CN101047391A - Low density parity check coding method, device and parity check matrix generating method - Google Patents

Abstract

A LDPC coding method includes confirming number L of cyclic sub-matrix required to generate odd-even calibration matrix according to coding efficiency preset by system, generating L numbers of cyclic sub-matrixes as per code length of LDPC code and confirmed number L, ensuring one of said sub-matrixes to be reversible cyclic sub-matrix, deriving out generating matrix of LDPC code according to generated cyclic sub-matrixes and obtaining bit sequence to be sent by carrying out LDPC coding on information bit to be sent according to said generating matrix. The device used for realizing said method is also disclosed.

Description

Low density parity check coding method, device and parity check matrix generating method

Technical field

The present invention relates to the channel coding technology in the communication system, specially refer to the coding method and the device of a kind of low-density checksum (LDPC, Low-Density Parity Check) sign indicating number, and a kind of generation method of LDPC sign indicating number parity matrix.

Background technology

The effect of communication system is by communication channel information to be sent to another place from a place.Because have influences such as noise, interference in the communication channel, information may make a mistake in transmission course, thereby causes receiving terminal correctly to receive.In order to improve the transmission performance of communication system,, can find or correct the information errors that takes place in the transmission course, to recover correct information by in information transmitted, adding some redundant informations.Above-mentioned process of adding redundant information in information transmitted is called error correction coding again, and error correction coding has a variety of coded systems, and wherein, the LDPC sign indicating number is the very excellent error correction coding mode of finding in recent years of a kind of performance.

The LDPC sign indicating number is a kind of linear block codes, uses the parity check matrix H of this LDPC sign indicating number correspondence to be described usually.The essential characteristic of LDPC sign indicating number is exactly the sparse property of its parity check matrix H, and promptly the number of nonzero element is far smaller than the size of matrix in the parity check matrix H of this LDPC sign indicating number.Matrix shown in the following formula (1) is the parity check matrix H of a LDPC sign indicating number.

$H=\left[\begin{array}{cccccccccccccccccccc}1& 0& 1& 0& 0& 1& 0& 0& 1& 0& 0& 0& 1& 0& 0& 0& 1& 0& 0& 0\\ 0& 1& 0& 1& 0& 0& 1& 0& 0& 1& 0& 0& 0& 1& 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 1& 1& 0& 0& 1& 0& 0& 1& 0& 0& 0& 1& 0& 0& 0& 1& 0\\ 0& 0& 1& 0& 0& 1& 0& 0& 1& 0& 0& 1& 0& 0& 0& 1& 0& 0& 0& 1\\ 0& 1& 0& 0& 0& 1& 1& 0& 0& 1& 0& 0& 1& 0& 0& 0& 1& 0& 0& 0\\ 1& 0& 0& 0& 1& 0& 0& 1& 0& 0& 1& 0& 0& 1& 0& 0& 0& 1& 0& 0\\ 0& 0& 1& 0& 0& 0& 1& 0& 1& 0& 0& 1& 0& 0& 1& 0& 0& 0& 1& 0\\ 0& 0& 0& 1& 0& 0& 0& 1& 0& 1& 0& 0& 1& 0& 0& 1& 0& 0& 0& 1\\ 1& 0& 0& 0& 1& 0& 0& 0& 1& 0& 1& 0& 0& 1& 0& 0& 1& 0& 0& 0\\ 0& 1& 0& 0& 0& 1& 0& 0& 0& 1& 0& 1& 0& 0& 1& 0& 0& 1& 0& 0\end{array}\right]---\left(1\right)$

From the parity check matrix H shown in the above-mentioned formula (1) as can be seen, code length corresponding to the LDPC sign indicating number of this parity check matrix H, the i.e. number of this parity check matrix H row, be n=20, the number of the parity check equation that is comprised corresponding to the LDPC sign indicating number of this parity check matrix H, promptly the number of this parity check matrix H row is k=10, therefore, the code efficiency that obtains this LDPC sign indicating number is (n-k)/n=0.5.The same with all linear block codess, can derive generator matrix G from this parity check matrix H corresponding to the LDPC sign indicating number of this parity check matrix H, HG promptly satisfies condition ^T=0 matrix G, wherein, G ^TTransposition for described generator matrix G.After deriving described generator matrix G, promptly can carry out the LDPC coding by described generator matrix G.

In communication system, if the information bit sequence x that will to send a length be n-k, then the transmitting terminal of communication system needs at first carry out the LDPC coding to this information bit sequence.Wherein, the process of LDPC coding can abstractly be the matrix multiple computing of LDPC sign indicating number generator matrix G and this information bit sequence x, i.e. y=G ^TX will be created in the bit sequence y that the length of transmitting in the communication channel is n after the computing.When in channel, transmitting through the bit sequence y after the LDPC coding, may be subjected to the influence of factors such as noise and interference and change and mistake occurs, therefore, receiving terminal need carry out LDPC decoding to the bit sequence y that receives, and promptly utilizes redundant information to recover correct information bit.If redundant information is not enough to recover correct information, promptly decoding back information bit still may include mistake, and this will cause certain error rate.At present, the decoding of LDPC sign indicating number can be used belief propagation iterative decoding algorithm and various shortcut calculation thereof.Just because of the sparse property of LDPC sign indicating number parity matrix, iterative decoding algorithm can be finished at a high speed.

The excellent properties of LDPC sign indicating number has caused people's extensive attention, and has done a large amount of research from aspects such as theory analysis, building method, coding and decoding method, practical applications.But these researchs mainly concentrate on the application of LDPC sign indicating number in systems such as mobile communication, satellite communication and magnetic storage.Because optical fiber telecommunications system and these systems are very different, especially the specific (special) requirements of the two-forty of optical fiber telecommunications system, high efficiency and low volume, decoding complexity makes these researchs and result thereof be difficult to be applied to optical fiber telecommunications system.

Summary of the invention

In order to solve the problems of the technologies described above, the invention provides the coding method of a kind of LDPC, be applicable to have two-forty, the communication system of high efficiency and low complex degree LDPC coding requirement.

The present invention also provides a kind of code device of low complex degree LDCP sign indicating number, can realize the LDPC coding at a high speed, efficiently.

In addition, the present invention also provides a kind of generation method of LDPC sign indicating number parity matrix, make the ringlet of the parity matrix generated grow up in 4, circle 4 circulations have promptly been avoided, can have simultaneously maximum smallest hamming distance, guarantee to have good coding efficiency according to the LPDC sign indicating number that this parity matrix generated.

According to one of them aspect of the present invention, low-density checksum LDPC of the present invention coding method comprises:

A, determine the number L of the circulation submatrix of the parity matrix needs that generate according to communication system code efficiency given in advance, wherein, L is a natural number;

B, according to the code length of described LDPC sign indicating number and the number L of described circulation submatrix, generate L circulation submatrix, and guarantee that wherein at least one is the Reversible Cycle submatrix;

C, derive the generator matrix of LDPC sign indicating number, and carry out the LDPC coding according to described generator matrix to sent information bit and obtain bit sequence to be sent according to the L that is generated a circulation submatrix.

The described definite number L that generates the circulation submatrix of parity matrix needs of steps A is: establish the redundancy that ε is the LDPC sign indicating number, according to formula Calculate the number L of the circulation submatrix that needs, wherein, operator Represent to round up computing.

The step of L circulation submatrix of the described generation of step B comprises:

B1, determine the length of the cycle of each circulation submatrix according to the number of the code length of LDPC sign indicating number and determined circulation submatrix;

B2, to set one of them circulation submatrix be the Reversible Cycle submatrix, and determine the nonzero element number in the multinomial of this Reversible Cycle submatrix of expression according to the number of the code length of LDPC sign indicating number and determined circulation submatrix;

B3, satisfy the reversible submultinomial of distance restraint condition, and generate reversible subcycle matrix according to described reversible submultinomial according to the length of the cycle of each circulation submatrix and determined nonzero element number structure;

B4, produce other L-1 submultinomial satisfy the distance restraint condition successively, and obtain the individual sub-circular matrix of L-1 according to a described L-1 submultinomial.

Above-mentioned steps B1 is described to determine that the step of the length of the cycle of each circulation submatrix comprises: the code length of establishing the LDPC sign indicating number is n, adopts formula m=n/L to calculate the length of the cycle m of described each circulation submatrix.

Nonzero element number w in the multinomial of described this Reversible Cycle submatrix of definite expression of above-mentioned steps B2 ₀Step comprise: the code length of establishing the LDPC sign indicating number is n, according to formula ${\mathrm{LC}}_w^{}$ ${}_2^{}\≤n/2L$ The maximum integer w of this formula requirement is satisfied in calculating, if the w that calculates is an even number, then makes w ₀=w+1; Otherwise, make w ₀=w.

The step that the described structure of above-mentioned steps B3 satisfies the reversible submultinomial of distance restraint condition comprises:

B31, according to nonzero element number w ₀Requirement, select w at random the integer of the m-1 from 1 to m-1 ₀-1 different integer a1, a2 ₂..., aw ₀Position 0 is added in-1 position as nonzero element, constitutes multinomial 1+x ^A1+ x ^A2+ ...+x ^Aw0-1;

B32, multinomial 1+x that calculating constitutes ^A1+ x ^A2+ ...+x ^Aw0-1Distance between-any two nonzero elements, and judge whether the distance that calculates is repeated to use, if, then return step B31, produce described multinomial again; Otherwise, execution in step B33.

B33, judge whether full rank of the subcycle matrix that obtains by described multinomial cyclic shift, if, updated space put and finishing then; Otherwise, return step B31, produce described multinomial again.

Described method further comprised before described step B31: a number of attempt counter is set;

When execution in step B31 first, it is 1 that described number of attempt counter is set;

After first, before every execution in step B31, described number of attempt counter is added 1, and judge whether described number of attempt Counter Value surpasses predefined higher limit, if then represent described nonzero element number w ₀Require too highly, then reducing described nonzero element number w ₀Value after, carry out described step B31 again; Otherwise, direct execution in step B31.

Other L-1 the sub polynomial steps that the distance restraint condition is satisfied in the described generation of above-mentioned steps B4 comprise:

B41, according to nonzero element number w ₀Requirement, select w at random according to available position record ₀-1 different integer a1, a2 ₂..., aw ₀Position 0 is added in-1 position as nonzero element, constitutes multinomial 1+x ^A1+ x ^A2+ ...+x ^Aw0-1

B42, evaluator 1+x ^A1+ x ^A2+ ...+x ^Aw0-1Distance between any two nonzero elements, and judge whether the distance that calculates is repeated to use, if, then return step B41, produce described multinomial again; Otherwise the updated space put also finishes.

Described method further comprised before described step B41: a number of attempt counter is set;

When execution in step B41 first, it is 1 that described number of attempt counter is set;

After first, before every execution in step B41, described number of attempt counter is added 1, and judge whether described number of attempt Counter Value surpasses predefined higher limit, if then represent described nonzero element number w ₀Require too highly, then reducing described nonzero element number w ₀Value after, carry out described step B41 again; Otherwise, direct execution in step B41.

Above-mentioned updated space put is specially: remove the position that institute's generator polynomial is occupied from available position record.Described position is the distance between any two nonzero elements in the described multinomial.

The described step of deriving the generator matrix of LDPC sign indicating number according to the L that is generated a circulation submatrix of above-mentioned steps C comprises: according to formula $g=\left[\begin{array}{ccccc}& & & & G_1\\ & & & & G_2\\ & I& & & \·\\ & & & & \·\\ & & & & \·\\ & & & & G_{L-1}\end{array}\right]$ Calculate described generator matrix G, wherein, $G_k={\left(A_L^{-1}{A}_k\right)}^T,k=1..L-1,$ I representation unit matrix, A _LBe a reversible subcycle matrix that is generated, A _kFor removing described reversible subcycle matrix A _LOutside other L-1 sub-circular matrixes, operator () ^TThe transposition computing of representing matrix.

According to a further aspect in the invention, described low-density checksum LDPC code device comprises:

L-1 length is the circulating register of m, and wherein L and m are natural number;

L-1 corresponding one by one with described circulating register and connect m input binary adder;

And the output with described L-1 m input binary adder that is connected to described L-1 m input binary adder is imported binary adder as the L-1 that imports.

Wherein, the annexation between the m position output of m input of described L-1 m input binary adder and its corresponding circulating register is definite by the generator matrix of LDPC sign indicating number.

Wherein, described L-1 m input binary adder and described L-1 input binary adder are realized by the XOR gate circuit.

According to a further aspect of the invention, the present invention also provides a kind of generation method of low-density checksum LDPC sign indicating number parity matrix, wherein, described parity matrix is by L circulation submatrix, L is a natural number, it is characterized in that, described method comprises: according to the code length of described LDPC sign indicating number and the number L of described circulation submatrix, generate L circulation submatrix successively, and derive the parity matrix of LDPC sign indicating number according to the L that is generated a circulation submatrix, make the ringlet of described parity matrix grow up and have a maximum smallest hamming distance in 4.

Wherein, the described method that generates L circulation submatrix successively comprises:

A, determine the nonzero element number w in the multinomial of this Reversible Cycle submatrix of expression according to the number L of the code length of LDPC sign indicating number and determined circulation submatrix ₀

B, according to nonzero element number w ₀Requirement, select w at random according to available nonzero element position record ₀-1 different integer a1, a2 ₂..., aw ₀Position 0 is added in-1 position as nonzero element, constitutes multinomial 1+x ^A1+ x ^A2+ ...+x ^Aw0-1

C, evaluator 1+x ^A1+ x ^A2+ ...+x ^Aw0-1Distance between any two nonzero elements, and judge whether the distance calculate is repeated to use, if, illustrate that then the ringlet length of described parity matrix is less than or equal to 4, next return step b, produce described multinomial again; Otherwise, obtain a circulation submatrix according to the multinomial that this step generated through cyclic shift, upgrade described position record according to the position of nonzero element in the described multinomial then, and return step b and continue to generate next circulation submatrix, until generating whole L circulation submatrixs.

In generating a polynomial process of son, further comprise: a number of attempt counter is set, and the initial value of described number of attempt counter is set to 1; Before inferior every execution in step b, described number of attempt counter is added 1, and judge whether described number of attempt Counter Value surpasses predefined higher limit, if then represent described nonzero element number w ₀Require too high, and with described nonzero element number w ₀Subtract after 1, carry out described step b again; Otherwise, direct execution in step b.

Nonzero element number w in the multinomial of described this Reversible Cycle submatrix of definite expression of above-mentioned steps a ₀Method be: according to formula ${\mathrm{LC}}_w^{}$ ${}_2^{}\≤n/2L$ The maximum integer w of this formula requirement is satisfied in calculating, if the w that calculates is an even number, then makes w ₀=w+1; Otherwise, make w ₀=w.

Described position is the distance between any two nonzero elements in the described multinomial; The described updated space put of step c is specially: remove the distance between any two nonzero elements in institute's generator polynomial the distance record between available any two nonzero elements.

Comprise at least one Reversible Cycle submatrix in the L that is generated the circulation submatrix; In the process that generates described Reversible Cycle submatrix, described step c is after judging distance between the nonzero element and not reusing, further comprise: judge whether full rank of the subcycle matrix that obtains by described multinomial cyclic shift, if, then root obtains a circulation submatrix according to the multinomial that this step generated through cyclic shift, upgrades described nonzero element position record according to the position of nonzero element in the described multinomial then; Otherwise, return step b, produce described Reversible Cycle submatrix again.

This shows, can obtain following beneficial effect by LDPC coding method of the present invention and code device:

1, the LDPC sign indicating number generator matrix that is generated has pseudo-cyclic shift structure, and therefore, LDPC encodes and can realize by shift register, and need not to use complicated multiplication operations circuit, thereby satisfies the requirement of two-forty, high efficiency and low encoder complexity;

2, the parity matrix of the LDPC sign indicating number by the method for the invention and device construction has been taken into account the requirement of the long and smallest hamming distance of ringlet, when avoiding 4 circulations occurring enclosing, bigger smallest hamming distance can be obtained, thereby the bit error rate performance of sign indicating number can be improved.

Description of drawings

Fig. 1 is the described LDPC sign indicating number coding of a preferred embodiment of the present invention flow chart;

Fig. 2 is the described method flow diagram that generates reversible submultinomial at random of the preferred embodiment of the present invention;

Fig. 3 is the described method flow diagram that generates submultinomial at random of the preferred embodiment of the present invention;

Fig. 4 is the internal structure schematic diagram of the described LDPC code encoding device of the preferred embodiment of the present invention;

Fig. 5 has shown at the bit error rate performance of this LDPC sign indicating number that calculates under the fiber channel model under belief propagation decoding algorithm and Min-Sum decoding algorithm and RS (255,239) yard bit error rate performance schematic diagram commonly used.

Embodiment

For the purpose, technical scheme and the advantage that make invention is clearer, below with reference to the accompanying drawing embodiment that develops simultaneously, the present invention is described in further detail.

Treating the basic demand that the information transmitted bit carries out LDPC coding is to satisfy application system, and for example the bit error rate performance requirement of system such as communication system, magnetic-memory system also will take into account requirements such as coding and decoding complexity, cost simultaneously.Usually the factor that influence LDPC sign indicating number bit error rate performance is many, and wherein, two important factors are that the ringlet of the pairing parity matrix of LDPC sign indicating number is grown and smallest hamming distance.Therefore, an important content of design LDPC sign indicating number is exactly that suitable parity check matrix H of structure makes the long and smallest hamming distance of its ringlet satisfy certain requirement.Be known as and realize correct LDPC decoding, require the ringlet of the parity matrix of LDPC sign indicating number to grow up usually, require its smallest hamming distance to be the bigger the better simultaneously in 4.

In a preferred embodiment of the invention, provided a kind of method that generates parity matrix, guaranteed when generating parity matrix, can take into account the requirement of the long and smallest hamming distance of ringlet simultaneously, with the extraordinary LDPC sign indicating number of obtained performance.

Regulation at first, the parity check matrix H of the LDPC sign indicating number by the present embodiment method construct has the structure shown in the following formula (2):

H＝[A ₁A ₂...A _L](2)

The characteristics of this parity check matrix H are: it is by L the circulation submatrix A that size is identical _iForm, wherein, i=1...L, and L is a natural number.By the represented LDPC sign indicating number of such parity check matrix H is a kind of pseudo-circulation LDPC (QC-LDPC, Quasi-Cyclic Low Density ParityCheck Code) sign indicating number.Wherein, each circulation submatrix A _iThe characteristics that all have cyclic shift, promptly its any delegation or any row can be obtained by previous row or previous column cyclic shift.For example, the matrix A of following formula (3) is exactly a circular matrix, every row of this matrix and every row all have and have only two nonzero elements, and its any delegation all can obtain by the previous row cyclic shift, and its any row all can be obtained by its previous column cyclic shift.Obviously, as long as first row of a known circular matrix or first row just can be determined this circular matrix fully by cyclic shift.

$A=\left[\begin{array}{cccccc}1& 0& 1& 0& 0& 0\\ 0& 1& 0& 1& 0& 0\\ 0& 0& 1& 0& 1& 0\\ 0& 0& 0& 1& 0& 1\\ 1& 0& 0& 0& 1& 0\\ 0& 1& 0& 0& 0& 1\end{array}\right]---\left(3\right)$

For these reasons, circular matrix can also be described with polynomial method, the circular matrix A shown in the formula (3) for example, and its first row can be expressed as x with polynomial method ⁰+ x ²=1+x ², wherein, the index coefficient of x has been represented the position of nonzero element, the nonzero element here is respectively zero-bit and second.According to the characteristic of circular matrix, the D of described circular matrix A is capable can be passed through multinomial 1+x ²Carry out cyclic shift and obtain, because its length of the cycle is 6, therefore, the D of described circular matrix A is capable can be expressed as x ^D(1+x ²)=x ^D+ x ^D+2Mod (x ⁶-1).

From foregoing description as can be seen, because each circular matrix all can be described with polynomial method, therefore, the parity check matrix H of QC-LDPC sign indicating number as shown in Equation (2) can be used L polynomial repressentation, wherein, each multinomial has been represented first row of the circulation submatrix that this parity check matrix H comprised.

As previously mentioned, in order to guarantee the bit error rate performance of designed LDPC sign indicating number, need to guarantee that the long and smallest hamming distance of the ringlet of parity check matrix H of LDPC sign indicating number reaches certain requirement.

Wherein, long basic demand is that its ringlet of requirement is grown up in 4 to the LDPC sign indicating number for the ringlet of its parity check matrix H, promptly avoids enclosing the appearance of 4 circulations.For the convenience of describing, at first define in the multinomial distance between any two nonzero elements and be Dist (a, b)=min (| a-b|, m-|a-b|), wherein a, b are respectively the position of any two nonzero elements in the multinomial, m is polynomial length of the cycle.For example, the cyclic polynomial of the circular matrix A correspondence shown in the formula (3) is 1+x ², it has two nonzero elements, and respectively in the position 0 and 2, therefore polynomial length of the cycle m=6, is 2 by calculating the distance that can obtain between these two nonzero elements.Those skilled in the art can prove, for all multinomials of forming the QC-LDPC sign indicating number, if the distance between these multinomial nonzero elements does not duplicate, the QC-LDPC sign indicating number that is obtained by these multinomial cyclic shifts can avoid enclosing the existence of 4 circulations so, thereby the ringlet that guarantees the parity matrix that generated is grown up in 4.To form distance between all polynomial nonzero elements of QC-LDPC sign indicating number does not here duplicate this constraints and is called the distance restraint condition.As can be seen from the above analysis, the parity check matrix H of the LDPC sign indicating number that is generated in the preferred embodiment of the present invention must satisfy above-mentioned distance restraint condition.

In addition, corresponding to the requirement of smallest hamming distance,, require the parity check matrix H smallest hamming distance of LDPC sign indicating number to be the bigger the better in order to guarantee the bit error rate performance of LDPC sign indicating number.If hypothesis form the QC-LDPC sign indicating number the number of the nonzero element in L the multinomial of corresponding parity check matrix H be respectively w _iI=1...L wherein, then those skilled in the art can prove, if the multinomial that in the L that this parity check matrix H the comprised multinomial two or more nonzero element numbers to be arranged be w, the smallest hamming distance of this parity check matrix H is less than or equal to 2w so.

This shows, can improve the smallest hamming distance of parity check matrix H by the number that improves nonzero element in the multinomial that parity check matrix H comprised.Yet, after the number of nonzero element in the multinomial of forming parity check matrix H increases,, thereby will more difficultly satisfy above-mentioned distance restraint condition with the distance between the more unduplicated nonzero element of needs.Therefore, in the number that increases nonzero element, also must guarantee to satisfy above-mentioned distance restraint condition.Those skilled in the art can prove that for the multinomial that a nonzero element number is w, the distance between its nonzero element needs C altogether _w ²Individual.Like this,, the following formula (4) of satisfying must be arranged then,, the constraints of formula (4) is called smallest hamming distance constraints here if require the distance between as shown in Equation (2) parity check matrix H nonzero element not duplicate:

${\mathrm{<figure-callout\; id="2"\; label="LC\; w"\; filenames="A20061007608200241.png"\; state="\{\{state\}\}">LC</figure-callout>}}_w^{}\&le;n/2L---\left(4\right)$

Wherein, n/2L represents is half of length of each circulation submatrix.

From above-mentioned smallest hamming distance constraints can obtain when the QC-LDPC sign indicating number is constructed the upper limit of the multinomial nonzero element number that can use, therefore this upper limit can be satisfied the initial value of nonzero element number of the submultinomial of distance restraint condition as search.

By above description as can be seen, in order to guarantee the bit error rate performance of LDPC sign indicating number, when generating this corresponding parity check matrix H of LDPC sign indicating number institute, need consider above-mentioned distance restraint condition and smallest hamming distance constraints simultaneously.That is to say,, and when having big as far as possible smallest hamming distance, can guarantee that designed LDPC sign indicating number has good bit error rate performance if the parity check matrix H that is generated satisfies above-mentioned distance restraint condition.

By the description of front as can be known, after the parity check matrix H that generates the LDPC sign indicating number, the parity check matrix H of passing through to be generated can be derived the generator matrix G corresponding to the LDPC sign indicating number of this parity check matrix H, thereby carries out the LDPC coding by described generator matrix G.Yet, sparse though generally the parity check matrix H that is generated is sparse from the general right and wrong of generator matrix G that the parity check matrix H derivation obtains, the normally very big operation of amount of calculation of matrix multiple computing when therefore carrying out the LDPC coding.For this reason, the preferred embodiments of the present invention spy has provided and has a kind ofly derived the method for generator matrix G according to parity check matrix H, can reduce greatly and utilize generator matrix G to carry out the complexity of LDPC coding.

There is one to be reversible in the circulation submatrix that parity check matrix H comprised of assumption (2) definition, establishes A here _LReversible, and its inverse matrix is A _L ^-1, then the generator matrix G by the represented QC-LDPC sign indicating number of this parity check matrix H can calculate by following formula (5):

$G=\left[\begin{array}{ccccc}& & & & G_1\\ & & & & G_2\\ & I& & & \&CenterDot;\\ & & & & \&CenterDot;\\ & & & & \&CenterDot;\\ & & & & G_{L-1}\end{array}\right]---\left(5\right)$

Wherein, $G_k={\left(A_L^{-1}{A}_k\right)}^T,k=1..L-1,$ I representation unit matrix.By said method, though from sparse matrix A _kThe matrix G that obtains _kSparse matrix not necessarily, but each G _kStill all be circular matrix, therefore, can directly realize with the multiplication mutually of information sequence to be sent by the resulting generator matrix G of formula (5) by circulating register, and need not a large amount of multiply operations, thereby can significantly reduce LDPC calculation of coding amount, reduce the complexity of LDPC coding.

Method by the generation parity matrix that provides above and derive the method for generator matrix by parity matrix, a preferred embodiment of the present invention has provided a kind of LDPC coding method.This method mainly may further comprise the steps as shown in Figure 1:

A, determine the number L of the circulation submatrix of the parity matrix needs that generate according to communication system code efficiency given in advance;

In this step, the concrete grammar that number adopted of described definite circulation submatrix is: according to the requirement of code efficiency 1-ε, wherein, ε is the redundancy of LDPC sign indicating number, calculates the number L of the circulation submatrix that needs, to satisfy condition

Wherein, operator

Represent to round up computing.This shows that the number of circulation submatrix is many more, code efficiency is high more, but also will cause the smallest hamming distance of the parity matrix that generates more little simultaneously.

B, determine the length of the cycle m of each circulation submatrix according to the number of the code length of LDPC sign indicating number and determined circulation submatrix.

This step is described determines that the concrete grammar that length of the cycle m adopted of each circulation submatrix is: the code length of establishing the LDPC sign indicating number is n, and the number of described circulation submatrix is L, adopts formula m=n/L to calculate the length of the cycle m of described each circulation submatrix.

C, to set one of them circulation submatrix be the Reversible Cycle submatrix, and determine the nonzero element number w in the multinomial of this Reversible Cycle submatrix of expression according to the number of the code length of LDPC sign indicating number and determined circulation submatrix ₀

In this step, described definite nonzero element number w ₀Concrete grammar be: calculate according to above-mentioned formula (4) and satisfy the maximum integer w that this formula requires,, then make w if the w that calculates is an even number ₀=w+1; Otherwise, make w ₀=w.Wherein, be even number w in season at the w that calculates ₀The reason of=w+1 is to prove that when the number of the polynomial nonzero element of representing a circular matrix was even number, the circular matrix that produces by cyclic shift can not be reversible.

D, according to the length of the cycle m and the determined nonzero element number w of each circulation submatrix ₀Structure satisfies the reversible submultinomial of distance restraint condition, and generates reversible subcycle matrix according to described reversible submultinomial.

The reversible submultinomial that the described structure of this step satisfies the distance restraint condition can adopt algebraic method or random device to realize, show by analysis, when the ringlet length of the subcycle matrix that is generated is 6 and smallest hamming distance when identical, the performance difference of the QC-LDPC sign indicating number that distinct methods produces is little.

Specifically introduce a kind of method that produces reversible submultinomial at random in the present embodiment, concrete grammar sees also Fig. 2, mainly comprises:

D1, according to nonzero element number w ₀Requirement, select w at random the integer of the m-1 from 1 to m-1 ₀-1 different integer a1, a2 ₂..., aw ₀Position 0 is added in-1 position as nonzero element, constitutes multinomial 1+x ^A1+ x ^A2+ ...+x ^Aw0-1

In this step, a number of attempt counter also will be set, when execution in step D1 first, it is 1 that described number of attempt counter is set, after this, and before every execution in step D1, at first described number of attempt counter is added 1, and judge whether described number of attempt Counter Value surpasses predefined higher limit, if then represent described nonzero element number w ₀Require too highly, then reducing described nonzero element number w ₀Value after, be about to described nonzero element number w ₀Subtract after 1, reconstitute described multinomial again.It should be noted that because the subcycle matrix that is generated in step D need be reversible circular matrix, therefore, described nonzero element number w ₀Value can not be even number.

D2, evaluator 1+x ^A1+ x ^A2+ ...+x ^Aw0-1Distance between any two nonzero elements, and judge whether the distance that calculates is repeated to use, if, then return step D1, produce described multinomial again; Otherwise, execution in step D3.

D3, judge whether full rank of the subcycle matrix that obtains by described multinomial cyclic shift, if, updated space put and finishing then; Otherwise, return step D1, produce described multinomial again.

The described updated space put of this step specifically comprises: remove the position that institute's generator polynomial is occupied from available position record.Described position specifically can be expressed as the distance between any two nonzero elements in the multinomial.The main purpose of updated space put is that the distance in all multinomials that guarantee to be generated between any two nonzero elements does not repeat, to satisfy described distance restraint condition.

In this step, judge the subcycle matrix that obtains by described multinomial cyclic shift whether the purpose of full rank be to judge whether this subcycle matrix reversible, if completely be lost, illustrate that then this subcycle matrix is reversible.

E, produce other L-1 submultinomial satisfy the distance restraint condition successively, and obtain the individual sub-circular matrix of L-1 according to a described L-1 submultinomial.

The method and the described method of above-mentioned steps D1～D3 of the described generation submultinomial of this step are similar, and concrete grammar sees also Fig. 3, mainly comprises:

E1, according to nonzero element number w ₀Requirement, select w at random according to available position record ₀-1 different integer a1, a2 ₂..., aw ₀Position 0 is added in-1 position as nonzero element, constitutes multinomial 1+x ^A1+ x ^A2+ ...+x ^Aw0-1

In this step, a number of attempt counter also will be set, when execution in step E1 first, it is 1 that described number of attempt counter is set, after this, and before every execution in step E1, at first described number of attempt counter is added 1, and judge whether described number of attempt Counter Value surpasses predefined higher limit, if then represent described nonzero element number w ₀Require too highly, then reducing described nonzero element number w ₀Value after, be about to described nonzero element number w ₀Subtract after 1, reconstitute described multinomial again.

E2, evaluator 1+x ^A1+ x ^A2+ ...+x ^Aw0-1Distance between any two nonzero elements, and judge whether the distance that calculates is repeated to use, if, then return step e 1, produce described multinomial again; Otherwise the updated space put also finishes.

F, according to step D and the resulting L of step e sub-circular matrix, derive the generator matrix G of LDPC sign indicating number by formula (5).

Wherein, can directly obtain characterizing the parity check matrix H of LDPC sign indicating number according to described L sub-circular matrix and formula (2).

H, carry out LDPC coding according to described generator matrix G to sent information bit x and obtain bit sequence y to be sent, and send to the receiving terminal of communication system by communication channel.

The receiving terminal of described communication system can adopt existing interpretation method to realize for the decoding of bit sequence y.

In order to realize above-mentioned LDPC coding method, the present invention gives a kind of LDPC code device, and its internal structure as shown in Figure 4.

The described LDPC code device of present embodiment mainly comprises: L-1 length is the circulating register of m, the individual m corresponding one by one with described circulating register and that connect of L-1 imports binary adder, also comprises a L-1 input binary adder that is connected to the output of described L-1 m being imported binary adder of described L-1 m input binary adder as input in addition.Wherein, each corresponding one by one and connect circulating register and m input binary adder and sub-circular matrix G _k, k=1...L-1 is corresponding one by one.In addition, the annexation between the m position output of the input of described L-1 m input binary adder and its corresponding circulating register is by its corresponding subcycle matrix G _kDetermine.Particularly, by characterizing described circulation submatrix G _kThe position of polynomial nonzero element determine, promptly in the position of corresponding nonzero element, the output of described circulating register is connected to the corresponding input of described m input binary adder; And, then do not need to set up the output of described circulating register to the connection between the corresponding input of described m input binary adder in the position of corresponding neutral element.For example, if characterize described circulation submatrix G _kMultinomial be 1+x ², then only need the 0th of described circulating register and the 2nd output the 0th and the 2nd input, and do not need to carry out other connections to its corresponding m input binary adder.

LDPC code device by said structure can carry out the LDPC coding, and its concrete cataloged procedure is as follows:

Suppose that information sequence to be encoded is X _S, its length is m * (L-1).This information sequence will be as the list entries of described LDPC code device, and through the LDPC coding, the bit sequence of described LDPC code device output is (X _S, X _P), wherein, X _PBe the redundant bit that coding generates, its length is m.

At first, with described information sequence X _SBe divided into the L-1 section, be input to a described L-1 circulating register respectively simultaneously, carry out the segmentation cyclic shift;

Bit of every cyclic shift, the m of each circulating register correspondence input binary adder will export a binary system with, and its output is directly inputted to described L-1 input binary adder, by redundant bit of this L-1 input binary adder output.When a cyclic shift m bit, when also promptly circulating a week, described L-1 input binary adder will be exported m redundant bit altogether, and this m redundant bit is X _P

This shows, when utilizing above-mentioned LDPC code device to carry out the LDPC coding, can only can realize the LDPC coding, and the realization of binary adder can be very simple, for example can realize with exclusive or logic gate by cyclic shift and binary add operation.Thereby this LDPC code device can demonstrate fully the low encoder complexity advantage of LDPC coding of the present invention, thereby satisfies the coding requirement of two-forty, high efficiency and low encoder complexity.

For better the performance of the described LDPC coding of the explanation preferred embodiment of the present invention, forward error correction coding commonly used in the contrast optical fiber telecommunications system below---(RS, Reed-Solomon) sign indicating number describes Read-Solomon.The RS sign indicating number that often uses in optical fiber telecommunications system is RS (255,239), and its code length is 2040, and code efficiency is 93.7%.Now according to the described LDPC coding method of the preferred embodiment of the present invention, construct the QC-LDPC sign indicating number with same-code efficient, its code length is 4080, and its parity matrix has 16 circulation submatrixs.Design by the described method of the preferred embodiment of the present invention, can obtain that reversible polynomial nonzero element number is 5 in the submultinomial that above-mentioned parity matrix comprises 16 circulation submatrixs, other polynomial nonzero element numbers are 5 or 4, therefore, the smallest hamming distance of this LDPC sign indicating number is 8.Fig. 5 shown at this LDPC sign indicating number that calculates under the fiber channel model under the belief propagation decoding algorithm and the bit error rate performance under the Min-Sum decoding algorithm, respectively as band among Fig. 5 * number and be with+number curve shown in; In addition, also comprised the bit error rate performance of RS (255,239) sign indicating number commonly used among Fig. 5, shown in the curve of band circle among Fig. 5.Wherein, the transverse axis of Fig. 5 is the general parameter that is used to characterize the received signal quality quality in the optical fiber telecommunications system---a Q value, wherein, the Q value is big more, shows that received signal quality is good more, and the error rate is also low more, the Q value is more little, shows that received signal quality is poor more, and the error rate is high more; The longitudinal axis of Fig. 5 is represented the error rate.As can be seen from Figure 5, utilize the coding method of the described LDPC of the preferred embodiment of the present invention, under the essentially identical prerequisite of code efficiency, compare, the coding gain of about 2dB can be provided with described RS (255,239) sign indicating number.Though the belief propagation decoding algorithm has more performance, yet the Min-Sum decoding algorithm can reduce decoding complexity greatly by sacrificing the coding gain of about 0.2dB, is easier to circuit simultaneously and realizes.

The above only is preferred embodiment of the present invention, and is in order to restriction the present invention, within the spirit and principles in the present invention not all, any modification of being done, is equal to replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (21)

1, a kind of low-density checksum LDPC coding method is characterized in that, comprising:

A, determine the number L of the circulation submatrix of the parity matrix needs that generate according to communication system code efficiency given in advance, wherein, L is a natural number;

B, according to the code length of described LDPC sign indicating number and the number L of described circulation submatrix, generate L circulation submatrix, and guarantee that wherein at least one is the Reversible Cycle submatrix;

C, derive the generator matrix of LDPC sign indicating number, and carry out the LDPC coding according to described generator matrix to sent information bit and obtain bit sequence to be sent according to the L that is generated a circulation submatrix.

2, LDPC coding method according to claim 1 is characterized in that, the described definite number L that generates the circulation submatrix of parity matrix needs of steps A is:

If ε is the redundancy of LDPC sign indicating number, according to formula

Calculate the number L of the circulation submatrix that needs, wherein, operator

Represent to round up computing.

3, LDPC coding method according to claim 1 is characterized in that, the step of L circulation submatrix of the described generation of step B comprises:

B1, determine the length of the cycle of each circulation submatrix according to the number of the code length of LDPC sign indicating number and determined circulation submatrix;

B2, to set one of them circulation submatrix be the Reversible Cycle submatrix, and determine the nonzero element number w in the multinomial of this Reversible Cycle submatrix of expression according to the number L of the code length of LDPC sign indicating number and determined circulation submatrix ₀

B3, according to the length of the cycle and the determined nonzero element number w of each circulation submatrix ₀Structure satisfies the reversible submultinomial of distance restraint condition, and generates reversible subcycle matrix according to described reversible submultinomial;

B4, produce other L-1 submultinomial satisfy the distance restraint condition successively, and obtain the individual sub-circular matrix of L-1 according to a described L-1 submultinomial.

4, LDPC coding method according to claim 3, it is characterized in that, step B1 is described to determine that the step of the length of the cycle of each circulation submatrix comprises: the code length of establishing the LDPC sign indicating number is n, adopts formula m=n/L to calculate the length of the cycle m of described each circulation submatrix.

5, LDPC coding method according to claim 3 is characterized in that, the nonzero element number w in the multinomial of described this Reversible Cycle submatrix of definite expression of step B2 ₀Step comprise: the code length of establishing the LDPC sign indicating number is n, according to formula ${\mathrm{LC}}_w^2\&le;n/2L$ The maximum integer w of this formula requirement is satisfied in calculating, if the w that calculates is an even number, then makes w ₀=w+1; Otherwise, make w ₀=w.

6, LDPC coding method according to claim 3 is characterized in that, the step that the described structure of step B3 satisfies the reversible submultinomial of distance restraint condition comprises:

B31, according to nonzero element number w ₀Requirement, select w at random the integer of the m-1 from 1 to m-1 ₀-1 different integer a1, a2 ..., aw ₀Position 0 is added in-1 position as nonzero element, constitutes multinomial 1+x ^A1+ x ^A2+ ...+x ^Aw0-1

B32, multinomial 1+x that calculating constitutes ^A1+ x ^A2+ ...+x ^Aw0-1Distance between any two nonzero elements, and judge whether the distance that calculates is repeated to use, if, then return step B31, produce described multinomial again; Otherwise, execution in step B33;

B33, judge whether full rank of the subcycle matrix that obtains by described multinomial cyclic shift, if, then according to the position updated space put of nonzero element in the multinomial that this step generated and finish; Otherwise, return step B31, produce described multinomial again.

7, LDPC coding method according to claim 6 is characterized in that, further comprises before described step B31: a number of attempt counter is set;

When execution in step B31 first, it is 1 that described number of attempt counter is set;

After first, before every execution in step B31, described number of attempt counter is added 1, and judge whether described number of attempt Counter Value surpasses predefined higher limit, if then represent described nonzero element number w ₀Require too high, and with described nonzero element number w ₀Subtract after 1, carry out described step B31 again; Otherwise, direct execution in step B31.

8, LDPC coding method according to claim 3 is characterized in that, the step that other submultinomials of distance restraint condition are satisfied in the described generation of step B4 comprises:

B41, according to nonzero element number w ₀Requirement, select w at random according to available position record ₀-1 different integer a1, a2 ₂..., aw ₀Position 0 is added in-1 position as nonzero element, constitutes multinomial 1+x ^A1+ x ^A2+ ...+x ^Aw0-1

B42, evaluator 1+x ^A1+ x ^A2+ ...+x ^Aw0-1Distance between any two nonzero elements, and judge whether the distance that calculates is repeated to use, if, then return step B41, produce described multinomial again; Otherwise, according to the position updated space put of nonzero element in the multinomial that this step generated.

9, LDPC coding method according to claim 8 is characterized in that, further comprises before described step B41: a number of attempt counter is set;

When execution in step B41 first, it is 1 that described number of attempt counter is set;

After first, before every execution in step B41, described number of attempt counter is added 1, and judge whether described number of attempt Counter Value surpasses predefined higher limit, if then represent described nonzero element number w ₀Require too high, and with described nonzero element number w ₀Subtract after 1, carry out described step B41 again; Otherwise, direct execution in step B41.

10, according to claim 6 or 8 described LDPC coding methods, it is characterized in that described updated space put is specially: from available position record, remove the position that institute's generator polynomial is occupied.

11, LDPC coding method according to claim 10 is characterized in that, described position is the distance between any two nonzero elements in the described multinomial.

12, LDPC coding method according to claim 1 is characterized in that, the described step of deriving the generator matrix of LDPC sign indicating number according to the L that is generated a circulation submatrix of step C comprises:

According to formula $G=\left[\begin{array}{cc}& G_1\\ & G_2\\ I& .\\ & .\\ & .\\ & G_{L-1}\end{array}\right]$ Calculate described generator matrix G, wherein, $G_k={\left(\begin{array}{cc}{A}_L^{-1}& A_k\end{array}\right)}^T,k=1..L-1,$ I representation unit matrix, A _LBe a reversible subcycle matrix that is generated, A _kFor removing described reversible subcycle matrix A _LOutside other L-1 sub-circular matrixes, operator () ^TThe transposition computing of representing matrix.

13, a kind of low-density checksum LDPC code device is characterized in that, comprising:

L-1 length is the circulating register of m, and wherein L and m are natural number;

L-1 corresponding one by one with described circulating register and connect m input binary adder;

And the output with described L-1 m input binary adder that is connected to described L-1 m input binary adder is imported binary adder as the L-1 that imports.

14, LDPC code device according to claim 13 is characterized in that, m input of described L-1 m input binary adder is definite by the generator matrix of LDPC sign indicating number with the annexation between the m position output of its corresponding circulating register.

According to claim 13 or 14 described LDPC code devices, it is characterized in that 15, described L-1 m input binary adder and described L-1 input binary adder are realized by the XOR gate circuit.

16, a kind of generation method of low-density checksum LDPC sign indicating number parity matrix, described parity matrix is by L circulation submatrix, and L is a natural number, it is characterized in that, and described method comprises:

According to the code length of described LDPC sign indicating number and the number L of described circulation submatrix, generate L circulation submatrix successively, and derive the parity matrix of LDPC sign indicating number according to the L that is generated a circulation submatrix, make the ringlet of described parity matrix grow up and have a maximum smallest hamming distance in 4.

17, LDPC sign indicating number parity check matrix generating method according to claim 16 is characterized in that, the described method that generates L circulation submatrix successively comprises:

A, determine the nonzero element number w in the multinomial of this Reversible Cycle submatrix of expression according to the number L of the code length of LDPC sign indicating number and determined circulation submatrix ₀

B, according to nonzero element number w ₀Requirement, select w at random according to available nonzero element position record ₀-1 different integer a1, a2 ₂..., aw ₀Position 0 is added in-1 position as nonzero element, constitutes multinomial 1+x ^A1+ x ^A2+ ...+x ^Aw0-1

C, evaluator 1+x ^A1+ x ^A2+ ...+x ^Aw0-1Distance between any two nonzero elements, and judge whether the distance calculate is repeated to use, if, illustrate that then the ringlet length of described parity matrix is less than or equal to 4, next return step b, produce described multinomial again; Otherwise, obtain a circulation submatrix according to the multinomial that this step generated through cyclic shift, upgrade described position record according to the position of nonzero element in the described multinomial then, and return step b and continue to generate next circulation submatrix, until generating whole L circulation submatrixs.

18, LDPC sign indicating number parity check matrix generating method according to claim 17 is characterized in that, in generating a polynomial process of son, further comprises:

A number of attempt counter is set, and the initial value of described number of attempt counter is set to 1;

Before inferior every execution in step b, described number of attempt counter is added 1, and judge whether described number of attempt Counter Value surpasses predefined higher limit, if then represent described nonzero element number w ₀Require too high, and with described nonzero element number w ₀Subtract after 1, carry out described step b again; Otherwise, direct execution in step b.

19, LDPC sign indicating number parity check matrix generating method according to claim 17 is characterized in that, the nonzero element number w in the multinomial of described this Reversible Cycle submatrix of definite expression of step a ₀Method be: according to formula ${\mathrm{LC}}_w^2\&le;n/2L$ The maximum integer w of this formula requirement is satisfied in calculating, if the w that calculates is an even number, then makes w ₀=w+1; Otherwise, make w ₀=w.

20, LDPC sign indicating number parity check matrix generating method according to claim 17 is characterized in that, described position is the distance between any two nonzero elements in the described multinomial;

The described updated space put of step c is specially: remove the distance between any two nonzero elements in institute's generator polynomial the distance record between available any two nonzero elements.

21, LDPC sign indicating number parity check matrix generating method according to claim 17 is characterized in that, comprises at least one Reversible Cycle submatrix in the L that is generated the circulation submatrix;

In the process that generates described Reversible Cycle submatrix, described step c is after judging distance between the nonzero element and not reusing, further comprise: judge whether full rank of the subcycle matrix that obtains by described multinomial cyclic shift, if, then root obtains a circulation submatrix according to the multinomial that this step generated through cyclic shift, upgrades described nonzero element position record according to the position of nonzero element in the described multinomial then; Otherwise, return step b, produce described Reversible Cycle submatrix again.

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