first check bit p during coding ₁=x ₁, then obtain successively ${\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA0000104845430000012.png"\; state="\{\{state\}\}">p</figure-callout>}}_2=x_2\&CirclePlus;{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA0000104845430000012.png"\; state="\{\{state\}\}">p</figure-callout>}}_1,$ ${\mathrm{<figure-callout\; id="3"\; label="p"\; filenames="HDA0000104845430000012.png"\; state="\{\{state\}\}">p</figure-callout>}}_3=x_3\&CirclePlus;{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA0000104845430000012.png"\; state="\{\{state\}\}">p</figure-callout>}}_2,...,p_{\mathrm{mP}}=x_{\mathrm{mP}}\&CirclePlus;p_{\mathrm{mP}-1}.$

Code word c=[c after coding ₁, c ₂, L, c _nP]=[s|p].

Below discuss the relation between two class LDPC codes.

At first contrast the difference part of both check matrixes:

The code word c that is obtained by check matrix H coding and the pass between H are:

cH ^T＝0(7)

By formula (7) as can be known, the row of check matrix H is exchanged the result that does not affect formula (6), namely do not affect coding result.We can be at first with H thus ¹Row adjust (matrix of note after adjusting is:

Make matrix after adjusting

Part meets Equations of The Second Kind LDPC code

Form, namely each size needs to meet characteristic of circular matrix for the matrix in block form of mP * P.For this reason, we discuss H ¹In matrix by H _{1, i}, H _{2, i}..., H _{M, i}The size that submatrix forms is mP * P matrix A _i(1≤i≤k) wherein:

$A_i=\left[\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="HDA0000104845430000012.png"\; state="\{\{state\}\}">H</figure-callout>}}_{1,i}\\ {\mathrm{<figure-callout\; id="2"\; label="H"\; filenames="HDA0000104845430000012.png"\; state="\{\{state\}\}">H</figure-callout>}}_{2,i}\\ M\\ H_{m,i}\end{array}\right]$

With A _iRow resequence, sort method is: extract each submatrix H _{1, i}, H _{2, i}..., H _{M, i}J capablely form in order a matrix and (be designated as B _j, 1≤j≤P), and then with B _jForm in order matrix A ' _i:

${A^{\&prime;}}_i=\left[\begin{array}{c}{B}_1\\ B_2\\ M\\ B_P\end{array}\right]$

Due to submatrix H _{I, j}Be to be obtained through cyclic shift by unit matrix I, have characteristic: element of a downward loopy moving of row just can obtain a+1 row (if 1 place behavior last column that a is listed as, next behavior the first row, referring to following formula).

$H_{i,j}=\left[\begin{array}{ccccccc}0& 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 0& 1\\ 1& 0& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0& 0\end{array}\right]$

Characteristic is easily found out A ' thus _iThe downward loopy moving m element of a row just can obtain a+1 and be listed as.That is to say A ' _iIt is circular matrix.Due to all A ' _i(wherein 1≤i≤k) obtains circular matrix so matrix through identical row adjustment

Meet Equations of The Second Kind LDPC code

Characteristic, wherein:

$H_s^{1\&prime;}=[{A^{\&prime;}}_1{A^{\&prime;}}_2..{A^{\&prime;}}_k]$

Must, with matrix H ¹Row rearrange in the following order, can make the matrix H after adjusting ¹'

Part meets Equations of The Second Kind LDPC code

Form:

1，P+1，...，(m-1) P+ 1，2，P+2，...，(m-1)P+2，P，2P，...，mP

(8)

By top analysis as can be known, with H ¹Be converted into the matrix H of equivalence through line ordering ¹' afterwards, H ¹With H ²Difference only be present in

With Part.

Analyze H ¹Cataloged procedure:

At first obtain first check bit p during coding ₁=x ₁, then obtain successively $p_{P+1}=x_{P+1}\&CirclePlus;{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA0000104845430000012.png"\; state="\{\{state\}\}">p</figure-callout>}}_1,$ $p_{2P+1}=x_{2P+1}\&CirclePlus;p_{P+1},...,p_{(m-1)P+1}=x_{(m-1)P+1}\&CirclePlus;p_{(m-2)\mathrm{<figure-callout\; id="1"\; label="P\; +"\; filenames="HDA0000104845430000012.png"\; state="\{\{state\}\}">P</figure-callout>}+1},{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA0000104845430000012.png"\; state="\{\{state\}\}">p</figure-callout>}}_2=x_2\&CirclePlus;p_{(m-1)\mathrm{<figure-callout\; id="1"\; label="P\; +"\; filenames="HDA0000104845430000012.png"\; state="\{\{state\}\}">P</figure-callout>}+1},...,$ $p_{\mathrm{mP}}=x_{\mathrm{mP}}\&CirclePlus;p_{(m-1)P}.$

If:

$x^{\&prime;}=s{\left(H_s^{1\&prime;}\right)}^T---\left(9\right)$

By formula (6) as can be known, x _iWith

Row corresponding one by one, according to

With

Corresponding relation as can be known the corresponding relation of x and x ' be:

{x ₁，x _P+1，...，x _(m-1)P+1，x ₂，x _P+2，...，x _(m-1)P+2，x _2P，...，x _mP}＝{x′ ₁，x′ ₂，x′ ₃，...，x′ _mP}(10)

Hence one can see that, and cataloged procedure becomes:

${\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA0000104845430000012.png"\; state="\{\{state\}\}">p</figure-callout>}}_1={x^{\&prime;}}_1,p_{P+1}={x^{\&prime;}}_2\&CirclePlus;{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA0000104845430000012.png"\; state="\{\{state\}\}">p</figure-callout>}}_1,p_{2P+1}={x^{\&prime;}}_3\&CirclePlus;p_{P+1},...,p_{(m-1)P+1}={x^{\&prime;}}_m\&CirclePlus;p_{(m-2)\mathrm{<figure-callout\; id="1"\; label="P\; +"\; filenames="HDA0000104845430000012.png"\; state="\{\{state\}\}">P</figure-callout>}+1},$ ${\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA0000104845430000012.png"\; state="\{\{state\}\}">p</figure-callout>}}_2={x^{\&prime;}}_{m+1}\&CirclePlus;p_{(m-1)\mathrm{<figure-callout\; id="1"\; label="P\; +"\; filenames="HDA0000104845430000012.png"\; state="\{\{state\}\}">P</figure-callout>}+1},...,p_{\mathrm{mP}}={x^{\&prime;}}_{\mathrm{mP}}\&CirclePlus;p_{(m-1)P}.$

Order

{p ₁，p _P+1，...，p _(m-1)P+1，p ₂，p _P+2，...，p _(m-1)P+2，p _P，p _2P，...，p _mP}＝{p′ ₁，p′ ₂，p′ ₃，...，p′ _mP}(11)

Cataloged procedure becomes:

${p^{\&prime;}}_1={x^{\&prime;}}_1,{p^{\&prime;}}_2={x^{\&prime;}}_2\&CirclePlus;{p^{\&prime;}}_1,{p^{\&prime;}}_3={x^{\&prime;}}_3\&CirclePlus;{p^{\&prime;}}_2,...,{p^{\&prime;}}_{mm}={x^{\&prime;}}_m\&CirclePlus;{p^{\&prime;}}_{m-1},{p^{\&prime;}}_{m+1}={x^{\&prime;}}_{m+1}\&CirclePlus;{p^{\&prime;}}_m,...,$ ${p^{\&prime;}}_{\mathrm{mP}}={x^{\&prime;}}_{\mathrm{mP}}\&CirclePlus;{p^{\&prime;}}_{\mathrm{mP}-1}.$

This process and H ²Cataloged procedure identical.From top derivation as can be known, H ¹With H ²Difference between code word is that the check digit order is different, and that the order correspondence of check digit is H _pThe order of rectangular array, hence one can see that, will

Row arrange according to the order shown in formula (7), H ¹' can meet H ²The characteristics of matrix.

Because just there is difference in the two class LDPC codes of constructing on the order of check digit, if therefore the coder of a known class LDPC code will be constructed the coder of another kind of LDPC code, only need to sort and get final product the input of the output of encoder and decoder, not need extra modification.

Known H ¹, obtain H after the sequence through row and column ²Process be not reversible.Suppose known H ², the matrix that obtains after sorting according to top inverse process is H ²',

${\mathrm{<figure-callout\; id="2"\; label="H"\; filenames="HDA0000104845430000012.png"\; state="\{\{state\}\}">H</figure-callout>}}^{2\&prime;}=\left[H_s^{2\&prime;}\right|{\mathrm{<figure-callout\; id="2"\; label="H\; p"\; filenames="HDA0000104845430000012.png"\; state="\{\{state\}\}">H</figure-callout>}}_p^{}]$

Wherein,

With H ¹In

Part-structure is identical, Have following structure:

$H_s^{2\&prime;}=\left[\begin{array}{cccc}{H^{\&prime;}}_{\mathrm{1,1}}& {H^{\&prime;}}_{\mathrm{1,2}}& L& {H^{\&prime;}}_{1,k}\\ {H^{\&prime;}}_{\mathrm{2,1}}& {H^{\&prime;}}_{\mathrm{2,2}}& L& {H^{\&prime;}}_{2,k}\\ M& M& O& M\\ {H^{\&prime;}}_{m,1}& {H^{\&prime;}}_{m,2}& L& {H^{\&prime;}}_{m,k}\end{array}\right]$

H ' wherein _{I, j}Be that size is the matrix of P * P, the row of each matrix is heavy for fixed value (being not limited to 1 and 0), when row is heavily r _wThe time, H ' _{I, j}By r _wThe unit matrix I of individual different process cyclic shift is cumulative to be obtained.

Above-described embodiment is the better execution mode of the present invention; but embodiments of the present invention are not limited by the examples; other any do not deviate from change, the modification done under Spirit Essence of the present invention and principle, substitutes, combination, simplify; all should be the substitute mode of equivalence, within being included in protection scope of the present invention.

Claims (5)

1.LDPC the building method of code, is characterized in that, comprises the following steps:

(1) determine the sparse check matrix H of first kind LDPC code ¹Structure, H ¹Size is mP * nP, has following form:

H in formula _i,jBe the matrix of P * P for size, the row of each matrix is heavy is fixed value 1 or 0, by unit matrix I or null matrix, through cyclic shift, is obtained; I=1 wherein, 2...m, j=1,2...n;

In formula

Corresponding informance bit part, size is mP * kP, wherein k=n-m;

Have following structure:

Wherein

The matrix that upper right corner a represents has following structure:

(2) select degree of parallelism P and the parameter n of ldpc code decoder according to the demand of designed communication system, the code length of LDPC code is nP, and wherein the value of parameter n is the common multiple of designed all code check denominators of communication system; According to P and n search parameter combination (w _row, w _col, k ₂); W wherein _rowFor

Row heavy, w _colFor

Column weight, k ₂=(mw _row-3k)/(w _col-3);

(3) according to the parameter combinations (w that searches _row, w _col, k ₂), structure motherboard Matrix C, described mother matrix Matrix C is defined as: use matrix H _i,jIn the first row, the row mark of 1 position replaces In H _i,j, use 0 matrix that replaces full null matrix to obtain;

Parameter combinations (the w that described basis searches _row, w _col, k ₂), structure motherboard Matrix C specifically comprises the following steps:

(3-1) design k ₂Individual column weight is w _colRow, be specially:

(3-1-1) produce at random w _colNumbers different between individual [1, m] are listed as the rower at non-zero element place, 1≤i≤k as i in the motherboard Matrix C ₂If the heavy w that equaled of the row that rower is corresponding _row, will equal the heavy rower of row and be adjusted into the heavy minimum rower of row in nonoptional rower in prostatitis;

(3-1-2) produce at random w _colThe nonzero element that number between individual [1, P] is listed as i in the motherboard Matrix C: described w _colNumber meets: the value of (1) adjacent two row nonzero elements is different; (2) this w _colThe value of any row corresponding row in individual value in any two values and the i-1 row that produce before is not identical;

(3-2) the design column weight is the k of 3 motherboard Matrix C ₁=k-k ₂Row are specially:

(3-2-1) produce at random the rower of numbers different between 3 [1, m] as i row non-zero element place in the motherboard Matrix C, k ₂+ 1≤i≤k; If the heavy w that equaled of the row that rower is corresponding _row, will equal the heavy rower of row and be adjusted into the heavy minimum rower of row in nonoptional rower in prostatitis;

(3-2-2) produce at random the nonzero element of 3 numbers between [1, P] as i row in the motherboard Matrix C: described 3 numbers meet: the value of (1) adjacent two row nonzero elements is different; (2) in these 3 values, the value of any row corresponding row in any two values and the i-1 row that produce before is not identical;

The k that (3-3) step (3-1) is produced ₂The k that row and step (3-2) produce ₁The row amalgamation forms the motherboard Matrix C together;

(4), according to the motherboard Matrix C of structure, use the submatrix H corresponding with each nonzero element in the motherboard Matrix C _ijSubstitute the nonzero element in the mother matrix Matrix C, use the neutral element in full null matrix replacement mother matrix Matrix C, obtain

In conjunction with

Obtain the check matrix of first kind LDPC code word

The submatrix H that wherein nonzero element is corresponding with it _i,jCorresponding relation as follows: the value of nonzero element is submatrix H _i,jThe first row in the row mark of 1 position.

2. the building method of LDPC code according to claim 1, is characterized in that, also constructs the step of the method for the Equations of The Second Kind LDPC code that is associated with described first kind LDPC code after completing steps (4):

(5) to H ¹The row of matrix sorts in the following order:

1,P+1,...,(m-1)P+1,2,P+2,...,(m-1)P+2,P,2P,...,mP；

After being resequenced

Submatrix in formula Size is mP * kP,

Size is mP * mP, wherein k=n-m;

Then with submatrix

Row arrange in the following order,

1,P+1,...,(m-1)P+1,2,P+2,...,(m-1)P+2,P,2P,...,mP，

Obtain the sparse check matrix H of Equations of The Second Kind LDPC code ²

3. the building method of LDPC code according to claim 1, is characterized in that, the submatrix of step (4) structure Meet following restrictive condition:

(a) the heavy w of row _rowIdentical, span is [3,40];

(b) value of column weight has at most two, and wherein less one is fixed value 3, and shared columns is designated as k ₁P, another one is designated as w _col, shared columns is designated as k ₂P, wherein k ₁+ k ₂=k;

(c) value of column weight is according to arranging from left to right from big to small, corresponding to information bit from the highest significant bit to minimum effective bit;

(d) with

The check matrix H that forms ¹Ring length is not 4 ring.

4. the building method of LDPC code according to claim 3, is characterized in that, the described search parameter combination of step (2) (w _row, w _col, k ₂), detailed process is:

Max (3,3k/m)≤w _row≤ 40 and 3≤w _colSearch in≤m scope, search and meet k ₂=(mw _row-3k)/(w _col-3), and k ₂Combination (w for nonnegative integer _row, w _col, k ₂) be rational combination.

5. the building method of LDPC code according to claim 1, it is characterized in that, completing steps (4) is also constructed the identical but process of the LDPC code check matrix that code length is different of the code check of the first kind LDPC code that obtains from step (4) afterwards: use the matrix of size as P' * P'

Nonzero element in the mother matrix Matrix C that replacement step (3) obtains, wherein P'〉P, use full null matrix replacement wherein the neutral element of size as P' * P', obtain matrix

Associate(d) matrix again

Obtain sparse check matrix $H^1\&prime;\&prime;=[H_S^1\&prime;\&prime;|H_p^1\&prime;\&prime;].$

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