CN100486119C - Structuring LDPC coding method - Google Patents

Abstract

This invention discloses a structured LDPC coding method including: inputting parameter N,K to generate a matrix Hp, which is the matrix of the N-K stage, selecting parameters a and b to generate a linear congruence AO, A1, K, AP and KAM-1, then generating a matrix Hd, checking the matrix H based on H=[Hp|Hd], inputting an information bit sequence cd={di}, seeking the checked bit p1 and utilizing the iteration to get the rest check bit to constitute the check vectorcp={cd|cp} to get the code words c=[ cd|dp].

Description

A kind of structurized LDPC coding method

Technical field

The invention belongs to communication technical field, relate to a kind of structurized LDPC coding method, this method is the product of electronics, communication and computer technology combination.

Background technology

Since Shannon information theory was set up, channel coding theorem mainly obtained practical application in following six fields: deep space communication and satellite communication, transfer of data, storage, mobile communication, file transfer and digital audio video transmission.Five class standards have been produced thus: the Aerospace Data Systems coding standard that is used for deep space and satellite communication, the trellis coded standard that is used for the high speed data modulations demodulation, the RS coding standard that is used for disk compression storage system, the convolution coding standard of mobile cellular communication system is used for the CRC coding standard of HDLC agreement.These are used and clearly to have explained error control coding method rich in the modern digital technology is used, diversity and importance.At present, the next generation network of studying (NGN) is organically blending of all new generation network technology such as soft switchcall server net, IPv6 data the Internet, 3G (Third Generation) Moblie net, various broadband access network and intelligent optical fiber transmission network, require network to have higher data transmission rate, bigger power system capacity, high spectrum utilization more, be more suitable for various channel conditions and Geng Gao QoS, can realize collecting the transmission that speech, image, video and data are the multimedia integration business of one.Challenge in the face of the next generation network application, existing error correction coding is difficult to satisfy its transmission requirement, so a collection of new and effective error correction coding arises at the historic moment, one of error correcting code that wherein performance is best, computation complexity is minimum is exactly low-density checksum (LDPC) sign indicating number.

Since the new discovery of LDPC code weight, communication enineer and coding theory man have carried out number of research projects, and these work comprise: 1, the limiting performance analysis of LDPC sign indicating number, as density Evolution Theory, capacity limit, minimum range limit etc.; 2, efficient iterative decoding algorithm research as BP algorithm, MP algorithm, sum-product algorithm, minimum-sum algorithm and bit flipping algorithm, comprises their performance evaluation and improvement, effectively realizes design and convergence analysis; 3, the design of structural analysis and building method, as structure based on the regular and irregular sign indicating number of sparse graph, factor graph or Tanner figure, the structure of finite group multi-element code, and the design of random structure sign indicating number and Algebraic Structure sign indicating number etc.; 4, encryption algorithm design mainly is the research of linear complexity encryption algorithm; 5, the LDPC sign indicating number is in the application of different field, as the LDPC sign indicating number at the magnetic recording channel, high speed optical fiber communication, deep space and satellite communication, Digital Subscriber Line is with combining of CDMA and OFDM technology, with combining of modulation technique etc.This, different aspects multi-faceted, great dynamics to the LDPC sign indicating number studies show that the LDPC sign indicating number is with a wide range of applications in the communications field of new generation.

Along with going deep into that LDPC sign indicating number encryption algorithm is studied, some good random coded building methods have appearred, though these methods have good error-correcting performance, be not suitable for practical application.Also occurred some deterministic algebraic coding methods now, these methods can generate check matrix fast, but often need higher encoder complexity.Therefore, designing deterministic encoder with uniform enconding complexity, is that the LDPC coding techniques moves towards practical key.This patent focuses on the research of the Algebraic Structure encoder with uniform enconding complexity of LDPC sign indicating number, propose a kind of algebraically building method of practicality, coding is simple, only needs linear complexity, only need Several Parameters can generate check matrix at the decoding end, saved memory space greatly.

Summary of the invention

The objective of the invention is to overcome the deficiency of more existing building methods, a kind of structurized LDPC coding method is provided, this method has reduced encoder complexity, has saved memory space.

The invention provides a kind of structurized LDPC coding method, the steps include:

(1) constructs biconjugate angular moment battle array H respectively ^pAnd matrix H ^d

According to input parameter N and K, wherein K is an information bit length, and N is a code word size, adopts the square formation on biconjugate angular moment formation formula generation N-K rank, as matrix H ^p

Choose parameter a, b, a, b is an integer, and satisfies following condition (C1)-(C11), generates linear conguential sequences A according to following formula (I) ₀, A ₁... A _P... A _M-1, again according to following formula (II) generator matrix H ^d

(C1) a＜M, b＜M, wherein M=3K;

(C2) b and M prime number each other;

(C3) for the prime number p that can divide exactly M arbitrarily, a-1 is its multiple;

(C4) a and M prime number each other;

(C5) a-1 is divided exactly M;

(C6)b>2(ρ-1)；

(C7)(a-1)>4b+2(ρ-1)；

(C8) X 〉=ρ or (a-1)≤(M/ ρ);

(C9) there is not the satisfied (i (1≤i≤ρ-1) of (a+1) * i) mod X=0;

(C10)2ρ-1<b；

(C11)2ρ-1<2b；

A _N+1=(aA _n+ b) mod M, 0≤n≤M-2 formula (I)

Formula (II)

λ=3 wherein, $\mathrm{\&rho;}=\frac{3K}{N-K}$

(2) according to H=[H ^p| H ^d] the structure check matrix H;

(3) input information bits sequence c ^d={ d _i, i=1 ..., K, (III) asks for check bit p by following formula ₁:

${\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="C200610019162E00151.png"\; state="\{\{state\}\}">p</figure-callout>}}_1=\underset{j=1}{\overset{K}{\mathrm{\&Sigma;}}}{h}_{1j}^d{d}_j$ Formula (III)

Wherein, $h_{1j}^d=H^d(1,j),$ d _j∈ c ^dInformation bit for input;

(4) utilize the iterative algorithm in the following formula (IV) to ask for all the other check bits, form check vector c ^p={ p _i, i=1 ..., N-K;

$p_i=p_{i-1}+\underset{j=1}{\overset{K}{\mathrm{\&Sigma;}}}{h}_{\mathrm{ij}}^d{d}_j$ I=2 ..., N-K formula (IV)

Wherein, $h_{\mathrm{ij}}^d=H^d(i,j),$ d _j∈ c ^dInformation bit for input;

(5) according to check vector c that above-mentioned steps obtained ^p={ p _i, and dope vector c ^d={ d _i, obtain coding codeword $c=\left[c^d\right|c^p].$

The present invention relies on platform, effectively in conjunction with electronic technology and computer technology, can realize the LDPC sign indicating number design of uniform enconding complexity.The present invention generates biconjugate angular moment battle array H respectively according to the parameter of input ^pAnd regular matrix H ^dBecause check matrix has adopted biconjugate angular moment battle array, encoder generates check vector according to the dope vector of input by alternative manner.Particularly, the present invention has the following advantages:

(1) coding has linear complexity.Owing to adopted biconjugate angular moment battle array, can generate check bit by iteration, and not need to carry out Gaussian elimination, reduced encoder complexity.

(2) save memory space.Owing to be the algebraic coding method, do not need to store check matrix at receiving terminal, only need the storage Several Parameters just can generate check matrix immediately, greatly saved memory space.

(3) coding that is obtained has preferable performance.This coded system is the coding method of quasi-regular, has effectively eliminated two wires circulation and the circulation of four lines, has excellent performance.

Description of drawings

Fig. 1 is LDPC sign indicating number applicating flow chart in wireless communication system.

Fig. 2 is the schematic flow sheet of the inventive method.

Fig. 3 is a LDPC sign indicating number decoding schematic flow sheet.

Fig. 4 is the Tanner schematic diagram (bipartite graph) of regular check matrix.

Embodiment

The present invention is described in detail below in conjunction with accompanying drawing and example.

As shown in Figure 1, the simulation flow of LDPC sign indicating number in communication system is: signal source is encoded through the LDPC code coder, the coding codeword that obtains is modulated through modulator, transmit through wireless channel, obtain soft demodulating information in the receiving terminal demodulation, decipher by ldpc decoder, recover information bit.This emulation mainly comprises: LDPC encoder, modulator, channel simulator, demodulator, ldpc decoder or the like.

At first provide the method for designing of the check matrix of LDPC sign indicating number, provide its iteration coding method then.The present invention is further illustrated below in conjunction with Fig. 2:

1 check matrix H

Check matrix constitutes H=[H by two submatrixs ^p| H ^d], introduce the building method of these two submatrixs below respectively.

1.1 biconjugate angular moment battle array H ^p

Input parameter N, K, wherein K is an information bit length, N is a code word size, generator matrix H ^p, H ^pBe the square formation on N-K rank, adopt biconjugate angular moment formation formula, in the following example shown in:

$H^p=\left[\begin{array}{cccccc}1& 0& L& 0& 0& 0\\ 1& 1& L& 0& 0& 0\\ 0& 1& 1& L& 0& 0\\ M& M& L& L& 0& 0\\ 0& 0& \mathrm{<figure-callout\; id="1"\; label="L"\; filenames="C200610019162E00151.png"\; state="\{\{state\}\}">L</figure-callout>}& 1& 1& 0\\ 0& 0& L& 0& 1& 1\end{array}\right]---\left(1\right)$

1.2 regular matrix H ^d

Input parameter N, K, a, b and A ₀, wherein K is an information bit length, N is a code word size, A ₀Be the initial value of formula (2), can get the arbitrary value between the 0:K λ, a, b are integer.

Matrix H ^dCan regard the check matrix of the LDPC sign indicating number of a canonical as, for the sparse property of taking into account check matrix and the performance of encoder, the weight of choosing every row is λ=3, and then the weight of every row is $\mathrm{\&rho;}=\frac{3K}{N-K}.$ Every row are regarded as be that information node, every row are regarded as and be check-node, each information node links to each other with 3 check-nodes, and each check-node links to each other with ρ information node, and then check matrix can be described by Fig. 4.As shown in Figure 4, λ=3, ρ=6.Information node and check-node have M=3K bar access path, matrix H ^dCan be that the mapping one by one of M generates by a length.

H ^dMatrix is constructed by linear conguential sequences, at first adopts the method for iteration to generate linear conguential sequences A ₀, A ₁, K A _p, K A _M-1

A _n+1＝(aA _n+b)mod?M，0≤n≤M-2 (2)

Then, according to sequence A ₀, A ₁, KA _p, K A _M-1By following formula generator matrix H ^d:

1.3 structure H ^dConstraints

Shine upon one by one between the connected node of information node and the connected node of check-node, its mapping must meet the following conditions:

1, an information node can not be connected to same check-node (avoiding the two wires circulation) by two paths.When

Or

The time, there is the two wires circulation.

2, do not have short circulation to exist, avoid the existence of four lines circulation (two information nodes are continuous with identical a pair of check-node).

For (2) formula, in order to be shone upon A one by one ₀Can get the arbitrary integer between the 0:M-1, a and b must meet the following conditions:

C1.a<M，b<M；

C2.b and M be prime number each other;

C3. for the prime number p that can divide exactly M arbitrarily, a-1 is its multiple.In addition, if M is 4 multiple, then a-1 must be 4 multiple;

C4.a and M be prime number each other.

4 conditions above satisfying, formula (2) energy iteration generates the arbitrary integer between the 0:M-1.

If increase followingly to a, the constraints of b can be so that the pairing bipartite graph of Hd has two wires circulation and the circulation of four lines.

λ=3, H ^dBy iterative formula A _N+1=(aA _n+ b) mod M produces, a, the b C1:C4 that satisfies condition, and X=(M/ (a-1)), if the increase condition:

C5.a-1 is divided exactly M;

C6.b>2(ρ-1)；

C7.(a-1)>4b+2(ρ-1)；

C8.X 〉=ρ or (a-1)≤(M/ ρ);

C9. there is not the satisfied (i (1≤i≤ρ-1) of (a+1) * i) mod X=0;

H then ^dCorresponding bipartite graph does not have two wires circulation and the circulation of four lines.

In order on the pairing bipartite graph of check matrix H, there not to be the circulation of four lines, must increase following condition:

C10.2ρ-1<b；

C11.2ρ-1<2b。

2 iteration coding

Because the application of biconjugate angular moment battle array does not need generator matrix G just can generate check bit by iteration in cataloged procedure.Pairing code vector c is decomposed into the corresponding check vector C with the H matrix ^pWith dope vector c ^d, c=[c is promptly arranged ^pc ^d], following relation is arranged between check matrix H and the code vector c:

${\mathrm{Hc}}^T=\left(H^p{H}^d\right)\left[\begin{array}{c}{c}^p\\ c^d\end{array}\right]=H^p{c}^p+H^d{c}^d=0^T---\left(3\right)$

2.1 ask for check bit p ₁

If input information vector C ^d={ d _i, i=1, L, K can ask for check vector c according to (3) formula ^p={ p _i, i=1, L, N-K is easy to try to achieve check bit p according to equation (4) ₁Value:

${\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="C200610019162E00151.png"\; state="\{\{state\}\}">p</figure-callout>}}_1=\underset{j=1}{\overset{K}{\mathrm{\&Sigma;}}}{h}_{1j}^d{d}_j---\left(4\right)$

Wherein $h_{1j}^d=H^d(1,j),$ d _j∈c ^d。

2.2 ask for all the other check bits

Utilize iterative algorithm, the restriction relation of establishing according to check matrix generates all the other check bits, thereby obtains coding codeword, and all the other can get by recursion:

$p_i=p_{i-1}+\underset{j=1}{\overset{K}{\mathrm{\&Sigma;}}}{h}_{\mathrm{ij}}^d{d}_j$ i＝2，L，N-K (5)

Wherein $h_{\mathrm{ij}}^d=H^d(i,j),$ d _j∈c ^d。Check vector c ^pWith known dope vector c ^dMerge, obtain coding codeword $c=\left[c^p\right|c^d].$

Hence one can see that: given any one dope vector c ^d, needn't invert to check matrix H, can iteration try to achieve c according to top method ^p, coding has linear complexity.

As shown in Figure 3, at the decoding end, the soft information that demodulation obtains is sent into decoder with the check matrix H that generates according to input parameter as Given information, through iterative decoding, and the information bit that obtains transmitting.

Fig. 4 is the Tanner figure of regular LDPC sign indicating number, i.e. bipartite graph.By this figure, can introduce regular matrix H intuitively ^dBuilding method.

In order to further specify, provide a simplified example of the present invention as follows.

Input parameter N=64, K=32, because λ=3, ρ=3 then, M=3 * 32=2 ⁵* 3, according to top restrictive condition, a-1 can be decomposed into the form that prime factor multiplies each other, and has only two factors 2,3.

According to condition C 3, a-1 can only get 12,24,48,96.

Condition C 8 requires (a-1)≤32, and C6 requires b〉4, C7 requires (a-1)〉4b+2 (ρ-1)〉20, therefore (a-1)=24 are so a=25 gets b=5, A simultaneously ₀=0.

Therefore, in the specific implementation process, input parameter is N=64, K=32, a=25, b=5, A ₀=0, can obtain following matrix.

H ^p：

1?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0

1?1?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0

0?1?1?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0

0?0?1?1?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0

0?0?0?1?1?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0

0?0?0?0?1?1?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0

0?0?0?0?0?1?1?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0

0?0?0?0?0?0?1?1?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0

0?0?0?0?0?0?0?1?1?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0

0?0?0?0?0?0?0?0?1?1?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0

0?0?0?0?0?0?0?0?0?1?1?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0

0?0?0?0?0?0?0?0?0?0?1?1?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0

0?0?0?0?0?0?0?0?0?0?0?1?1?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0

0?0?0?0?0?0?0?0?0?0?0?0?1?1?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0

0?0?0?0?0?0?0?0?0?0?0?0?0?1?1?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0

0?0?0?0?0?0?0?0?0?0?0?0?0?0?1?1?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0

0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?1?1?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0

0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?1?1?0?0?0?0?0?0?0?0?0?0?0?0?0?0

0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?1?1?0?0?0?0?0?0?0?0?0?0?0?0?0

0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?1?1?0?0?0?0?0?0?0?0?0?0?0?0

0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?1?1?0?0?0?0?0?0?0?0?0?0?0

0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?1?1?0?0?0?0?0?0?0?0?0?0

0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?1?1?0?0?0?0?0?0?0?0?0

0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?1?1?0?0?0?0?0?0?0?0

0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?1?1?0?0?0?0?0?0?0

0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?1?1?0?0?0?0?0?0

0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?1?1?0?0?0?0?0

0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?1?1?0?0?0?0

0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?1?1?0?0?0

0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?1?1?0?0

0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?1?1?0

0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?1?1

H ^dFor:

1?0?0?0?0?0?0?0?0?1?0?1?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0

1?0?0?0?0?1?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?1?0?0?0?0?0?0?0?0?0

0?0?1?0?0?0?0?0?0?0?0?0?0?1?0?0?0?0?0?0?0?0?0?0?0?0?0?1?0?0?0?0

0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?1?0?0?0?0?1?1?0?0?0?0?0?0?0

0?0?0?0?1?0?0?0?0?0?0?0?0?1?0?1?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0

0?0?0?0?1?0?0?0?0?1?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?1?0?0?0?0?0

0?0?0?0?0?0?1?0?0?0?0?0?0?0?0?0?0?1?0?0?0?0?0?0?0?0?0?0?0?0?0?1

0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?1?0?0?0?0?1?1?0?0?0

0?0?0?0?0?0?0?0?1?0?0?0?0?0?0?0?0?1?0?1?0?0?0?0?0?0?0?0?0?0?0?0

0?0?0?0?0?0?0?0?1?0?0?0?0?1?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?1?0

0?0?0?1?0?0?0?0?0?0?1?0?0?0?0?0?0?0?0?0?0?1?0?0?0?0?0?0?0?0?0?0

1?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?1?0?0?0?0?1

0?0?0?0?0?0?0?0?0?0?0?0?1?0?0?0?0?0?0?0?0?1?0?1?0?0?0?0?0?0?0?0

0?0?1?0?0?0?0?0?0?0?0?0?1?0?0?0?0?1?0?0?0?0?0?0?0?0?0?0?0?0?0?0

0?0?0?0?0?0?0?1?0?0?0?0?0?0?1?0?0?0?0?0?0?0?0?0?0?1?0?0?0?0?0?0

0?0?0?1?1?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?1?0

0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?1?0?0?0?0?0?0?0?0?1?0?1?0?0?0?0

0?0?0?0?0?0?1?0?0?0?0?0?0?0?0?0?1?0?0?0?0?1?0?0?0?0?0?0?0?0?0?0

0?0?0?0?0?0?0?0?0?0?0?1?0?0?0?0?0?0?1?0?0?0?0?0?0?0?0?0?0?1?0?0

0?0?1?0?0?0?0?1?1?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0

0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?1?0?0?0?0?0?0?0?0?1?0?1

0?0?0?0?0?0?0?0?0?0?1?0?0?0?0?0?0?0?0?0?1?0?0?0?0?1?0?0?0?0?0?0

0?1?0?0?0?0?0?0?0?0?0?0?0?0?0?1?0?0?0?0?0?0?1?0?0?0?0?0?0?0?0?0

0?0?0?0?0?0?1?0?0?0?0?1?1?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0

0?1?0?1?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?1?0?0?0?0?0?0?0

0?0?0?0?0?0?0?0?0?0?0?0?0?0?1?0?0?0?0?0?0?0?0?0?1?0?0?0?0?1?0?0

0?0?0?0?0?1?0?0?0?0?0?0?0?0?0?0?0?0?0?1?0?0?0?0?0?0?1?0?0?0?0?0

0?0?0?0?0?0?0?0?0?0?1?0?0?0?0?1?1?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0

0?0?0?0?0?1?0?1?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?1?0?0?0

0?1?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?1?0?0?0?0?0?0?0?0?0?1?0?0?0

0?0?0?0?0?0?0?0?0?1?0?0?0?0?0?0?0?0?0?0?0?0?0?1?0?0?0?0?0?0?1?0

0?0?0?0?0?0?0?0?0?0?0?0?0?0?1?0?0?0?0?1?1?0?0?0?0?0?0?0?0?0?0?0

The coding implementation procedure is as follows:

Suppose that the input information bits sequence is 01010101010101010101010101010101, according to (4) formula, can try to achieve

${\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="C200610019162E00151.png"\; state="\{\{state\}\}">p</figure-callout>}}_1=\underset{j=1}{\overset{K}{\mathrm{\&Sigma;}}}{h}_{1j}^d{d}_j=0,$

Remaining check bit can get by (5) formula recursion: 1100110011001100110011001100110, therefore the verification sequence that obtains of encoding is: 01100110011001100110011001100110, and coding codeword is 01,010,101,010,101,010,101,010,101,010,101,011,001,100,110,011,001,100,110 01100110.

Coding codeword transmits by channel after modulating, at the decoding end, and according to input parameter N, K, a, b and A ₀, can reduce top check matrix H.Give decoder with the soft message transmission that matrix H and demodulation obtain, can obtain information sequence through iterative decoding.

Adopt the encoder of the inventive method design to have definite coding structure, only need Several Parameters just can recover check matrix, greatly saved memory space, for the practicality of LDPC sign indicating number has stepped solid step forward at the decoding end.

Claims (1)

1, a kind of structurized LDPC coding method the steps include:

(1) constructs biconjugate angular moment battle array H respectively ^pAnd matrix H ^d

According to input parameter N and K, wherein K is an information bit length, and N is a code word size, adopts the square formation on biconjugate angular moment formation formula generation N-K rank, as matrix H ^p

Choose parameter a, b, a, b is an integer, and satisfies following condition (C1)-(C11), generates linear conguential sequences A according to following formula (I) ₀, A ₁... A _p... A _M-1, again according to following formula (II) generator matrix H ^d

(C1) a＜M, b＜M, wherein M=3K;

(C2) b and M prime number each other;

(C3) for the prime number p that can divide exactly M arbitrarily, a-1 is its multiple;

(C4) a and M prime number each other;

(C5) a-1 is divided exactly M;

(C6)b>2(ρ-1)；

(C7)(a-1)>4b+2(ρ-1)；

(C8) X 〉=ρ or (a-1)≤(M/ ρ);

(C9) there are not satisfied (i of (a+1) * i) modX=0, wherein 1≤i≤ρ-1;

(C10)2ρ-1<b；

(C11)2ρ-1<2b；

A _N-1=(aA _n+ b) modM, 0≤n≤M-2 formula (I)

Formula (II)

λ=3 wherein, $\mathrm{\&rho;}=\frac{3K}{N-K}$

(2) according to H=[H ^p| H ^d] the structure check matrix H;

(3) input information bits sequence c ^d={ d _i, i=1 ..., K, (III) asks for check bit p by following formula ₁:

$p_1=\underset{j=1}{\overset{K}{\mathrm{\&Sigma;}}}{h}_{1j}^d{d}_j$ Formula (III)

Wherein, $h_{1j}^d=H^d(1,j),$ d _i∈ c ^dInformation bit for input;

(4) utilize the iterative algorithm in the following formula (IV) to ask for all the other check bits, form check vector c ^p={ p _i, i=1 ..., N-K;

$p_i=p_{i-1}+\underset{j=1}{\overset{K}{\mathrm{\&Sigma;}}}{h}_{1j}^d{d}_j$ I=2 ..., N-K formula (IV)

Wherein, $h_{\mathrm{ij}}^d=H^d(i,j),$ d _j∈ c ^dInformation bit for input;

(5) according to check vector c that above-mentioned steps obtained ^p={ p _i, and dope vector c ^d={ d _i, obtain coding codeword c=[c ^d| c ^p].

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