CN101335528A - Construction method and encoding method for multiple LDPC code - Google Patents

Abstract

The invention belongs to the communication technology field, particularly relates to a structuring method of a multi-LDPC code. The method comprises steps as follows: the check matrix H of the multi-LDPC code is a partitioned matrix which consists of (m multiplying n) sub-matrixes of H<i, j>, and each sub-matrix H<i, j> is obtained from that a scale factor beta<i, j> epsilon GF(q) is multiplied by a unit matrix of (1 multiplying 1) and then left moved by s<i, j> times according to a line cycle; wherein, GF(q) is a finite field having q elements; the check matrix H of the multi-LDPC code can be divided into two parts, namely, H is equal to (H1H2); wherein, the H2 is a dual partitioned diagonal matrix with a size of m multiplying m and the H1 consists of sub-matrixes left in the H; the H1 corresponds to information symbols and the H2 corresponds to check symbols. In addition, the invention also provides a fast coding method applicable to the invented multi-LDPC code.

Description

A kind of building method of multielement LDPC code and coding method

Technical field

The invention belongs to communication technique field, particularly a kind of building method of multielement LDPC code and coding method.

Technical background

Low-density parity check sign indicating number (LDPC sign indicating number) is a kind of linear block codes of the Shannon of approaching limit, can be described by check matrix.As far back as 1962, Gallager just proposed the LDPC sign indicating number, and had proved that this sign indicating number can be than other error correcting code more near the Shannon limit.Yet,, do not attracting much attention at that time because its complexity is higher.Along with the proposition of Turbo code, nineteen ninety-five, Mackay and Neal have found the LDPC sign indicating number again.From then on the LDPC sign indicating number causes people's extensive concern.

According to the production process of check matrix, the LDPC sign indicating number can be divided into stochastic pattern and structural type two big classes.When code length is longer, produce the check matrix of a sparse matrix at random as the LDPC sign indicating number, the performance of this yard just can be limit near Shannon very much.Yet the encoder complexity of stochastic pattern LDPC sign indicating number is higher, is only applicable to the theoretical research aspect.In recent years, people had proposed the structural type LDPC sign indicating number of a lot of function admirables on the basis of algebraical sum finite geometry.

At present, most research work and patent of invention are at binary LDPC sign indicating number.Some have efficiently, the structural type binary LDPC sign indicating number of fast coding algorithm is widely applied in the various communication standards, as 3GPP2,802.16e, 802.11n or the like.Compare with binary LDPC sign indicating number, the research work of multielement LDPC code is less relatively.Davey in 1998 and MacKay emulation have by experiment confirmed that under the same conditions the bit error rate of multielement LDPC code (BER) performance is better than binary LDPC sign indicating number, point out under the situation of identical BER, adopt multielement LDPC code can obtain the coding gain of about 1dB.Especially, multielement LDPC code can combine with high order modulation, thereby saves the transmitting power of limited bandwidth communication system.But there are a lot of problems in existing multielement LDPC code, comprises higher memory space and complicated aspects such as cataloged procedure.

Summary of the invention

At the shortcoming of prior art, the purpose of this invention is to provide a kind of building method and coding method of multielement LDPC code.The building method that is proposed has solved the memory space problem of multielement LDPC code; And the designed coding method that goes out can make multielement LDPC code better be applied in practice.

For achieving the above object, technical scheme of the present invention is: a kind of building method of multielement LDPC code, and it may further comprise the steps:

A. the check matrix H of multielement LDPC code is the matrix in block form on the finite field gf (q), by (m * n) individual submatrix constitutes; Be positioned at the capable submatrix H with j row crossover location of the i of check matrix H _IjBe by scale factor β _{I, j}∈ GF (q) multiply by one and (behind the unit matrix of l * l), presses row ring shift left s again _{I, j}Inferior obtaining, 0≤i≤m-1 wherein, 0≤j≤n-1,0≤s _{I, j}≤ l-1;

B. the check matrix of multielement LDPC code is adjusted in proper order through row and be divided into left and right sides two parts: H=(H ₁H ₂), H wherein ₂By (m * m) individual submatrix constitutes, and a corresponding m length is the syndrome sequence of l, and H ₁Be made of submatrix remaining in the check matrix H, corresponding (n-m) individual length is the information subsequence of l;

C. the matrix H of corresponding syndrome sequence in the check matrix H with multielement LDPC code ₂Through the space order be adjusted into a size for (the piecemeal biconjugate angular moment battle array of m * m),

$H_2=\left[\begin{array}{cccccccc}{H}_{0,\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">k</figure-callout>}}& 0& 0& 0& ...& 0& 0& 0\\ {\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">H</figure-callout>}}_{1,k}& {\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">H</figure-callout>}}_{1,k+1}& 0& 0& ...& 0& 0& 0\\ 0& H_{2,k+1}& H_{2,k+2}& 0& ...& 0& 0& 0\\ .& .& .& .& ...& .& .& .\\ .& .& .& .& ...& .& .& .\\ .& .& .& .& ...& .& .& .\\ 0& 0& 0& 0& ...& H_{m-2,n-3}& H_{m-2,n-2}& 0\\ 0& 0& 0& 0& ...& 0& H_{m-1,n-2}& H_{m-1,n-1}\end{array}\right]---\left(1.1\right),$

K=n-m wherein.

In step a, piecemeal submatrix H _{I, j}Be a yardstick circular matrix,

$H_{i,j}={\mathrm{\&beta;}}_{i,j}{P}^{s_{i,j}}---\left(1.2\right),$

Wherein P is by (the matrix that the unit matrix ring shift left of l * l) obtains for 1 time.

Matrix H ₂In, the scale factor of the submatrix on the leading diagonal is 1, and the scale factor of the submatrix on the minor diagonal is α, and wherein α is the primitive element of GF (q), at this moment H ₂Be specifically described as:

$H_2=\left[\begin{array}{cccccccc}{\mathrm{<figure-callout\; id="0"\; label="P\; s"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">P</figure-callout>}}^{s_{}}& 0& 0& 0& ...& 0& 0& 0\\ \mathrm{\&alpha;}{\mathrm{<figure-callout\; id="1"\; label="P\; s"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">P</figure-callout>}}^{s_{}}& P^{s_{}}{{}_{1,k+1}}^{}& 0& 0& ...& 0& 0& 0\\ 0& \mathrm{\&alpha;}{P}^{s_{2,k+1}}& P^{s_{2,k+2}}& 0& ...& 0& 0& 0\\ .& .& .& .& ...& .& .& .\\ .& .& .& .& ...& .& .& .\\ .& .& .& .& ...& .& .& .\\ 0& 0& 0& 0& ...& \mathrm{\&alpha;}{P}^{s_{m-2,n-3}}& P^{s_{m-2,n-2}}& 0\\ 0& 0& 0& 0& ...& 0& \mathrm{\&alpha;}{P}^{s_{m-1,n-2}}& P^{s_{m-1,n-1}}\end{array}\right]---\left(1.3\right).$

From GF (q), choose k nonzero element β ₀, β ₁..., β _K-1As matrix H ₁In the scale factor of k submatrix of the 0th row, the scale factor of k the submatrix that corresponding i is capable is respectively β ₀ ^I+1, β ₁ ^I+1..., β _K-1 ^I+1, this moment H ₁Be a class Fan Demeng matrix, be specifically described as:

${\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">H</figure-callout>}}_1=\left[\begin{array}{cccc}{\mathrm{\&beta;}}_0{\mathrm{<figure-callout\; id="0"\; label="P\; s"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">\; <figure-callout\; id="0"\; label="P\; s"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">P</figure-callout>\; </figure-callout>}}^{s_{}{}_{}}& {\mathrm{\&beta;}}_1{\mathrm{<figure-callout\; id="0"\; label="P\; s"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">\; <figure-callout\; id="1"\; label="P\; s"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">P</figure-callout>\; </figure-callout>}}^{s_{}{}_{}}& ...& {\mathrm{\&beta;}}_{k-1}{\mathrm{<figure-callout\; id="0"\; label="P\; s"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">P</figure-callout>}}^{s_{}}\\ {\mathrm{\&beta;}}_0^2{\mathrm{<figure-callout\; id="1"\; label="P\; s"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">\; <figure-callout\; id="0"\; label="P\; s"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">P</figure-callout>\; </figure-callout>}}^{s_{}{}_{}}& {\mathrm{\&beta;}}_1^2{\mathrm{<figure-callout\; id="1"\; label="P\; s"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">\; <figure-callout\; id="1"\; label="P\; s"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">P</figure-callout>\; </figure-callout>}}^{s_{}{}_{}}& ...& {\mathrm{\&beta;}}_{k-1}^2{\mathrm{<figure-callout\; id="1"\; label="P\; s"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">P</figure-callout>}}^{s_{}}\\ .& .& ...& .\\ .& .& ...& .\\ .& .& ...& .\\ {\mathrm{\&beta;}}_0^m{P}^{s_{m-\mathrm{1,0}}}& {\mathrm{\&beta;}}_1^m{P}^{s_{m-\mathrm{1,1}}}& ...& {\mathrm{\&beta;}}_{k-1}^m{P}^{s_{m-1,k-1}}\end{array}\right]---\left(1.4\right).$

In addition, the invention provides a kind of coding method of multielement LDPC code, the coding method of multielement LDPC code directly realizes by the check matrix of above-mentioned multielement LDPC code; Regard codeword sequence the set of length as for a plurality of subsequences of l, c=( u ⁽⁰⁾, u ⁽¹⁾..., u ^(k-1), v ⁽⁰⁾, v ⁽¹⁾..., v ^(m-1)), wherein u ^(j)(0≤j≤k-1) be long be the information subsequence of l, v ⁽ⁱ⁾(0≤i≤m-1) be long be the syndrome sequence of l, coding method may further comprise the steps:

(1) initialization is the information sequence of kl with length uBe divided into k subsequence, u=( u ⁽⁰⁾, u ⁽¹⁾..., u ^(k-1)Order v ⁽¹⁾= 0

(2), calculate i syndrome sequence according to the flow process of accompanying drawing 1 for 0≤i≤m-1 v ⁽ⁱ⁾: for 0≤j≤k-1, j information subsequence u ^(j)At first be recycled the s that moves to right _{I, j}Inferior, and then multiply by scale factor β _j ^I+1, the vector beta that to obtain a length be l _j ^I+1 u ^(j)h _{I, j} ^T, h wherein _{I, j}Be by (the unit matrix ring shift left s of l * l) _{I, j}Inferior obtaining, $h_{i,j}=P^{s_{i,j}};$ With i-1 syndrome sequence v ^(i-1)Ring shift right S _{I, k+i-1}The vector inferior, and then multiply by scale factor α, that to obtain a length be l v ^(i-1)h _{I, k+i-1} ^TWith all vector additions that the operation of its first two steps obtains, obtain a length and be l's and vector; This and vector be multiply by-1, and then ring shift left s _{I, k+i}Inferior, obtain vector ${\underset{\&OverBar;}{v}}^{\left(i\right)}=-(\underset{j=0}{\overset{k-1}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_j^{i+1}{\underset{\&OverBar;}{u}}^{\left(j\right)}{h}_{i,j}^T+\mathrm{\&alpha;}{\underset{\&OverBar;}{v}}^{(i-1)}{h}_{i,k+i-1}^T){\left(h_{i,k+i}^T\right)}^{-1}.$

Compared with prior art, the present invention constructs a kind of multielement LDPC code, and this sign indicating number is a kind of systematic code.Because check matrix is to be made of yardstick piecemeal circulation submatrix, therefore reduced the memory space of multielement LDPC code.On the basis of new building method, design a kind of efficiently coding method fast, multielement LDPC code can finely be got be applied in practice.

Description of drawings

Fig. 1 calculates the flow chart of i syndrome sequence for the present invention;

Fig. 2 is the BER performance curve of multielement LDPC code of the present invention.

Embodiment

Embodiment 1

If GF (q) is a finite field with q element, α is a primitive element.A code length is N, and dimension is that the multielement LDPC code C of K can be described by a polynary check matrix H.The dimension of this check matrix is (M * N).A vector c=(c ₁, c ₂..., c _N-1) be that and if only if for a code word among the C cH ^T= 0, H wherein ^TThe transposition of representing matrix H, 0Represent one long be the full null vector of M.

The structure of multielement LDPC code mainly is divided into two and goes on foot greatly: the structure of matrix in block form and the replacement of nonzero element, and it may further comprise the steps:

A. the check matrix H of multielement LDPC code is the matrix in block form on the finite field gf (q), by (m * n) individual submatrix constitutes; Be positioned at the capable submatrix H with j row crossover location of the i of check matrix H _{I, j}Be by scale factor β _{I, j}∈ GF (q) multiply by one and (behind the unit matrix of l * l), presses row ring shift left s again _{I, j}Inferior obtaining, 0≤i≤m-1 wherein, 0≤j≤n-1,0≤s _{I, j}≤ l-1;

B. the check matrix of multielement LDPC code is adjusted in proper order through row and be divided into left and right sides two parts: H=(H ₁H ₂), H wherein ₂By (m * m) individual submatrix constitutes, and a corresponding m length is the syndrome sequence of l, and H ₁Be made of submatrix remaining in the check matrix H, corresponding (n-m) individual length is the information subsequence of l;

C. the matrix H of corresponding syndrome sequence in the check matrix H with multielement LDPC code ₂Through the space order be adjusted into a size for (the piecemeal biconjugate angular moment battle array of m * m),

$H_2=\left[\begin{array}{cccccccc}{H}_{0,\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">k</figure-callout>}}& 0& 0& 0& ...& 0& 0& 0\\ {\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">H</figure-callout>}}_{1,k}& {\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">H</figure-callout>}}_{1,k+1}& 0& 0& ...& 0& 0& 0\\ 0& H_{2,k+1}& H_{2,k+2}& 0& ...& 0& 0& 0\\ .& .& .& .& ...& .& .& .\\ .& .& .& .& ...& .& .& .\\ .& .& .& .& ...& .& .& .\\ 0& 0& 0& 0& ...& H_{m-2,n-3}& H_{m-2,n-2}& 0\\ 0& 0& 0& 0& ...& 0& H_{m-1,n-2}& H_{m-1,n-1}\end{array}\right]---\left(1.1\right),$

K=n-m wherein.

In step a, piecemeal submatrix H _{I, j}Be a yardstick circular matrix,

$H_{i,j}={\mathrm{\&beta;}}_{i,j}{P}^{s_{i,j}}---\left(1.2\right),$

Wherein P is by (the matrix that the unit matrix ring shift left of l * l) obtains for 1 time.

Matrix H ₂In, the scale factor of the submatrix on the leading diagonal is 1, and the scale factor of the submatrix on the minor diagonal is α, and wherein α is the primitive element of GF (q), at this moment H ₂Be specifically described as:

$H_2=\left[\begin{array}{cccccccc}{\mathrm{<figure-callout\; id="0"\; label="P\; s"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">P</figure-callout>}}^{s_{}}& 0& 0& 0& ...& 0& 0& 0\\ \mathrm{\&alpha;}{\mathrm{<figure-callout\; id="1"\; label="P\; s"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">P</figure-callout>}}^{s_{}}& P^{s_{}}{{}_{1,k+1}}^{}& 0& 0& ...& 0& 0& 0\\ 0& \mathrm{\&alpha;}{P}^{s_{2,k+1}}& P^{s_{2,k+2}}& 0& ...& 0& 0& 0\\ .& .& .& .& ...& .& .& .\\ .& .& .& .& ...& .& .& .\\ .& .& .& .& ...& .& .& .\\ 0& 0& 0& 0& ...& \mathrm{\&alpha;}{P}^{s_{m-2,n-3}}& P^{s_{m-2,n-2}}& 0\\ 0& 0& 0& 0& ...& 0& \mathrm{\&alpha;}{P}^{s_{m-1,n-2}}& P^{s_{m-1,n-1}}\end{array}\right]---\left(1.3\right).$

From GF (q), choose k nonzero element β ₀, β ₁..., β _K-1As matrix H ₁In the scale factor of k submatrix of the 0th row, the scale factor of k the submatrix that corresponding i is capable is respectively β ₀ ^I+1, β ₁ ^I+1..., β _K-1 ^I+1, this moment H ₁Be a class Fan Demeng matrix, be specifically described as:

${\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">H</figure-callout>}}_1=\left[\begin{array}{cccc}{\mathrm{\&beta;}}_0{\mathrm{<figure-callout\; id="0"\; label="P\; s"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">\; <figure-callout\; id="0"\; label="P\; s"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">P</figure-callout>\; </figure-callout>}}^{s_{}{}_{}}& {\mathrm{\&beta;}}_1{\mathrm{<figure-callout\; id="0"\; label="P\; s"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">\; <figure-callout\; id="1"\; label="P\; s"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">P</figure-callout>\; </figure-callout>}}^{s_{}{}_{}}& ...& {\mathrm{\&beta;}}_{k-1}{\mathrm{<figure-callout\; id="0"\; label="P\; s"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">P</figure-callout>}}^{s_{}}\\ {\mathrm{\&beta;}}_0^2{\mathrm{<figure-callout\; id="1"\; label="P\; s"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">\; <figure-callout\; id="0"\; label="P\; s"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">P</figure-callout>\; </figure-callout>}}^{s_{}{}_{}}& {\mathrm{\&beta;}}_1^2{\mathrm{<figure-callout\; id="1"\; label="P\; s"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">\; <figure-callout\; id="1"\; label="P\; s"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">P</figure-callout>\; </figure-callout>}}^{s_{}{}_{}}& ...& {\mathrm{\&beta;}}_{k-1}^2{\mathrm{<figure-callout\; id="1"\; label="P\; s"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">P</figure-callout>}}^{s_{}}\\ .& .& ...& .\\ .& .& ...& .\\ .& .& ...& .\\ {\mathrm{\&beta;}}_0^m{P}^{s_{m-\mathrm{1,0}}}& {\mathrm{\&beta;}}_1^m{P}^{s_{m-\mathrm{1,1}}}& ...& {\mathrm{\&beta;}}_{k-1}^m{P}^{s_{m-1,k-1}}\end{array}\right]---\left(1.4\right).$

Given check matrix H=(H ₁H ₂) and length be the information sequence of kl u=(u ₀, u ₁..., u _Kl-1), u wherein _i∈ GF (q), with uCorresponding codeword sequence can be written as c=( Uv), vIt is the long verification sequence of ml that is.Satisfy relation between codeword sequence and the check matrix

( uv)H ^T＝ 0 (1.7)

Therefore verification sequence can be calculated as

$\underset{\&OverBar;}{v}=-\underset{\&OverBar;}{u}{\mathrm{<figure-callout\; id="1T"\; label="H"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">H</figure-callout>}}_1^T{\left(H_2^T\right)}^{-1}---\left(1.8\right)$

The purpose of coding method is exactly the calculation check sequence vCalculate for convenience, regard codeword sequence the set of length as, promptly for a plurality of subsequences of l c=( u ⁽⁰⁾, u ⁽¹⁾..., u ^(k-1), v ⁽⁰⁾, v ⁽¹⁾..., v ^(m-1), wherein u ^(j)(0≤j≤k-1) be long be the information subsequence of l, v ⁽ⁱ⁾(0≤i≤m-1) be long be the syndrome sequence of l.The specific coding algorithm is as follows:

1. initialization.

(1) initialization is the information sequence of kl with length uBe divided into k subsequence, u=( u ⁽⁰⁾, u ⁽¹⁾..., u ^(k-1)); Order v ⁽¹⁾= 0

(2), calculate i syndrome sequence according to the flow process of accompanying drawing 1 for 0≤i≤m-1 v ⁽ⁱ⁾: for 0≤j≤k-1, j information subsequence u ^(j)At first be recycled the s that moves to right _{I, j}Inferior, and then multiply by scale factor β _j ^I+1, the vector beta that to obtain a length be l _j ^I+1 u ^(j)h _{I, j} ^T, h wherein _{I, j}Be by (the unit matrix ring shift left s of l * l) _{I, j}Inferior obtaining, $h_{i,j}=P^{s_{i,j}};$ With i-1 syndrome sequence v ^(i-1)Ring shift right S _{I, k+i-1}The vector inferior, and then multiply by scale factor α, that to obtain a length be l v ^(i-1)h _{I, k+i-1} ^TWith all vector additions that the operation of its first two steps obtains, obtain a length and be l's and vector; This and vector be multiply by-1, and then ring shift left s _{I, k+i}Inferior, obtain vector ${\underset{\&OverBar;}{v}}^{\left(i\right)}=-(\underset{j=0}{\overset{k-1}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_j^{i+1}{\underset{\&OverBar;}{u}}^{\left(j\right)}{h}_{i,j}^T+\mathrm{\&alpha;}{\underset{\&OverBar;}{v}}^{(i-1)}{h}_{i,k+i-1}^T){\left(h_{i,k+i}^T\right)}^{-1}.$

Complexity analyzing, if given parameter l, α and b, the multielement LDPC code of being invented can be unique by k field element β ₀, β ₁..., β _K-1Come to determine, thereby solved the memory space problem of multielement LDPC code.

From the encryption algorithm of being invented, as can be seen, calculate a syndrome sequence that length is l, only need (k+1) l multiplying and the computing of kl sub-addition.Say on the average meaning, calculate a checking symbol, only need k+1 multiplying and the computing of k sub-addition.Therefore its encoder complexity linear increase along with the increase of code length.

Applicating example

One, GF (16) goes up multielement LDPC code

1. parameter setting:

L=277, a=48, b=7; Can verify the rank m=3 of a, the rank n=12 of b.

2. non-null sequence is chosen:

(β ₀，β ₁，…β ₈)＝(α ²，α ⁶，α ⁹，α ³，α ⁷，α ¹¹，α ⁴，α ¹，α ¹²)。

3. correspondence code parameter

Code length: 3324; Dimension: 2493; Code check: 3/4.

4. experiment simulation

Adopt 16-QAM modulation system and awgn channel model.BER curve and corresponding Shannon limit are as shown in Figure 2.

Two, GF (32) goes up multielement LDPC code

1. parameter setting:

L=211, a=196, b=137; Can verify the rank m=3 of a, the rank n=15 of b.

2. non-null sequence is chosen:

(β ₀，β ₁，…β ₁₁)＝(α ¹，α ⁶，α ²⁶，α ²，α ⁷，α ¹²，α ¹⁷，α ²²，α ²⁷，α ³，α ⁸，α ¹³)。

3. correspondence code parameter

Code length: 3165; Dimension: 2532; Code check: 4/5.

4. experiment simulation

Adopt 32-QAM modulation system and awgn channel model.BER curve and corresponding Shannon limit are as shown in Figure 2.

Three, GF (64) goes up multielement LDPC code

1. parameter setting:

L=181, a=48, b=119; Can verify the rank m=3 of a, the rank n=18 of b.

2. non-null sequence is chosen:

(β ₀，β ₁，…β ₁₄)＝(α ¹⁹，α ²⁵，α ³¹，α ³⁷，α ⁴³，α ⁴⁹，α ⁵⁵，α ²，α ⁸，α ¹⁴，α ²⁰，α ²⁶，α ¹，α ³⁸，α ⁴⁴)。

3. correspondence code parameter

Code length: 3258; Dimension: 2715; Code check: 5/6.

4. experiment simulation

Adopt 64-QAM modulation system and awgn channel model.BER curve and corresponding Shannon limit are as shown in Figure 2.

Embodiment 2

Present embodiment illustrates the building method of multielement LDPC code with the replacement of the structure of biradical matrix and nonzero element.

1) structure of biradical matrix

To any positive integer l, all are constituted set Z less than l and those positive integers coprime with it _l ^*, these positive integers constitute a multiplicative group under mould l multiplying.Point out in the article that Tanner delivered in calendar year 2001 " LDPCBlock and Convolutional Codes Based on Circulant Matrices ": if Z _l ^*In have two element a, b, and the rank of a are arranged is m, the rank of b are n, then can be constructed as follows binary matrix H ^(b)

$H^{\left(b\right)}=\left[\begin{array}{cccc}{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">h</figure-callout>}}_{0,0}& {\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">\; <figure-callout\; id="1"\; label="h"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">h</figure-callout>\; </figure-callout>}}_{\mathrm{0,1}}& ...& {\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">h</figure-callout>}}_{0,n-1}\\ {\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">h</figure-callout>}}_{\mathrm{1,0}}& {\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">\; <figure-callout\; id="1"\; label="h"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">h</figure-callout>\; </figure-callout>}}_{\mathrm{1,1}}& ...& {\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">h</figure-callout>}}_{1,n-1}\\ .& .& ...& .\\ .& .& ...& .\\ .& .& ...& .\\ h_{m-\mathrm{1,0}}& h_{m-\mathrm{1,1}}& ...& h_{m-1,n-1}\end{array}\right]---\left(1.1\right),$

H wherein _{I, j}(submatrix of l * l), it is by unit matrix ring shift right s to be one _{I, j}=a ⁱb ^jInferior obtaining.。

Resulting binary matrix H ^(b)(sparse matrix of ml * nl), wherein the number of nonzero element is mnl to be one.This binary matrix can be written as left and right sides two parts $H^{\left(b\right)}=\left(\begin{array}{cc}{H}_1^{\left(b\right)}& H_2^{\left(b\right)}\end{array}\right),$ H wherein ₂ ^(b)Be by H ^(b)In (the individual submatrix of m * m) constitutes H ₁ ^(b)Be by H ^(b)In remaining submatrix constitute.The deletion matrix H ₂ ^(b)In some elements, be piecemeal biconjugate angular moment battle array, shown in (1.2).

${\tilde{H}}_2^{\left(b\right)}=\left[\begin{array}{cccccccc}{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">h</figure-callout>}}_{0,\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">k</figure-callout>}}& 0& 0& 0& ...& 0& 0& 0\\ {\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">h</figure-callout>}}_{1,\mathrm{<figure-callout\; id="1"\; label="k\; h"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">k</figure-callout>}}& h_{}{}_{1,k+1}& 0& 0& ...& 0& 0& 0\\ 0& h_{2,k+1}& h_{2,k+2}& 0& ...& 0& 0& 0\\ .& .& .& .& ...& .& .& .\\ .& .& .& .& ...& .& .& .\\ .& .& .& .& ...& .& .& .\\ 0& 0& 0& 0& ...& h_{m-2,n-3}& h_{m-2,n-2}& 0\\ 0& 0& 0& 0& ...& 0& h_{m-1,n-2}& h_{m-1,n-1}\end{array}\right]---(1.2)$

K=n-m wherein.

Matrix ${\tilde{H}}^{\left(b\right)}=\left(\begin{array}{cc}{H}_1^{\left(b\right)}& {\tilde{H}}_2^{\left(b\right)}\end{array}\right)$ It is the basic matrix of structure multielement LDPC code.

2) replacement of nonzero element

In order to construct multielement LDPC code, we will be the biradical matrix ${\tilde{H}}^{\left(b\right)}=\left(\begin{array}{cc}{H}_1^{\left(b\right)}& {\tilde{H}}_2^{\left(b\right)}\end{array}\right)$ In " 1 " with the element substitution in finite field gf (q).For conserve storage, our replacement principle is: each piecemeal submatrix h _{I, j}In nonzero element by same field element β _{I, j}∈ GF (q) substitutes, and is about to the piecemeal submatrix h in the biradical matrix _{I, j}Become yardstick piecemeal submatrix β _{I, j}h _{I, j}, β wherein _{I, j}Be called scale factor.

Submatrix

The Substitution Rules of middle nonzero element are: the scale factor of the piecemeal submatrix on the leading diagonal is 1; The scale factor of the piecemeal submatrix on the minor diagonal is α (α is the primitive element of GF (q)), promptly

$H_2=\left[\begin{array}{cccccccc}{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">h</figure-callout>}}_{0,\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">k</figure-callout>}}& 0& 0& 0& ...& 0& 0& 0\\ \mathrm{\&alpha;}{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">h</figure-callout>}}_{1,\mathrm{<figure-callout\; id="1"\; label="k\; h"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">k</figure-callout>}}& h_{}{}_{1,k+1}& 0& 0& ...& 0& 0& 0\\ 0& \mathrm{\&alpha;}{h}_{2,k+1}& h_{2,k+2}& 0& ...& 0& 0& 0\\ .& .& .& .& ...& .& .& .\\ .& .& .& .& ...& .& .& .\\ .& .& .& .& ...& .& .& .\\ 0& 0& 0& 0& ...& \mathrm{\&alpha;}{h}_{m-2,n-3}& h_{m-2,n-2}& 0\\ 0& 0& 0& 0& ...& 0& \mathrm{\&alpha;}{h}_{m-1,n-2}& h_{m-1,n-1}\end{array}\right]---\left(1.4\right)$

Submatrix H ₁ ^(b)The Substitution Rules of middle nonzero element are: according to certain optimization criterion (such as maximum entropy criterion), choose k nonzero element β from GF (q) ₀, β ₁..., β _K-1As H ₁ ^(b)In the scale factor of k piecemeal submatrix of the 0th row; For H ₁ ^(b)In k capable piecemeal submatrix of i, its scale factor is respectively β ₀ ^I+1, β ₁ ^I+1..., β _K-1 ^I+1, promptly

${\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">H</figure-callout>}}_1=\left[\begin{array}{cccc}{\mathrm{\&beta;}}_0{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">\; <figure-callout\; id="0"\; label="h"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">h</figure-callout>\; </figure-callout>}}_{\mathrm{0,0}}& {\mathrm{\&beta;}}_1{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">\; <figure-callout\; id="1"\; label="h"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">h</figure-callout>\; </figure-callout>}}_{\mathrm{0,1}}& ...& {\mathrm{\&beta;}}_{k-1}{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">h</figure-callout>}}_{0,k-1}\\ {\mathrm{\&beta;}}_0^2{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">\; <figure-callout\; id="0"\; label="h"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">h</figure-callout>\; </figure-callout>}}_{\mathrm{1,0}}& {\mathrm{\&beta;}}_1^2{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">\; <figure-callout\; id="1"\; label="h"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">h</figure-callout>\; </figure-callout>}}_{\mathrm{1,1}}& ...& {\mathrm{\&beta;}}_{k-1}^2{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="A20081003006200141.png"\; state="\{\{state\}\}">h</figure-callout>}}_{1,k-1}\\ .& .& ...& .\\ .& .& .& ...\\ .& .& ...& .\\ {\mathrm{\&beta;}}_0^m{h}_{m-1,0}& {\mathrm{\&beta;}}_1^m{h}_{m-1,1}& ...& {\mathrm{\&beta;}}_{k-1}^m{h}_{m-1,k-1}\end{array}\right]---\left(1.5\right)$

Through aforesaid operations, can be expressed as with multielement LDPC code corresponding check matrix H

H＝(H ₁?H ₂)(1.6)

The multielement LDPC code of being described by check matrix H is a kind of systematic code, its code length N=nl, dimension K=kl, code check r=k/n.

Claims (5)

1, a kind of building method of multielement LDPC code is characterized in that may further comprise the steps:

A. the check matrix H of multielement LDPC code is the matrix in block form on the finite field gf (q), by (m * n) individual submatrix constitutes; Be positioned at the capable submatrix H with j row crossover location of the i of check matrix H _{I, j}Be by scale factor β _{I, j}∈ GF (q) multiply by one and (behind the unit matrix of l * l), presses row ring shift left s again _{I, j}Inferior obtaining, 0≤i≤m-1 wherein, 0≤j≤n-1,0≤s _{I, j}≤ l-1;

B. the check matrix of multielement LDPC code is adjusted in proper order through row and be divided into left and right sides two parts: H=(H ₁H ₂), H wherein ₂By (m * m) individual submatrix constitutes, and a corresponding m length is the syndrome sequence of l, and H ₁Be made of submatrix remaining in the check matrix H, corresponding (n-m) individual length is the information subsequence of l;

C. the matrix H of corresponding syndrome sequence in the check matrix H with multielement LDPC code ₂Through the space order be adjusted into a size for (the piecemeal biconjugate angular moment battle array of m * m),

$H_2=\left[\begin{array}{cccccccc}{H}_{0,k}& 0& 0& 0& \&CenterDot;\&CenterDot;\&CenterDot;& 0& 0& 0\\ H_{1,k}& H_{1,k+1}& 0& 0& \&CenterDot;\&CenterDot;\&CenterDot;& 0& 0& 0\\ 0& H_{2,k+1}& H_{2,k+2}& 0& \&CenterDot;\&CenterDot;\&CenterDot;& 0& 0& 0\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& & \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& & \&CenterDot;& \&CenterDot;& \&CenterDot;\\ 0& 0& 0& 0& \&CenterDot;\&CenterDot;\&CenterDot;& H_{m-2,n-3}& H_{m-2,n-2}& 0\\ 0& 0& 0& 0& \&CenterDot;\&CenterDot;\&CenterDot;& 0& H_{m-1,n-2}& H_{m-1,n-1}\end{array}\right]---\left(1.1\right),$

K=n-m wherein.

2, the building method of multielement LDPC code according to claim 1 is characterized in that: in step a, and piecemeal submatrix H _{I, j}Be a yardstick circular matrix,

$H_{i,j}={\mathrm{\&beta;}}_{i,j}{P}^{s_{i,j}}---\left(1.2\right),$

Wherein P is by (the matrix that the unit matrix ring shift left of l * l) obtains for 1 time.

3, the building method of multielement LDPC code according to claim 2 is characterized in that: matrix H ₂In, the scale factor of the submatrix on the leading diagonal is 1, and the scale factor of the submatrix on the minor diagonal is α, and wherein α is the primitive element of GF (q), at this moment H ₂Be specifically described as:

$H_2=\left[\begin{array}{cccccccc}{P}^{s_{0,k}}& 0& 0& 0& \&CenterDot;\&CenterDot;\&CenterDot;& 0& 0& 0\\ {\mathrm{\&alpha;P}}^{s_{1,k}}& P^{s_{1,k+1}}& 0& 0& \&CenterDot;\&CenterDot;\&CenterDot;& 0& 0& 0\\ 0& {\mathrm{\&alpha;P}}^{s_{2,k+1}}& P^{s_{2,k+2}}& 0& \&CenterDot;\&CenterDot;\&CenterDot;& 0& 0& 0\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& & \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& & \&CenterDot;& \&CenterDot;& \&CenterDot;\\ 0& 0& 0& 0& \&CenterDot;\&CenterDot;\&CenterDot;& {\mathrm{\&alpha;P}}^{s_{m-2,n-3}}& P^{s_{m-2,n-2}}& 0\\ 0& 0& 0& 0& \&CenterDot;\&CenterDot;\&CenterDot;& 0& {\mathrm{\&alpha;P}}^{s_{m-1,n-2}}& P^{s_{m-1,n-1}}\end{array}\right]---(1.3).$

4, the building method of multielement LDPC code according to claim 2 is characterized in that: choose k nonzero element β from GF (q) ₀, β ₁..., β _K-1As matrix H ₁In the scale factor of k submatrix of the 0th row, the scale factor of k the submatrix that corresponding i is capable is respectively β ₀ ^I+1, β ₁ ^I+1..., β _K-1 ^I+1, this moment H ₁Be a class Fan Demeng matrix, be specifically described as:

$H_1=\left[\begin{array}{cccc}{\mathrm{\&beta;}}_0{P}^{s_{\mathrm{0,0}}}& {\mathrm{\&beta;}}_1{P}^{s_{\mathrm{0,1}}}& \&CenterDot;\&CenterDot;\&CenterDot;& {\mathrm{\&beta;}}_{k-1}{P}^{s_{0,k-1}}\\ {\mathrm{\&beta;}}_0^2{P}^{s_{\mathrm{1,0}}}& {\mathrm{\&beta;}}_1^2{P}^{s_{\mathrm{1,1}}}& \&CenterDot;\&CenterDot;\&CenterDot;& {\mathrm{\&beta;}}_{k-1}^2{P}^{s_{1,k-1}}\\ \&CenterDot;& & & \&CenterDot;\\ \&CenterDot;& & \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\\ \&CenterDot;& & & \&CenterDot;\\ {\mathrm{\&beta;}}_0^m{P}^{s_{m-\mathrm{1,0}}}& {\mathrm{\&beta;}}_1^m{P}^{s_{m-\mathrm{1,1}}}& \&CenterDot;\&CenterDot;\&CenterDot;& {\mathrm{\&beta;}}_{k-1}^m{P}^{s_{m-1,k-1}}\end{array}\right]---\left(1.4\right).$

5, a kind of coding method of multielement LDPC code is characterized in that: the coding method of multielement LDPC code directly realizes by the check matrix of the described multielement LDPC code of claim 1; Regard codeword sequence the set of length as for a plurality of subsequences of l, c=( u ⁽⁰⁾, u ⁽¹⁾..., u ^(k-1), v ⁽⁰⁾, v ⁽¹⁾..., v ^(m-1)), wherein u ^(j)(0≤j≤k-1) be long be the information subsequence of l, v ⁽ⁱ⁾(0≤i≤m-1) be long be the syndrome sequence of l, coding method may further comprise the steps:

(1) initialization is the information sequence of kl with length uBe divided into k subsequence, u=( u ⁽⁰⁾, u ⁽¹⁾..., u ^(k-1)); Order v ⁽¹⁾= 0

(2), calculate i syndrome sequence for 0≤i≤m-1 v ⁽ⁱ⁾: for 0≤j≤k-1, j information subsequence u ^(j)At first be recycled the s that moves to right _{I, j}Inferior, and then multiply by scale factor β _j ^I+1, the vector beta that to obtain a length be l _j ^I+1 u ^(j)h _{I, j} ^T, h wherein _{I, j}Be by (the unit matrix ring shift left s of l * l) _{I, j}Inferior obtaining, $h_{i,j}=P^{s_{i,j}};$ With i-1 syndrome sequence v ^(i-1)Ring shift right s _{I, k+i-1}The vector inferior, and then multiply by scale factor α, that to obtain a length be l v ^(i-1)h _{I, k+i-1} ^TWith all vector additions that the operation of its first two steps obtains, obtain a length and be l's and vector; This and vector be multiply by-1, and then ring shift left s _{I, k+i}Inferior, obtain vector ${\underset{\&OverBar;}{v}}^{\left(i\right)}=-(\underset{j=0}{\overset{k-1}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_j^{i+1}{\underset{\&OverBar;}{u}}^{\left(j\right)}{h}_{i,j}^T+\mathrm{\&alpha;}{\underset{\&OverBar;}{v}}^{(i-1)}{h}_{i,k+i-1}^T){\left(h_{i,k+i}^T\right)}^{-1}.$

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