CN101272223A - Decoding method and device for low-density generating matrix code - Google Patents

Abstract

The invention relates to an interpretation method and device for generating a matrix code with low density. The method comprises the following contents: a known bit is filled in a received codeword sequence R and a codeword sign erased by a channel in R is deleted to obtain Re; a row erased by the channel from Gldgct is deleted to obtain Ge; a row replacement is carried out on Ge to generate the right formula that A relates to a triangle phalanx under M order; Gaussian elimination is carried out on Ga to generate Gb so as to lead the phalanx consisting of L lines before Gb to be a unit phalanx; simultaneously replacement and adding operations of corresponding elements are carried out on Re according to the line replacement and line adding operations are carried out during the Gaussian elimination process to generate Re'; It' is obtained according to a relation formula that Gb multiplied by It' is equal to Re' and It' is carried out reversed replacement according to a row replacement corresponding relation to obtain It; st is obtained according to the relation formula that Gldgct (0:L-1, 0:L-1) multiplied by It is equal to st; the filled L-K known bits are deleted from st to obtain the information sequence of the K bit.

Description

A kind of interpretation method of low density generated matrix code and device

Technical field

The present invention relates to the data decoding and coding field, relate in particular to a kind of interpretation method and device of low density generated matrix code.

Background technology

In data transmission procedure, if the packet check errors that receiving terminal receives, then the data segment with mistake abandons, and is equivalent to wipe, and this channel model is a kind of important channel model erasure channel.File is based on data packet communication when transmitting on the internet, the termination that is received of each packet or zero defect is received usually, or just is not received termination and receives at all.In the transmission control protocol (Transmission Control Protocol, be called for short TCP), be the error detection retransmission mechanism at the way of Network Packet Loss, the packet that promptly utilizes input need retransfer to the feedback channel control of output.When receiving terminal detects packet loss, produce one and resend control signal, up to correctly receiving complete data packet; And when receiving terminal receives packet, to produce a confirmation of receipt signal equally.Transmitting terminal also can be followed the tracks of each packet up to receiving the affirmation signal that feeds back, otherwise will resend.

Data broadcast service based on stream mode and file downloading mode is the business of point to multiple spot, does not allow feedback, and traditional error detection retransmission mechanism can't use, and needs to use forward error correction (FEC) to guarantee the reliable transmission of data.Classical application layer FEC comprise RS (Reed-Solomon, Reed. the Saloman) sign indicating number and digital fountain sign indicating number (Fountain codes) etc.The coding and decoding complexity of RS sign indicating number is higher, generally only is applicable to the situation that code length is smaller.LT (Luby Transform, Lu Bai conversion) sign indicating number and Raptor (Rui Pute) but yard be the digital fountain sign indicating number of two kinds of practical applications.The LT sign indicating number has linear coding and decoding time, and the raising of essence is arranged with respect to the RS sign indicating number; And therefore the Raptor sign indicating number has higher decoding efficiency owing to adopted precoding technique.At 3GPP (3rd Generation Partnership Project, third generation partner program) multicast and broadcast multimedia service (Multimedia Broadcast/MulticastService, abbreviation MBMS) and in the digital video broadcasting (Digital Video Broadcasting is called for short DVB) all adopted the Raptor sign indicating number of Digital Fountain (digital fountain) company as its FEC encoding scheme.

If the preceding K position of coding back code word is identical with information bit, then claim this sign indicating number to be systematic code.The process of coding is exactly to generate the long process of N bit code by K information bit, by increasing the purpose that N-K check digit reaches EDC error detection and correction.The LT sign indicating number is the coded system of back-up system sign indicating number not, so the LT sign indicating number is difficult to satisfy some actual FEC coding demand; Raptor sign indicating number back-up system sign indicating number, but the Raptor sign indicating number needs independent precoding process, promptly needs a pre-coding matrix, and therefore the complexity of coding is higher.

Because therefore the shortcoming of above-mentioned coding method has introduced LDGC (Low Density GeneratorMatrix Codes, low density generated matrix code).LDGC is a kind of linear block codes, and the nonzero element in its generator matrix (encoder matrix) is normally sparse, and simultaneously, the LDGC sign indicating number still is a kind of systematic code.

The coding of LDGC is to utilize the corresponding relation of information bit in the systematic code (being data to be sent) and intermediate variable to obtain intermediate variable earlier, and then multiply by code word after generator matrix obtains encoding with intermediate variable.Specifically, cataloged procedure is to produce L bit sequence s after earlier K bit information sequence m being filled d=L-K known bits, then according to equation group relational expression: I * G _Ldgc(0:L-1,0:L-1)=s, the group of solving an equation generates L bit intermediate variable sequence I, and then multiply by generator matrix by intermediate variable, i.e. I * G _Ldgc(0:L-1,0:N+d-1) the codeword sequence C ' of generation N+d bit (comprising d filling bit) _Ldgc, C ' _LdgcD filling bit do not need transmission, thereby that real transmission is the codeword sequence C of N bit _LdgcC _LdgcThrough (may wipe) behind the channel, the codeword sequence that receiving terminal receives is R.Wherein, s is the vector of 1 * L, and I is the vector of 1 * L, and R is the vector of 1 * N, G _Ldgc(0:L-1 0:L-1) is L * L square formation, this square formation normally one go up triangle or lower triangular matrix, G _Ldgc(0:L-1 0:N+d-1) is the matrix of L * (N+d).The detailed process of coding can referenced patent " coding method of low density generated matrix code and device, and interpretation method and device ".

The decode procedure of LDGC sign indicating number is earlier to utilize to receive codeword sequence R (comprise filling bit, following reception codeword sequence all is meant and comprises filling bit), LDGC generator matrix G _LdgcAnd equation group relations I * G of intermediate variable I _Ldgc(0:L-1,0:N+d-1)=R, the group of solving an equation is tried to achieve intermediate variable I; Then according to relation " I * G of information bit s (comprising filling bit) and intermediate variable I _Ldgc(0:L-1,0:L-1)=s " obtain information bit s, remove filling bit and just obtain original information sequence m.

Wherein, the step of most critical is to ask intermediate variable, often needs to separate large-scale system of linear equations.On the engineering, separate system of linear equations and can adopt methods such as Gaussian elimination method or iterative method, according to the characteristics of LDGC sign indicating number, Gaussian elimination method is more suitable for the decoding of LDGC sign indicating number.Thereby the speed of Gaussian elimination process directly has influence on the speed of LDGC sign indicating number decoding.

According to the needs of describing Gaussian elimination method, every in the following narration is that following target " vector " or " matrix " all represent it is the transposition of former " vector " or " matrix " with small letter t, vector or matrix and its transposition are duplicate from content, can represent same object sometimes.For example, definition G _LdgctBe G _LdgcTransposition, I _tBe the transposition of I, R _tBe the transposition of R, because of I and R are row vector, I here _tAnd R _tIt all is column vector.

Fig. 1 is the LDGC generator matrix G behind the transposition _LdgctSchematic diagram.As shown in Figure 1, G _LdgctIn the capable correspondence of preceding L square formation normally one go up triangle or lower triangular matrix.Wherein, the x among Fig. 1, y can be 0.

According to system of linear equations G _Ldgct(0:N+d-1,0:L-1) * I _t=R _tFind the solution intermediate variable I _tProcess in, the Gaussian elimination that is carried out need be to G _LdgctMatrix is done " line replacement, row addition and column permutation " three kinds of elementary transformations.According to the linear algebra principle, in order to guarantee the correctness of equation group, to G _LdgctWhen matrix carries out elementary transformation, need be to I _tAnd R _tDo following corresponding processing:

1) if line replacement is G _LdgctThe capable and j of i advance line replacement, then R _tI bit and j bit need replace;

2) go addition, if G _LdgctCapable and capable addition, the then R of carrying out of j of i _tI bit and j bit need carry out addition (mould 2 adds);

3) if column permutation is G _LdgctI row and j be listed as and replace, I then _tI bit and j bit need replace.

Because final result need obtain I _t, and I _tIn element at G _LdgctCorrespondingly done displacement when making column permutation, thereby need be to I _tThe displacement situation note down so that the replacement process of inverting of back.On the engineering, can write down I by an array _tThe displacement situation.And R _tNot the data that finally need, can not need to write down its disposition directly to its processing.

Because these transformation relations are strict corresponding, and the main complexity of Gaussian elimination is embodied in G _LdgctProcessing on, easy for what narrate, every below at G _LdgctElementary transformation, correspondingly to I _tAnd R _tProcessing need to handle in strict accordance with three kinds of top situations.In order to give top priority to what is the most important, simplify I sometimes below _tAnd R _tThe description of processing.

In the prior art, there are 2 deficiencies in the Gaussian elimination method of LDGC decoding employing standard: the first, can not make full use of in the strictness that LDGC sign indicating number generator matrix has triangle or down triangle characteristics (as shown in Figure 1) simplify the unit that disappears and operate; The second, can not utilize the structurized characteristics of LDGC sign indicating number generator matrix to come the index of direct generator matrix nonzero element, need the whole generator matrix of storage, the complexity that has increased storage and calculated.Thereby the Gaussian elimination method of the standard of employing, the efficient of decoding is lower.

Summary of the invention

Technical problem to be solved by this invention is, overcomes the deficiencies in the prior art, proposes a kind of high efficiency LDGC interpretation method.

In order to address the above problem, the invention provides a kind of interpretation method of low density generated matrix code, the bit information sequence through the back transmission of LDGC coding that receives is deciphered, it is characterized in that this method comprises following content:

S1: in the codeword sequence R that receives, fill L-K known bits and with R in deleted by the code-word symbol of channel erase, obtain R _eAnd with above-mentioned by the transposed matrix G of the row of the code-word symbol correspondence of channel erase from the LDGC generator matrix _LdgctMiddle deletion obtains G _e

S2: to G _eCarry out column permutation, generate $G_a=\left[\begin{array}{cc}A& C\\ D& B\end{array}\right],$ Wherein A is a triangle square formation under the M rank, and record G _eAnd G _aThe column permutation corresponding relation;

S3: to G _aCarry out Gaussian elimination and generate G _b, make G _bThe square formation of the capable composition of preceding L be unit matrix; Simultaneously according to line replacement that is carried out in the above-mentioned Gaussian elimination process and row add operation mutually, to R _eCarry out the displacement of respective element and add operation mutually, generate Re ';

S4: according to relational expression G _b* I ' _t=Re ' solves I ' _t, and according to above-mentioned column permutation corresponding relation to I ' _tCarry out inverse permutation and obtain I _t

S5: according to relational expression G _Ldgct(0:L-1,0:L-1) * I _t=s _tObtain s _t, and from s _tL-K known bits of the above-mentioned filling of middle deletion obtains the information sequence of K bit;

Above-mentioned G _Ldgct, L column matrix capable for N+L-K.

In addition, described M=L-X _L, X _LFor in preceding L the code-word symbol of R by the bit number of channel erase.

In addition, establish Xset _LIn preceding L the code-word symbol of filling R behind the described d known bits, the set of the sequence number of deleted code-word symbol, the sequence number number in this set is described X _L

Among the step S2, with described G _eMiddle row sequence number belongs to Xset _LRow move to G _eLow order end, the position that respective column is vacated does not belong to Xset by the subsequent column sequence number _LLeu time fill, obtain described G _a

In addition, among the step S3, to G _aCarry out Gaussian elimination and specifically comprise following substep:

S31: to described G _aIn A and D carry out Gaussian elimination, make A become M rank unit matrix E _M, simultaneously D is become element and is entirely 0 (N-K-(X _T-X _L)) row M column matrix, that is:

${G_a}^{,}=\left[\begin{array}{cc}{E}_M& A^{-1}C\\ 0& B-{\mathrm{DA}}^{-1}C\end{array}\right];$

S32: to G _a' in B-DA ^-1C carries out Gaussian elimination, and making the square formation of the capable correspondence of its preceding L-M is unit matrix, and with A ^-1It is 0 the capable L-M column matrix of M entirely that C disappears for element, that is:

$G_b=\left[\begin{array}{cc}{\mathrm{<figure-callout\; id="0"\; label="E\; M"\; filenames="A20081009664400191.png,A20081009664400201.png"\; state="\{\{state\}\}">E</figure-callout>}}_M& 0\\ 0& E_{L-M}^{\&prime;}\end{array}\right].$

In addition, among the step S31, judge the capable y column element of the x H[x among A and the D by the following method, y] whether be nonzero element, and A and D are carried out described Gaussian elimination according to the position of nonzero element:

S311: the sequence number set Xset according to code-word symbol deleted among the R behind d known bits of filling obtains above-mentioned H[x, y] at G _LdgctIn the ranks position: x ', y ';

S312: if $G_{\mathrm{bt}}^{\mathrm{uniform}}[x_z,y_z]=0,$ H[x then, y] be neutral element, this flow process finishes, otherwise carries out next step;

S313: if ix _z=mod (iy _z+ offset, z), A[x then, y] be nonzero element; Otherwise, A[x, y] and be neutral element;

Wherein: z is a spreading factor, z _MaxBe the largest extension factor;

x _z＝floor(x’/z)，y _z＝floor(y’/z)；

ix _z＝mod(x’，z)，iy _z＝mod(y’，z)；

$\mathrm{offset}=\mathrm{floor}\left(G_{\mathrm{bt}}^{\mathrm{uniform}}\right[x_z,y_z]\&CenterDot;z/z_{\max }).$

The present invention also provides a kind of code translator of low density generated matrix code, and the bit information sequence through the back transmission of LDGC coding that receives is deciphered, and it is characterized in that, this device comprises: fill erase unit, the column permutation unit, Gaussian elimination unit, information sequence generation unit; Wherein:

Fill erase unit, be used for filling d known bits and will being deleted generation and output R by the code-word symbol of channel erase at the codeword sequence R that receives _eAnd with above-mentioned by the transposed matrix G of the row of the code-word symbol correspondence of channel erase from the LDGC generator matrix _LdgctMiddle deletion generates also output G _e

The column permutation unit is used for the G to described filling erase unit output _eCarry out column permutation, generate and output $G_a=\left[\begin{array}{cc}A& C\\ D& B\end{array}\right],$ Wherein A is a triangle square formation under the M rank, and output G _eAnd G _aThe column permutation correspondence relationship information;

The Gaussian elimination unit is used for the G to the output of described column permutation unit _aCarry out Gaussian elimination, generate and output G _b, make G _bThe square formation of the capable composition of preceding L be unit matrix; Simultaneously according to line replacement that is carried out in the above-mentioned Gaussian elimination process and row add operation mutually, to the R of described filling erase unit output _eCarry out the displacement of respective element and add operation mutually, generate and output Re ';

The information sequence generation unit is used for according to relational expression G _b* I ' _t=Re ' generates I ' _tAccording to the column permutation correspondence relationship information of described column permutation unit output to I ' _tCarry out inverse permutation and generate I _tAccording to relational expression G _Ldgct(0:L-1,0:L-1) * I _t=s _tGenerate s _t, and from s _tThe information sequence of output K bit behind d known bits of middle deletion;

Above-mentioned G _Ldgct, L column matrix capable for N+L-K.

In addition, described column permutation unit is a triangle square formation under the M rank through the described A that column permutation generates, M=L-X _L, X _LFor in preceding L the symbol of R by the bit number of channel erase.

In addition, establish Xset _LIn preceding L the code-word symbol of filling R behind the described d known bits, the set of the sequence number of deleted code-word symbol, the sequence number number in this set is described X _L

Described column permutation unit passes through G _eMiddle row sequence number belongs to Xset _LRow move to G _eLow order end, the position that respective column is vacated does not belong to Xset by the subsequent column sequence number _LLeu time fill, generate described G _a

In addition, described Gaussian elimination unit adopts following substep to G _aCarry out Gaussian elimination:

S31: to described G _aIn A and D carry out Gaussian elimination, make A become M rank unit matrix E _M, simultaneously D is become element and is entirely 0 (N-K-(X _T-X _L)) row M column matrix, that is:

${G_a}^{,}=\left[\begin{array}{cc}{E}_M& A^{-1}C\\ 0& B-{\mathrm{DA}}^{-1}C\end{array}\right];$

S32: to G _a' in B-DA ^-1C carries out Gaussian elimination, and making the square formation of the capable correspondence of its preceding L-M is unit matrix, and with A ^-1It is 0 the capable L-M column matrix of M entirely that C disappears for element, that is:

$G_b=\left[\begin{array}{cc}{\mathrm{<figure-callout\; id="0"\; label="E\; M"\; filenames="A20081009664400191.png,A20081009664400201.png"\; state="\{\{state\}\}">E</figure-callout>}}_M& 0\\ 0& E_{L-M}^{\&prime;}\end{array}\right].$

In addition, described Gaussian elimination unit is judged the capable y column element of the x H[x among A and the D, y by the following method] whether be nonzero element, and A and D are carried out described Gaussian elimination according to the position of nonzero element:

S311: the sequence number set Xset according to code-word symbol deleted among the R behind d known bits of filling obtains above-mentioned H[x, y] at G _LdgctIn the ranks position: x ', y ';

S312: if $G_{\mathrm{bt}}^{\mathrm{uniform}}[x_z,y_z]=0,$ H[x then, y] be neutral element, this flow process finishes, otherwise carries out next step;

S313: if ix _z=mod (iy _z+ offset, z), A[x then, y] be nonzero element; Otherwise, A[x, y] and be neutral element;

Wherein: z is a spreading factor, z _MaxBe the largest extension factor;

x _z＝floor(x’/z)，y _z＝floor(y’/z)；

ix _z＝mod(x’，z)，iy _z＝mod(y’，z)；

$\mathrm{offset}=\mathrm{floor}\left(G_{\mathrm{bt}}^{\mathrm{uniform}}\right[x_z,y_z]\&CenterDot;z/z_{\max }).$

Adopt LDGC interpretation method of the present invention, can make full use of the diagonalization characteristics that structuring LDGC encoder matrix is had, compare with the interpretation method of direct employing Gaussian reduction, can reduce decoding complexity greatly and accelerate decoding speed, LDGC be can be applicable in the communication system of two-forty.

Description of drawings

Fig. 1 is the LDGC generator matrix G behind the transposition _LdgctSchematic diagram;

Fig. 2 is the interpretation method flow chart of embodiment of the invention low density generated matrix code;

Fig. 3 is for wiping the schematic diagram of processing according to the erasure case that receives codeword sequence R to generator matrix;

Fig. 4 is that the embodiment of the invention is to wiping generator matrix G _eCarry out the schematic diagram of column permutation;

Fig. 5 is that the embodiment of the invention is to G _aCarry out the schematic diagram of Gaussian elimination;

Fig. 6 is that the embodiment of the invention is carried out the method flow diagram that neutral element is differentiated;

Fig. 7 is the code translator schematic diagram of embodiment of the invention low density generated matrix code.

Embodiment

In order to describe needs, the reception codeword sequence R (comprising filling bit) that establishes length earlier and be N+d altogether by channel erase X _TIndividual code-word symbol, this X _TThe individual set that is wiped free of the code-word symbol location index is Xset; Especially, all set of being formed less than the location index element of L are XSet among the Xset _L, XSet _LElement number be X _LIndividual, i.e. XSet _LExpression be among the R before in L symbol by channel erase X _LIndividual code-word symbol; If M=L-X _L

Because the basic element in the LDGC decoding in all objects all is from finite field gf (2), so the computing between object also all is the computing of finite field gf (2) definition.

Basic ideas of the present invention are that the diagonalization characteristics of utilizing structuring LDGC generator matrix to be had to carrying out column permutation through the LDGC generator matrix of wiping processing, make the LDGC generator matrix have earlier $\left[\begin{array}{cc}A& C\\ D& B\end{array}\right]$ Matrix form, wherein matrix A is M rank square formations, and has the strict characteristics of triangle down.And then to utilize A be the characteristics of strictly lower triangular matrix, and the structures that A and D had are simplified decoding.

Describe the present invention below in conjunction with drawings and Examples.

Fig. 2 is the interpretation method flow chart of embodiment of the invention low density generated matrix code.As shown in Figure 2, this method comprises following steps:

201: filling length in the relevant position that receives codeword sequence R is the known bits sequence of d=L-K, for example: and 1,1 ..., 1, delete simultaneously by the code-word symbol of channel erase, obtain R _e

Wherein K is the length of original information bits, and L is that original information bits is through filling the length of back coding.

202: according to receiving the situation that codeword sequence R is wiped free of, to LDGC generator matrix G _LdgctGo and wipe (deletion) processing, obtain wiping generator matrix G _e

Fig. 3 is for wiping the schematic diagram of processing according to the erasure case that receives codeword sequence R to generator matrix.As shown in Figure 3, through wiping the generator matrix G of processing _ePreceding L capable no longer be following triangle square formation.

Suppose to fill the R (r after the known bits sequence ₀, r ₁... r _N+d-1) in X _TIndividual symbol: { r _i, r _j' ..., r _pR _xFallen by channel erase, wherein, the X in the front L symbol _LIndividual symbol { r _i, r _j..., r _pFallen by channel erase; Xset={i then, j ..., p ..., x}; Xset _L=i, j ... p}.G correspondingly _LdgctIn i, j ..., p ..., x} is capable need to be wiped free of, and obtains G _e, G at this moment _eTop matrix has not been strict diagonalization, shown in Fig. 3 (c) owing to wiped several rows.

203: to wiping generator matrix G _eCarry out column permutation, make G _eIn be lower triangular matrix with (0,0) for the M rank square formation on summit, with G _eMatrix note after the displacement is made displacement generator matrix G _aWrite down G simultaneously _eAnd G _aThe column permutation corresponding relation, be used for follow-up to I _tMake corresponding replacement operator, generate I ' _t

Fig. 4 is to wiping generator matrix G _eCarry out the schematic diagram of column permutation.

Specifically, in order to obtain lower triangular matrix, with G _eMiddle row sequence number belongs to Xset _LRow move to G _eLow order end, the position that respective column is vacated does not belong to Xset by the subsequent column sequence number _LLeu time fill, obtain replacing generator matrix:

$G_a=\left[\begin{array}{cc}A& C\\ D& B\end{array}\right].$

Wherein, matrix A is M rank square formations, and has the strict characteristics of triangle down; Matrix C is the matrix of size for M * (L-M); Matrix D is (N-K-(X _T-X _L)) * matrix of M; Matrix B is (N-K-(X _T-X _L)) * (L-M) matrix.

According to G _LdgctThe column permutation situation, simultaneously to I _tMake corresponding replacement operator, establish I _tBecome I ' after the displacement _tI _tTo I ' _tDisplacement relation can come record by an array, be used for the replacement process of inverting of back.

204: to displacement generator matrix G _aCarry out Gaussian elimination, make G _aThe L rank square formation of the preceding capable composition of L becomes a L rank unit matrix (if G _aFull rank), the matrix note that disappears after the unit is made G _b, promptly $G_b=\left[\begin{array}{c}{\mathrm{<figure-callout\; id="0"\; label="E\; L"\; filenames="A20081009664400191.png,A20081009664400201.png"\; state="\{\{state\}\}">E</figure-callout>}}_L\\ 0\end{array}\right];$ Simultaneously to R _eCarry out the displacement of respective element and add operation mutually, establish R _eBecome R after the conversion _e';

Above-mentioned E _LExpression L rank unit matrix.

Because G _aHave following characteristics:

1) on the diagonal of A nonzero element is arranged all, A has the strict characteristics of triangle down;

2) nonzero element among A and the D can directly be calculated by the defined formula of when coding structure generator matrix, so in fact A and D do not need storage.

Thereby, to G _aThe Gaussian elimination process can regard as and comprise following three subprocess:

204a) utilize the characteristics of A to carry out Gaussian elimination: A is transformed into M rank unit matrix E _M

When A is carried out Gaussian elimination, can directly calculate the position of each nonzero element among the A, and A be done the add operation of row phase, therefore need not the actual storage matrix A according to the position of each nonzero element.

The concrete grammar (judging that in other words whether each element among the A is 0 method) that calculates each nonzero element position among the A is described in more detail below.

By A being carried out Gaussian elimination (add operation of row phase), A can be transformed into M rank unit matrix E _MAbove-mentioned " row addition " operation can act on the C simultaneously, final result be equivalent to A and C simultaneously premultiplication A ^-1, that is:

204b) utilize unit matrix E _MD is carried out Gaussian elimination, D is become complete 0 matrix; Correspondingly, B need deduct D premultiplication A ^-1The result of C, the subtraction of element is equivalent to the nodulo-2 addition of element between matrix between matrix here, and final result is equivalent to:

Equally, when D is carried out Gaussian elimination, can directly calculate the position of each nonzero element among the D, and D be done the add operation of row phase, therefore need not the actual storage matrix D according to the position of each nonzero element.The concrete grammar (judging that in other words whether each element among the D is 0 method) that calculates each nonzero element position among the D is described in more detail below.

Said process is shown in Fig. 5 (a), Fig. 5 (b).

In order to simplify description, establish S=B-DA ^-1C.

204c) S is carried out Gaussian elimination;

If G _aBe full rank, S can be transformed into a matrix (matrix of the capable correspondence of L-M is a unit matrix promptly) that comprises (L-M) rank unit matrix by Gaussian elimination, and the while is the A of cancellation top fully ^-1C.Be G _aFinally can become following form by Gaussian elimination:

Above-mentioned E ' _L-ML-M rank of the capable composition of preceding L-M unit matrix, the row of back is complete zero row.Shown in Fig. 5 (c).

If G _aFull rank not, decoding failure then, this method finishes.

Equally, according to G _aMake line replacement and row add operation mutually that Gaussian elimination carries out, to R _eCarry out the displacement of respective element and add operation mutually, establish R _eBecome R after the conversion _e'.

205: according to equation group relational expression G _b* I ' _t=R _e', can obtain equation I ' _t=R _e' (1:L); Can directly obtain I ' by this equation _tPass through I then _tTo I ' _tDisplacement relation (be G _eTo G _aColumn permutation relation) carry out inverse permutation, can be by I ' _tTry to achieve I _t

206: according to the relation of information bit s (comprising filling bit) and intermediate variable I:

G _Ldgct(0:L-1,0:L-1) * I _t=s _tObtain information bit s _t, remove s _tIn d known filling bit just obtain the information sequence m of K bit.

Whether will be example with A below, be that the method for nonzero element is described to judging each element among A and the D.Judgement to element among the D is identical with A.

Fig. 6 is that the embodiment of the invention is carried out the method flow diagram that neutral element is differentiated.

At first each symbol that uses in this method of discrimination is described:

G _b ^Uniform: be the LDGC basis matrix that defines in the CMMB standard; G _b ^NuniformSize be k _b* n _b=12 * 40, the basis matrix G behind the transposition then _b ^UniformSize is n _b* k _b=40 * 12;

Spreading factor z=ceil (L/k _b); Ceil () expression rounds downwards;

Largest extension factor z _Max=683.

As shown in Figure 6, this method adopts following steps to A[x, y] whether be 0 to judge:

601: obtain A[x, y] at the G that wipes before handling according to deleted line index Xset _LdgctIn the ranks position: x ', y '; Be A[x, y] be G _LdgctIn x ' OK, y ' column element;

602: calculate x _z=floor (x '/z), y _z=floor (y '/z);

Floor () expression rounds up.

603: according to G _Bt ^UniformIn x _zOK, y _zThe element of row, i.e. G _Bt ^Uniform[x _z, y _z] whether be zero judgement A[x, y] whether be zero:

If $G_{\mathrm{bt}}^{\mathrm{uniform}}[x_z,y_z]=0,$ A[x then, y]=0;

If $G_{\mathrm{bt}}^{\mathrm{uniform}}[x_z,y_z]>0,$ A[x then, y] might non-zero, need to carry out follow-up decision operation.

604: calculate ix _z=mod (x ', z), iy _z=mod (y ', z);

605: the correction formula according to the CMMB standard definition is calculated side-play amount offset;

Correction formula is: floor (z (g _{I, j} ^b) _Uniform/ z _Max); (g _{I, j} ^b) _UniformBe exactly G _b ^Uniform[i, j], or G _Bt ^Uniform[j, i];

$\mathrm{offset}=\mathrm{floor}\left(G_{\mathrm{bt}}^{\mathrm{uniform}}\right[x_z,y_z]\&CenterDot;z/z_{\max }).$

606: according to ix _zWhether equal mod (iy _z+ offset z) judges A[x, y] whether be 0:

If ix _z=mod (iy _z+ offset, z), A[x then, y] be nonzero element;

Otherwise, A[x, y] and be neutral element.

Judge element D[x among the D, y] whether be that the method for neutral element is identical with above-mentioned steps.

Fig. 7 is the code translator schematic diagram of embodiment of the invention low density generated matrix code.As shown in Figure 7, this device comprises: fill erase unit, column permutation unit, Gaussian elimination unit, information sequence generation unit.Wherein,

Fill erase unit, be used for filling d known bits and will being deleted generation and output R by the code-word symbol of channel erase at the codeword sequence R that receives _eAnd with above-mentioned by the transposed matrix G of the row of the code-word symbol correspondence of channel erase from the LDGC generator matrix _LdgctMiddle deletion generates also output G _e

The column permutation unit is used for the G to described filling erase unit output _eCarry out column permutation, make G _eIn be that the M rank square formation A on summit is a lower triangular matrix with the 0th row, the 0th column element, generate also output $G_a=\left[\begin{array}{cc}A& C\\ D& B\end{array}\right],$ And output G _eAnd G _aThe column permutation correspondence relationship information;

Described M=L-X _L, X _LFor in preceding L the symbol of R by the bit number of channel erase.

The column permutation unit can be with G _eMiddle row sequence number belongs to Xset _LRow move to G _eLow order end, the position that respective column is vacated does not belong to Xset by the subsequent column sequence number _LLeu time fill, obtain described G _a

The Gaussian elimination unit is used for the G to the output of described column permutation unit _aCarry out Gaussian elimination (concrete steps as mentioned above), generate and output G _b, make G _bThe square formation of the capable composition of preceding L be L rank unit matrix; Simultaneously according to line replacement that is carried out in the above-mentioned Gaussian elimination process and row add operation mutually, to the R of described filling erase unit output _eCarry out the displacement of respective element and add operation mutually, generate and output Re ';

In above-mentioned Gaussian elimination process, the Gaussian elimination unit also judges according to formula whether the element among A and the D is nonzero element, and concrete determination methods as mentioned above.

The information sequence generation unit is used for according to relational expression G _b* I ' _t=Re ' generates I ' _tAccording to the column permutation correspondence relationship information of described column permutation unit output to I ' _tCarry out inverse permutation and generate I _tAccording to relational expression G _Ldgct(0:L-1,0:L-1) * I _t=s _tGenerate s _t, and from s _tOutput bit information sequence behind d known bits of middle deletion.

As from the foregoing, adopt interpretation method of the present invention and device, can accelerate the processing speed of Gaussian elimination for the LDGC generator matrix.

According to basic principle of the present invention, the foregoing description can also have multiple mapping mode:

For the LDGC generator matrix of other shape, for example, preceding L behavior upper triangular matrix can be transformed into it and adopt interpretation method of the present invention behind lower triangular matrix.

The above is embodiments of the invention only, is not limited to the present invention, and for a person skilled in the art, the present invention can have various changes and variation.Within the spirit and principles in the present invention all, any modification of being done, be equal to replacement, improvement etc., all should be included within the claim scope of the present invention.

Claims (10)

1, a kind of interpretation method of low density generated matrix code is deciphered the bit information sequence through the back transmission of LDGC coding that receives, and it is characterized in that this method comprises following content:

S1: in the codeword sequence R that receives, fill L-K known bits and with R in deleted by the code-word symbol of channel erase, obtain R _eAnd with above-mentioned by the transposed matrix G of the row of the code-word symbol correspondence of channel erase from the LDGC generator matrix _LdgctMiddle deletion obtains G _e

S2: to G _eCarry out column permutation, generate $G_a=\left[\begin{array}{cc}A& C\\ D& B\end{array}\right],$ Wherein A is a triangle square formation under the M rank, and record G _eAnd G _aThe column permutation corresponding relation;

S3: to G _aCarry out Gaussian elimination and generate G _b, make G _bThe square formation of the capable composition of preceding L be unit matrix; Simultaneously according to line replacement that is carried out in the above-mentioned Gaussian elimination process and row add operation mutually, to R _eCarry out the displacement of respective element and add operation mutually, generate Re ';

S4: according to relational expression G _b* I ' _t=Re ' solves I ' _t, and according to above-mentioned column permutation corresponding relation to I ' _tCarry out inverse permutation and obtain I _t

S5: according to relational expression G _Ldgct(0:L-1,0:L-1) * I _t=s _tObtain s _t, and from s _tL-K known bits of the above-mentioned filling of middle deletion obtains the information sequence of K bit;

Above-mentioned G _Ldgct, L column matrix capable for N+L-K.

2, the method for claim 1 is characterized in that,

Described M=L-X _L, X _LFor in preceding L the code-word symbol of R by the bit number of channel erase.

3, method as claimed in claim 2 is characterized in that,

If Xset _LIn preceding L the code-word symbol of filling R behind the described d known bits, the set of the sequence number of deleted code-word symbol, the sequence number number in this set is described X _L

Among the step S2, with described G _eMiddle row sequence number belongs to Xset _LRow move to G _eLow order end, the position that respective column is vacated does not belong to Xset by the subsequent column sequence number _LLeu time fill, obtain described G _a

4, method as claimed in claim 2 is characterized in that,

Among the step S3, to G _aCarry out Gaussian elimination and specifically comprise following substep:

S31: to described G _aIn A and D carry out Gaussian elimination, make A become M rank unit matrix E _M, simultaneously D is become element and is entirely 0 (N-K-(X _T-X _L)) row M column matrix, that is:

${G_a}^{,}=\left[\begin{array}{cc}{E}_M& A^{-1}C\\ 0& B-{\mathrm{DA}}^{-1}C\end{array}\right];$

S32: to G _a' in B-DA ^-1C carries out Gaussian elimination, and making the square formation of the capable correspondence of its preceding L-M is unit matrix, and with A ^-1It is 0 the capable L-M column matrix of M entirely that C disappears for element, that is:

$G_b=\left[\begin{array}{cc}{E}_M& 0\\ 0& E_{L-M}^{\&prime;}\end{array}\right].$

5, method as claimed in claim 4 is characterized in that,

Among the step S31, judge the capable y column element of the x H[x among A and the D by the following method, y] whether be nonzero element, and A and D are carried out described Gaussian elimination according to the position of nonzero element:

S311: the sequence number set Xset according to code-word symbol deleted among the R behind d known bits of filling obtains above-mentioned H[x, y] at G _LdgctIn the ranks position: x ', y ';

S312: if $G_{\mathrm{bt}}^{\mathrm{uniform}}[x_z,y_z]=0,$ H[x then, y] be neutral element, this flow process finishes, otherwise carries out next step;

S313: if ix _z=mod (iy _z+ offset, z), A[x then, y] be nonzero element; Otherwise, A[x, y] and be neutral element;

Wherein: z is a spreading factor, z _MaxBe the largest extension factor;

x _z＝floor(x’/z)，y _z＝floor(y’/z)；

ix _z＝mod(x’，z)，iy _z＝mod(y’，z)；

$\mathrm{offset}=\mathrm{floor}\left(G_{\mathrm{bt}}^{\mathrm{uniform}}\right[x_z,y_z]\&CenterDot;z/z_{\max }).$

6, a kind of code translator of low density generated matrix code is deciphered the bit information sequence through the back transmission of LDGC coding that receives, and it is characterized in that, this device comprises: fill erase unit, the column permutation unit, Gaussian elimination unit, information sequence generation unit; Wherein:

Fill erase unit, be used for filling d known bits and will being deleted generation and output R by the code-word symbol of channel erase at the codeword sequence R that receives _eAnd with above-mentioned by the transposed matrix G of the row of the code-word symbol correspondence of channel erase from the LDGC generator matrix _LdgctMiddle deletion generates also output G _e

The column permutation unit is used for the G to described filling erase unit output _eCarry out column permutation, generate and output $G_a=\left[\begin{array}{cc}A& C\\ D& B\end{array}\right],$ Wherein A is a triangle square formation under the M rank, and output G _eAnd G _aThe column permutation correspondence relationship information;

The Gaussian elimination unit is used for the G to the output of described column permutation unit _aCarry out Gaussian elimination, generate and output G _b, make G _bThe square formation of the capable composition of preceding L be unit matrix; Simultaneously according to line replacement that is carried out in the above-mentioned Gaussian elimination process and row add operation mutually, to the R of described filling erase unit output _eCarry out the displacement of respective element and add operation mutually, generate and output Re ';

The information sequence generation unit is used for according to relational expression G _b* I ' _t=Re ' generates I ' _tAccording to the column permutation correspondence relationship information of described column permutation unit output to I ' _tCarry out inverse permutation and generate I _tAccording to relational expression G _Ldgct(0:L-1,0:L-1) * I _t=s _tGenerate s _t, and from s _tThe information sequence of output K bit behind d known bits of middle deletion;

Above-mentioned G _Ldgct, L column matrix capable for N+L-K.

7, device as claimed in claim 6 is characterized in that,

Described column permutation unit is a triangle square formation under the M rank through the described A that column permutation generates, M=L-X _L, X _LFor in preceding L the symbol of R by the bit number of channel erase.

8, device as claimed in claim 7 is characterized in that,

If Xset _LIn preceding L the code-word symbol of filling R behind the described d known bits, the set of the sequence number of deleted code-word symbol, the sequence number number in this set is described X _L

Described column permutation unit passes through G _eMiddle row sequence number belongs to Xset _LRow move to G _eLow order end, the position that respective column is vacated does not belong to Xset by the subsequent column sequence number _LLeu time fill, generate described G _a

9, device as claimed in claim 7 is characterized in that,

Described Gaussian elimination unit adopts following substep to G _aCarry out Gaussian elimination:

S31: to described G _aIn A and D carry out Gaussian elimination, make A become M rank unit matrix E _M, simultaneously D is become element and is entirely 0 (N-K-(X _T-X _L)) row M column matrix, that is:

${G_a}^{,}=\left[\begin{array}{cc}{E}_M& A^{-1}C\\ 0& B-{\mathrm{DA}}^{-1}C\end{array}\right];$

S32: to G _a' in B-DA ^-1C carries out Gaussian elimination, and making the square formation of the capable correspondence of its preceding L-M is unit matrix, and with A ^-1It is 0 the capable L-M column matrix of M entirely that C disappears for element, that is:

$G_b=\left[\begin{array}{cc}{E}_M& 0\\ 0& E_{L-M}^{\&prime;}\end{array}\right].$

10, device as claimed in claim 9 is characterized in that,

Described Gaussian elimination unit is judged the capable y column element of the x H[x among A and the D, y by the following method] whether be nonzero element, and A and D are carried out described Gaussian elimination according to the position of nonzero element:

S311: the sequence number set Xset according to code-word symbol deleted among the R behind d known bits of filling obtains above-mentioned H[x, y] at G _LdgctIn the ranks position: x ', y ';

S312: if $G_{\mathrm{bt}}^{\mathrm{uniform}}[x_z,y_z]=0,$ H[x then, y] be neutral element, this flow process finishes, otherwise carries out next step;

S313: if ix _z=mod (iy _z+ offset, z), A[x then, y] be nonzero element; Otherwise, A[x, y] and be neutral element;

Wherein: z is a spreading factor, z _MaxBe the largest extension factor;

x _z＝floor(x’/z)，y _z＝floor(y’/z)；

ix _z＝mod(x’，z)，iy _z＝mod(y’，z)；

$\mathrm{offset}=\mathrm{floor}\left(G_{\mathrm{bt}}^{\mathrm{uniform}}\right[x_z,y_z]\&CenterDot;z/z_{\max }).$

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