CN102386932A - 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 sign indicating number

Technical field

The present invention relates to the communications field, particularly the building method of LDPC sign indicating number.

Background technology

Communication system adopts channel coding technology to guarantee the reliability in noisy communication channel communication usually.Such as, in satellite communication system, because there are a large amount of noise sources in geography and Effect of Environmental.These communication channels have its theoretic maximum communication capacity (just famous shannon limit), and this capacity can use the bit rate (bps) under the 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) sign indicating number.

The LDPC sign indicating number is a kind of linear block codes; It can obtain the performance near shannon limit in great amount of data transmission and memory channel; Be widely used in the various wireless communication systems; For example second generation satellite digital video broadcast standard (DVB-S2), China's military satellite communication system and global microwave H insert H interoperability technology (WiMax) etc., and 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 sign indicating number is not widely used, and is because there are a plurality of defectives in it, and one of them defective is exactly that the coding techniques of LDPC sign indicating number is very complicated.If use the generator matrix of LDPC sign indicating number that information is encoded, need non-sparse check matrix of storage, and for the performance of pursuing the LDPC sign indicating number requires the code length long enough, this just causes this sparse check matrix can be very big, brings very big problem to storage.Following defective is arranged aspect design of encoder: one, the check matrix of traditional LDPC sign indicating number has stochastic behaviour; Need store a non-sparse check matrix during decoding; And require the code length long enough for the performance of pursuing the LDPC sign indicating number; This just causes this sparse check matrix can be very big, brings very big problem to storage; Two, have contradiction between the decoder throughput of traditional LDPC sign indicating number and the implementation complexity, if use serial decoding, then throughput must be very low, if use complete parallel or part parallel decoding, then the read-write of memory control must become quite loaded down with trivial details.

Summary of the invention

In order to overcome the deficiency of prior art, the object of the present invention is to provide the building method of the LDPC sign indicating number of simplicity of design.

The object of the invention is realized through following technical scheme:

The building method of LDPC sign indicating number may further comprise the steps:

(1) confirms the sparse check matrix H of first kind LDPC sign indicating number 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 the formula _{I, j}For size is the matrix of P * P, the row of each matrix is heavy all to be fixed value 1 or 0, is obtained through cyclic shift by unit matrix I or null matrix; 1≤i≤m wherein, 1≤j≤n;

corresponding informance bit part in the formula; Size is mP * kP, wherein k=n-m;

has 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 represented of

upper right corner a 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 the degree of parallelism P and the parameter n of ldpc code decoder according to the demand of the communication system that is designed, then the code length of LDPC sign indicating number is nP, and wherein the value of parameter n is the common multiple of all code check denominators of communication system of being designed; 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, being defined as of said mother matrix Matrix C: use matrix H _{I, j}The row mark of 1 position replaces in first row

In H _{I, j}, the matrix that uses the full null matrix of 0 replacement to obtain;

(4) according to the motherboard Matrix C of structure, use with the motherboard Matrix C in the corresponding submatrix H of each nonzero element _{I, j}Substitute the nonzero element in the mother matrix Matrix C, use full null matrix to replace the neutral element in the 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 following: the value of nonzero element is submatrix H _{I, j}First row in the row mark of 1 position.

Can also construct the step of the method for the second type of LDPC sign indicating number that is associated with said first kind LDPC sign indicating number behind the completing steps (4):

(5) to H ¹The row of matrix is pressed following rank order:

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

Submatrix

size is mP * kP in formula after obtaining resequencing;

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

Then the row of submatrix

are arranged according to following order

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

Promptly obtain the sparse check matrix H of second type of LDPC sign indicating number ²

The submatrix of step (4) structure also satisfies following restrictive condition:

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

(b) value of column weight has two at most, 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 arrange from big to small from left to right, corresponding to information bit from the highest significant bit to minimum effective bit;

(d) with

The check matrix H of forming ¹Ring length is not 4 ring.

Parameter combinations (the w that the said basis of step (3) searches _Row, w _Col, k ₂), structure motherboard Matrix C specifically may further comprise the steps:

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

(3-1-1) produce w at random _ColNumbers different between individual [1, m] are listed as the rower that non-0 element belongs to, 1≤i≤k as i in the motherboard Matrix C ₂If the heavy w that equaled of the row that rower is corresponding _Row, then will equal the heavy rower of row and be adjusted into the heavy minimum rower of row in nonoptional rower in the prostatitis;

(3-1-2) produce w at random _ColThe nonzero element that number between individual [1, P] is listed as as i in the motherboard Matrix C: said w _ColNumber satisfies: the value of (1) adjacent two row nonzero elements is different; (2) this w _ColThe value of any row corresponding row during any two values are listed as with the i-1 that produces before in the individual value is inequality;

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

(3-2-1) produce numbers different between 3 [1, m] at random and be listed as the rower that non-0 element belongs to, k as i in the motherboard Matrix C ₂+ 1≤i≤k; If the heavy w that equaled of the row that rower is corresponding _Row, then will equal the heavy rower of row and be adjusted into the heavy minimum rower of row in nonoptional rower in the prostatitis;

(3-2-2) produce the nonzero element of 3 numbers between [1, P] as i row among the C at random: said 3 numbers satisfy: the value of (1) adjacent two row nonzero elements is different; The value of any row corresponding row during (2) any two values are listed as with the i-1 that produces before in these 3 values is inequality;

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

The said 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 the scope, search and satisfy 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 sign indicating number that obtains with 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 uses size to replace neutral element wherein as the full null matrix of 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 simply be searched for just can construct and had uniform enconding complexity and the low first kind LDPC sign indicating number of required storage;

(2) sparse check matrix of the first kind LDPC sign indicating number of structure can be obtained the check matrix of second type of LDPC sign indicating number through the ordering of simple row and column; These two kinds of LDPC sign indicating number close relation; In practical application; If known a kind of yard coder then can simply sort to check digit at the input of the output of encoder and decoder and can obtain the coder of another kind of sign indicating number, greatly simplified design difficulty;

(3) in the first kind LDPC sign indicating number construction process, it is identical just to construct a plurality of code checks through simple substitution, and the first kind LDPC sign indicating number that code length is different has been simplified design difficulty greatly.

Description of drawings

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

Fig. 2 is the cycle characteristics sketch map of the sparse check matrix of second type of LDPC sign indicating number.

Embodiment

Below in conjunction with embodiment and accompanying drawing, the present invention is done to specify further, but execution mode of the present invention is not limited thereto.

Embodiment

As shown in Figure 1, the building method of LDPC sign indicating number of the present invention may further comprise the steps:

(1) confirms the sparse check matrix H of first kind LDPC sign indicating number 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 the formula _{I, j}For size is the matrix of P * P, the row of each matrix is heavy to be fixed value 1 or 0 all, is to be obtained through cyclic shift by unit matrix I or null matrix; 1≤i≤m wherein, 1≤j≤n;

corresponding informance bit part in the formula; Size is mP * kP, wherein k=n-m;

has 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 represented of

upper right corner a 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 sign indicating number coding has linear complexity, and the characteristics of

matrix have guaranteed that LDPC code coding/decoding utensil has lower memory space.

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

Simple and practical for the check matrix that makes structure, can do with limit

:

(a)

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

(b)

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

(d) with The check matrix H that the combination back is formed 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 any two adjacent non-zero submatrices H _{I, j}And H _{I+1, j}Inequality.According to

Characteristics can know, like this

With H after the combination ¹Just can not constitute ring length and be 4 ring.

Search procedure is specially:

Know w according to condition (b) _ColThe hunting zone be 3≤w _Col≤m, and by matrix

In 1 number is fixing can know:

(3k ₁+w _colk ₂)P＝mPw _row(1)

Again because w _Col>=3, k ₁+ k ₂=k, therefore:

k ₂＝(mw _row-3k)/(w _col-3)(2)

w _row≥3k/m (3)

To sum up can know w _RowThe hunting 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) in the scope of appointment, search for, search and satisfy 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, being defined as of said mother matrix Matrix C: use matrix H _{I, j}The row mark of 1 position substitutes in first row

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

In H _{I, j}

Specifically may further comprise the steps of structure motherboard Matrix C:

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

(3-1-1) produce w at random _ColNumbers different between individual [1, m] are listed as the rower that non-0 element belongs to, 1≤i≤k as i among the C ₂If the heavy w that equaled of the row that rower is corresponding _Row, then will equal the heavy rower of row and be adjusted into the heavy minimum rower of row in nonoptional rower in the prostatitis;

(3-1-2) produce w at random _ColThe nonzero element that number between individual [1, P] is listed as as i among the C: said w _ColNumber satisfies: the value of (1) adjacent two row nonzero elements is different; (2) this w _ColThe value of any row corresponding row during any two values are listed as with the i-1 that produces before in the individual value is inequality; If do not satisfy wherein one, then need adjust this w _ColThe position of number.If through the value that does not still satisfy condition after the several times adjustment, then need restart the search procedure of (3-1-2).Still do not find suitable value if pass through several times (3-1-2) process again, then return (3-1-1) and search for again till satisfying condition;

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

(3-2-1) produce numbers different between 3 [1, m] at random and be listed as the rower that non-0 element belongs to, k as i among the C ₂+ 2≤i≤k; If the heavy w that equaled of the row that rower is corresponding _Row, then will equal the heavy rower of row and be adjusted into the heavy minimum rower of row in nonoptional rower in the prostatitis;

(3-2-2) produce the nonzero element of 3 numbers between [1, P] as i row among the C at random: said 3 numbers satisfy: the value of (1) adjacent two row nonzero elements is different; The value of any row corresponding row during (2) any two values are listed as with the i-1 that produces before in these 3 values is inequality;

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

(4) according to the motherboard Matrix C of structure, use with the motherboard Matrix C in the corresponding submatrix H of each element value _{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 following: the value of nonzero element is submatrix H _{I, j}First row in the row mark of 1 position, for example nonzero element is 3, then its corresponding submatrix H _{I, j}First the row in 1 be positioned at the 3rd row.

Can be known by top search condition, if the motherboard Matrix C satisfies the search condition that parameter is P, then necessarily satisfy the structural environment of the motherboard matrix of P '＞P, be the submatrix H of P ' * P ' with size therefore _{I, j}Element in the replaced C can obtain the submatrix that parameter is P ' time

The LDPC sign indicating number 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 uses size to replace neutral element wherein as the full null matrix of P ' * P ', obtains matrix Associate(d) matrix again Obtain sparse check matrix

According to H ¹" encode;

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

If input information bits s=is [s ₁, s ₂, L, s _KP], the check bit p=[p that calculates ₁, p ₂, L, p _MP], then the coding method of first kind LDPC sign indicating number is following:

Step 1: utilize input information 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

representes the addition among the GF (2).

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

Code word c=[c behind the coding ₁, c ₂, L, c _NP]=[s|p].

Construct the sparse check matrix H of the second type of LDPC sign indicating number that is associated with first kind LDPC sign indicating number if desired ², then can carry out through following steps:

To H ¹The row of matrix is pressed following rank order:

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

Submatrix

size is mP * kP in

formula after obtaining resequencing;

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

Then the row of submatrix

are arranged according to 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 second type of LDPC sign indicating number ²

Second type of LDPC sign indicating number is that non-canonical repeats accumulation sign indicating number (IRA), the sparse check matrix H of such LDPC sign indicating number ²Following characteristic 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

is triangle battle array under the notch cuttype:

The characteristics of

matrix have guaranteed that LDPC sign indicating number coding has linear complexity, and the characteristics of

matrix have guaranteed that LDPC code coding/decoding utensil 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 among the figure representes that the element on the check matrix correspondence position is 1, and colourless square corresponds to 0.Can find out by Fig. 2; The row at the square of same numeral place number can be by the row number decision of the square of same label in any row; Therefore the square row difference of two row same numerals that face mutually is fixed as m=2mod (mP) (mod is modulo operation, wherein P=16), each A in this case _iOnly need in storage one row 1 row number, then the row through calculating other row number.Generally storing the row number at 1 place in the 1st row, also is initial verification address.

The coding of second type of LDPC sign indicating number (being the IRA sign indicating number) divides following two steps to carry out:

Step 1: utilize input information 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

representes the addition among the GF (2).

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

Code word c=[c behind the coding ₁, c ₂, L, c _NP]=[s|p].

Discuss the relation between two types of LDPC sign indicating numbers below.

At first contrast the difference part of both check matrixes:

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

cH ^T＝0(7)

Can know by formula (7), the row of check matrix H is exchanged the result who does not influence formula (6), just not influence coding result.We can be at first with H thus ¹Row adjust (matrix after the note adjustment is:

Matrix after the feasible adjustment

Part satisfies second type of LDPC sign indicating number

Form, just each size all need satisfy characteristic of circular matrix for the matrix in block form of mP * P.For this reason, we discuss H ¹In the matrix by H _{1, i}, H _{2, i}..., H _{M, i}The size that submatrix is formed 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 a matrix in order and (be designated as B _j, 1≤j≤P), and then with B _jForm in order matrix A ' _i:

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

Because submatrix H _{I, j}Be to be obtained through cyclic shift by unit matrix I, have characteristic: a is listed as the mobile element that circulates downwards just can obtain a+1 row (if 1 place behavior last column that a is listed as, then next behavior first is gone, 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 found out A ' easily thus _iThe circulation downwards of a row move m element and just can obtain a+1 and be listed as.That is to say A ' _iIt is circular matrix.Because all A ' _i(wherein 1≤i≤k) obtains circular matrix so matrix through identical row adjustment

Satisfy second type of LDPC sign indicating number

Characteristic, wherein:

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

Must, with matrix H ¹Row arrange again according to following order, can make the adjustment after matrix H ¹'

Part satisfies second type of LDPC sign indicating number

Form:

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

(8)

Can know by top analysis, 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, obtain successively then $p_{P+1}=x_{P+1}\&CirclePlus;{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA0000104845430000012.png"\; state="\{\{state\}\}">p</figure-callout>}}_1,$ $p_{2P+1}=x_{2P+1}\&CirclePlus;p_{P+1},...,p_{(m-1)P+1}=x_{(m-1)P+1}\&CirclePlus;p_{(m-2)\mathrm{<figure-callout\; id="1"\; label="P\; +"\; filenames="HDA0000104845430000012.png"\; state="\{\{state\}\}">P</figure-callout>}+1},{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA0000104845430000012.png"\; state="\{\{state\}\}">p</figure-callout>}}_2=x_2\&CirclePlus;p_{(m-1)\mathrm{<figure-callout\; id="1"\; label="P\; +"\; filenames="HDA0000104845430000012.png"\; state="\{\{state\}\}">P</figure-callout>}+1},...,$ $p_{\mathrm{MP}}=x_{\mathrm{MP}}\&CirclePlus;p_{(m-1)P}.$

If:

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

Can know x by formula (6) _iWith Row corresponding one by one, according to With

Corresponding relation can know that the corresponding relation of x and x ' is:

{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)

Then 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.Can know H from top derivation ¹With H ²Difference between the code word is that the check digit order is different, and that the order of check digit correspondence is H _pThe order of rectangular array, hence one can see that, will

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

Because just there is difference in two types of LDPC sign indicating numbers of being constructed on the order of check digit; If therefore the coder of known one type of LDPC sign indicating number will be constructed the coder of another kind of LDPC sign indicating number; Only need sort to the input of the output of encoder and decoder gets final product, and does not need extra modification.

Known H ¹, obtain H after the ordering 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', then

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

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 all to be fixed value (being not limited to 1 and 0), when row heavily is r _wThe time, H ' _{I, j}Be by r _wThe unit matrix I of individual different process cyclic shift adds up and obtains.

The foregoing description is a preferred implementation of the present invention; But execution mode of the present invention is not limited by the examples; Other any do not deviate from change, the modification done under spirit of the present invention and the principle, substitutes, combination, simplify; All should be the substitute mode of equivalence, be included within protection scope of the present invention.

Claims (6)

1.LDPC the building method of sign indicating number is characterized in that, may further comprise the steps:

(1) confirms the sparse check matrix H of first kind LDPC sign indicating number ¹Structure, H ¹Size is mP * nP, has following form:

$H^1=\left[H_s^1\right|H_p^1]=\left[\begin{array}{cccccc}{H}_{\mathrm{1,1}}& L& H_{1,k}& H_{1,k+1}& L& H_{1,n}\\ H_{\mathrm{2,1}}& L& H_{2,k}& H_{2,k+1}& L& H_{2,n}\\ M& O& M& M& O& M\\ H_{m,1}& L& H_{m,k}& H_{m,k+1}& L& H_{m,n}\end{array}\right]$

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

corresponding informance bit part in the formula; Size is mP * kP, wherein k=n-m;

has following structure:

$H_p^1=\left[\begin{array}{ccccccc}I& 0& 0& L& 0& 0& a\\ I& I& 0& L& 0& 0& 0\\ 0& I& I& L& 0& 0& 0\\ L& L& O& O& L& L& L\\ 0& 0& 0& L& I& 0& 0\\ 0& 0& 0& L& I& I& 0\\ 0& 0& 0& L& 0& I& I\end{array}\right];$

Wherein the matrix represented of upper right corner a 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 the degree of parallelism P and the parameter n of ldpc code decoder according to the demand of the communication system that is designed, then the code length of LDPC sign indicating number is nP, and wherein the value of parameter n is the common multiple of all code check denominators of communication system of being designed; 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, being defined as of said mother matrix Matrix C: use matrix H _{I, j}The row mark of 1 position replaces in first row

In H _{I, j}, the matrix that uses the full null matrix of 0 replacement to obtain;

(4) according to the motherboard Matrix C of structure, use with the motherboard Matrix C in the corresponding submatrix H of each nonzero element _{I, j}Substitute the nonzero element in the mother matrix Matrix C, use full null matrix to replace the neutral element in the 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 following: the value of nonzero element is submatrix H _{I, j}First row in the row mark of 1 position.

2. the building method of LDPC sign indicating number according to claim 1 is characterized in that, completing steps

(4) also construct the step of the method for the second type of LDPC sign indicating number that is associated with said first kind LDPC sign indicating number after:

(5) to H ¹The row of matrix is pressed following rank order:

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

Submatrix size is mP * kP in

formula after obtaining resequencing; size is mP * mP, wherein k=n-m;

Then the row of submatrix are arranged according to following order

1, P+1 ..., (m-1) P+1,2, P+2 ..., (m-1) P+2, P, 2P ..., mP obtains the sparse check matrix H of second type of LDPC sign indicating number ²

3. the building method of LDPC sign indicating number according to claim 1; It is characterized in that the submatrix

of step (4) structure satisfies following restrictive condition:

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

(b) value of column weight has two at most, 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 arrange from big to small from left to right, corresponding to information bit from the highest significant bit to minimum effective bit;

(d) with The check matrix H of forming ¹Ring length is not 4 ring.

4. the building method of LDPC sign indicating number according to claim 3 is characterized in that, the parameter combinations (w that the said basis of step (3) searches _Row, w _Col, k ₂), structure motherboard Matrix C specifically may further comprise the steps:

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

(3-1-1) produce w at random _ColNumbers different between individual [1, m] are listed as the rower that non-0 element belongs to, 1≤i≤k as i in the motherboard Matrix C ₂If the heavy w that equaled of the row that rower is corresponding _Row, then will equal the heavy rower of row and be adjusted into the heavy minimum rower of row in nonoptional rower in the prostatitis;

(3-1-2) produce w at random _ColThe nonzero element that number between individual [1, P] is listed as as i in the motherboard Matrix C: said w _ColNumber satisfies: the value of (1) adjacent two row nonzero elements is different; (2) this w _ColThe value of any row corresponding row during any two values are listed as with the i-1 that produces before in the individual value is inequality;

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

(3-2-1) produce numbers different between 3 [1, m] at random and be listed as the rower that non-0 element belongs to, k as i in the motherboard Matrix C ₂+ 1≤i≤k; If the heavy w that equaled of the row that rower is corresponding _Row, then will equal the heavy rower of row and be adjusted into the heavy minimum rower of row in nonoptional rower in the prostatitis;

(3-2-2) produce the nonzero element of 3 numbers between [1, P] as i row in the motherboard Matrix C at random: said 3 numbers satisfy: the value of (1) adjacent two row nonzero elements is different; The value of any row corresponding row during (2) any two values are listed as with the i-1 that produces before in these 3 values is inequality;

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

5. the building method of LDPC sign indicating number according to claim 3 is characterized in that, the said 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 the scope, search and satisfy k ₂=(mw _Row-3k)/(w _Col-3), and k ₂Combination (w for nonnegative integer _Row, w _Col, k ₂) be rational combination.

6. the building method of LDPC sign indicating number 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 sign indicating number that obtains with 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 uses size to replace neutral element wherein as the full null matrix of P ' * P ', obtains matrix

Associate(d) matrix again

Obtain sparse check matrix $H^{1\&prime;\&prime;}=\left[H_s^{1\&prime;\&prime;}\right|H_p^{1\&prime;\&prime;}].$

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