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

Decoding method and device for low-density generated matrix code

Technical Field

The invention relates to the field of data coding and decoding, in particular to a decoding method and device for a low-density generated matrix code.

Background

In the data transmission process, if the data packet received by the receiving end is checked to be wrong, the wrong data segment is discarded, which is equivalent to erasure. When files are transmitted over the internet, they are communicated on a packet basis, and each packet is typically received by the receiving end either error-free or not at all. In a Transmission Control Protocol (TCP), an error detection retransmission mechanism is used for network packet loss, that is, a feedback channel from an input end to an output end is used to Control a data packet to be retransmitted. When the receiving end detects packet loss, a retransmission control signal is generated until a complete data packet is correctly received; when the receiving end receives the data packet, a receiving confirmation signal is also generated. The sending end will also track each data packet until receiving the acknowledgement signal fed back, otherwise, it will be sent again.

The data broadcasting service based on the streaming mode and the file downloading mode is a point-to-multipoint service, does not allow feedback, cannot be used by a conventional error detection retransmission mechanism, and needs to use Forward Error Correction (FEC) to ensure reliable transmission of data. Classical application layer FEC includes RS (Reed-Solomon, Reed Solomon) codes and digital Fountain codes (Fountain codes), among others. The RS code has a high coding/decoding complexity and is generally only suitable for a case where the code length is small. LT (Luby Transform) codes and Raptor (Raptor) codes are two digital fountain codes that can be practically used. The LT code has linear coding and decoding time, and is substantially improved relative to the RS code; the Raptor code adopts a precoding technology, so that the Raptor code has higher decoding efficiency. The Multicast Broadcast Multimedia Service (MBMS) and Digital Video Broadcasting (DVB) of 3GPP (3rd Generation Partnership Project) both use the Raptor code of Digital Fountain as their FEC coding scheme.

If the first K bits of the coded code word are the same as the information bits, the code is called a systematic code. The encoding process is a process of generating N-bit code length by K information bits, and the purposes of error detection and error correction are achieved by adding N-K check bits. The LT code does not support the coding mode of the systematic code, so that the LT code cannot meet some practical FEC coding requirements easily; raptor codes support systematic codes, but Raptor codes require a separate precoding process, i.e., a precoding matrix, and thus the coding complexity is high.

Due to the disadvantages of the above encoding method, LDGC (Low Density generator matrix Codes) was introduced. LDGC is a linear block code whose non-zero elements in the generator matrix (coding matrix) are usually sparse, while LDGC code is also a systematic code.

The coding of the LDGC is to first determine an intermediate variable by using a corresponding relationship between an information bit (i.e., data to be transmitted) and the intermediate variable in a system code, and then multiply the intermediate variable by a generator matrix to obtain a coded codeword. Specifically, the encoding process is to fill d-L-K known bits into the K-bit information sequence m to generate an L-bit sequence s, and then according to the equation set: i G_ldgc(0: L-1) ═ s, the system of equations is solved to generate an L-bit intermediate variable sequence I, which is then multiplied by the intermediate variables to generate a matrix, i.e., I × G_ldgc(0: L-1, 0: N + d-1) produces a codeword sequence C 'of N + d bits (containing d padding bits)'_ldgc，C’_ldgcThe d padding bits do not need to be transmitted, so that the N-bit codeword sequence C is actually transmitted_ldgc。C_ldgcAfter passing through the channel (erasure may occur), the codeword sequence received by the receiving end is R. Where s is a 1 × L vector, I is a 1 × L vector, R is a 1 × N vector, G_ldgc(0: L-1) is an LxL square matrix, which is typically an upper or lower triangular matrix, G_ldgc(0: L-1, 0: N + d-1) is a matrix of Lx (N + d). For the detailed process of encoding, refer to the patent "encoding method and apparatus, and decoding method and apparatus of low density generator matrix code".

The decoding process of LDGC code is to use the receiving code word sequence R (containing filling bit, the following receiving code word sequence is all referred to as containing filling bit) and LDGC to generate matrix G_ldgcAnd inEquation set relation I G of inter-variable I_ldgc(0: L-1, 0: N + d-1) ═ R, solving the equation set to obtain an intermediate variable I; then according to the relation "I × G" of information bit s (containing stuffing bits) and intermediate variable I_ldgcThe information bit s is obtained by (0: L-1) ═ s ″, and the original information sequence m is obtained by removing the padding bits.

The most critical step is to solve intermediate variables, and a large linear equation system is often required to be solved. In engineering, the linear equation system can be solved by adopting a Gaussian elimination method or an iteration method, and the Gaussian elimination method is more suitable for decoding the LDGC code according to the characteristics of the LDGC code. Therefore, the speed of the gaussian elimination process directly affects the decoding speed of the LDGC code.

According to the requirement of describing the gaussian elimination method, in the following description, all the "vector" or "matrix" with the lower case t as a subscript represents the transpose of the original "vector" or "matrix", and the vector or the matrix and the transpose thereof are completely the same from the content aspect, and sometimes can represent the same object. For example, define G_ldgctIs G_ldgcTranspose of (I)_tIs the transpose of I, R_tIs the transpose of R, since both I and R are row vectors, where I is_tAnd R_tAre all column vectors.

FIG. 1 is a transposed LDGC generator matrix G_ldgctSchematic representation of (a). As shown in FIG. 1, G_ldgctThe square matrix corresponding to the first L rows in (a) is usually an upper triangular or lower triangular matrix. Wherein, x and y in fig. 1 may be 0.

According to a linear system of equations G_ldgct(0:N+d-1，0:L-1)×I_t＝R_tSolving intermediate variables I_tIn the process of (2), the Gaussian elimination performed needs to be on G_ldgctThe matrix is subjected to three elementary transformations of row permutation, row addition and column permutation. According to the linear algebra principle, for ensuring the correctness of the equation set, G_ldgctWhile performing elementary transformation on the matrix, I is required_tAnd R_tThe following corresponding treatments are carried out:

1) line replacement, if G_ldgctIth and jth lines ofBy substitution, then R_tThe ith bit and the jth bit of (a) need to be permuted;

2) line-wise addition, if G_ldgctIs added to the ith row and the jth row of_tThe ith bit and the jth bit of (a) need to be added (modulo-2 addition);

3) column replacement, if G_ldgctIs permuted between the ith column and the jth column, then I_tThe ith bit and the jth bit of (a) need to be permuted.

Since the final result requires obtaining I_tAnd I is_tIn (B) is in G_ldgctWhen the column is replaced, the corresponding replacement is performed, so that the I is required to be replaced_tThe replacement condition of (2) is recorded so as to facilitate the following inverse replacement process. Engineering, I can be recorded by an array_tThe replacement case of (2). And R is_tThe data which is not finally needed can be directly processed without recording the processing condition.

Since these transformation relationships are strictly corresponding and the main complexity of Gaussian elimination is reflected in the pair G_ldgctIn the following, for the sake of simplicity, all the treatments for G_ldgctIs transformed in equal time, correspondingly to I_tAnd R_tThe process of (2) is strictly handled according to the above three cases. To highlight the emphasis, the following sometimes simplifies the pair I_tAnd R_tA description of the process of (a).

In the prior art, the LDGC decoding adopts a standard Gaussian elimination method, and has two defects: first, the strict upper or lower triangular feature of the LDGC code generator matrix (as shown in fig. 1) cannot be fully utilized to simplify the elimination operation; secondly, the index of the non-zero element of the matrix cannot be directly generated by using the structural characteristic of the LDGC code generator matrix, and the whole generator matrix needs to be stored, so that the storage and calculation complexity is increased. Therefore, the decoding efficiency is low by adopting the standard Gaussian elimination method.

Disclosure of Invention

The invention aims to solve the technical problem of overcoming the defects of the prior art and provides a high-efficiency LDGC decoding method.

In order to solve the above problem, the present invention provides a method for decoding a low density generator matrix code, which decodes a received bit information sequence transmitted after being encoded by LDGC, the method comprising:

s1: filling L-K known bits in the received code word sequence R and deleting the code character number erased by the channel in R to obtain R_e(ii) a And generating a transposed matrix G of the matrix from the LDGC by the row corresponding to the code character number erased by the channel_ldgctIs deleted to obtain G_e；

S2: for G_ePerforming column replacement to generate $G_a=\left[\begin{array}{cc}A& C\\ D& B\end{array}\right],$ Where A is a lower triangular square matrix of order M and records G_eAnd G_aThe column permutation correspondence of (1);

s3: for G_aPerforming Gaussian elimination to generate G_bSo that G is_bThe square matrix formed by the first L rows is a unit matrix; simultaneously, R is subjected to line replacement and line addition operation in the Gaussian elimination process_eCarrying out replacement and addition operation on corresponding elements to generate Re';

s4: according to the relation G_b ×I′_tRe 'solution to obtain I'_tAnd is paired according to the column substitution correspondence relationship'_tReverse substitution to give I_t；

S5: according to the relation G_ldgct(0:L-1，0:L-1)×I_t＝s_tFind s_tAnd from s_tDeleting the filled L-K known bits to obtain an information sequence of K bits;

g above_ldgctIs a matrix with N + L-K rows and L columns.

Further, said M ═ L-X_L，X_LThe number of bits erased by the channel in the first L codeword symbols of R.

Further, let Xset_LA set of serial numbers of deleted code character numbers in the first L code character symbols of R after the d known bits are filled, wherein the number of the serial numbers in the set is X_L；

In step S2, the G_eThe middle column sequence number belongs to Xset_LIs shifted to G_eThe position vacated by the corresponding column does not belong to the Xset by the sequence number of the subsequent column_LIs sequentially filled to obtain the G_a。

In step S3, G is also designated_aThe gaussian elimination specifically comprises the following sub-steps:

s31: for the G_aA and D in (1) are subjected to Gaussian elimination, so that A becomes M-order unit array E_MWhile changing D to elements all 0 (N-K- (X)_T-X_L) Row M column matrix, i.e.:

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

s32: for G_a' B-DA of^-1C, Gaussian elimination is carried out, the square matrix corresponding to the front L-M lines is taken as a unit matrix, and A is added^-1C is eliminated as a matrix of M rows and L-M columns with all 0 elements, i.e.:

<math> <mrow> <msub> <mi>G</mi> <mi>b</mi> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>E</mi> <mi>M</mi> </msub> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <msubsup> <mi>E</mi> <mrow> <mi>L</mi> <mo>-</mo> <mi>M</mi> </mrow> <mo>&prime;</mo> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mo>.</mo> </mrow> </math>

further, in step S31, it is determined whether the xth row and yth column element H [ x, y ] in a and D is a non-zero element by the following method, and the gaussian elimination is performed for a and D according to the position of the non-zero element:

s311: according to the deleted code character number in R after filling d known bitsThe set of sequence numbers Xset of (1) yields the above-mentioned H [ x, y [ ]]At G_ldgctRow position in (2): x ', y';

s312: if it is not $G_{\mathrm{bt}}^{\mathrm{uniform}}[x_z,y_z]=0,$ Then H [ x, y]If the element is zero, the flow is finished, otherwise, the next step is executed;

s313: if ix_z＝mod(iy_z+ offset, z), then A [ x, y)]Is a non-zero element; otherwise, A [ x, y]Is a zero element;

wherein: z is a spreading factor, z_maxIs the maximum spreading factor;

x_z＝floor(x’/z)，y_z＝floor(y’/z)；

ix_z＝mod(x’，z)，iy_z＝mod(y’，z)；

<math> <mrow> <mi>offset</mi> <mo>=</mo> <mi>floor</mi> <mrow> <mo>(</mo> <msubsup> <mi>G</mi> <mi>bt</mi> <mi>uniform</mi> </msubsup> <mo>[</mo> <msub> <mi>x</mi> <mi>z</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>z</mi> </msub> <mo>]</mo> <mo>&CenterDot;</mo> <mi>z</mi> <mo>/</mo> <msub> <mi>z</mi> <mi>max</mi> </msub> <mo>)</mo> </mrow> <mo>.</mo> </mrow> </math>

the present invention also provides a decoding device for a low density generator matrix code, which decodes a received bit information sequence transmitted after being encoded by LDGC, the device comprising: the device comprises a filling erasing unit, a column replacing unit, a Gaussian elimination unit and an information sequence generating unit; wherein:

a filling and erasing unit for filling d known bits in the received code word sequence R and deleting the code word number erased by the channel, generating and outputting R_e(ii) a And generating a transposed matrix G of the matrix from the LDGC by the row corresponding to the code character number erased by the channel_ldgctDelete, generate and output G_e；

A column replacement unit for replacing G output from the filling and erasing unit_ePerforming column permutation, generating and outputting $G_a=\left[\begin{array}{cc}A& C\\ D& B\end{array}\right],$ Wherein A is a lower triangular square matrix of order M and outputs G_eAnd G_aThe column replacement correspondence information of (1);

a Gaussian elimination unit for G output from the column replacement unit_aPerforming Gaussian elimination, generating and outputting G_bSo that G is_bThe square matrix formed by the first L rows is a unit matrix; simultaneously, according to the row replacement and row addition operation in the Gaussian elimination process, the R output by the filling and erasing unit is subjected to_eCarrying out replacement and addition operation on corresponding elements to generate and output Re';

an information sequence generation unit for generating an information sequence according to the relation G_b×I′_tRe 'produces I'_t(ii) a According to the column replacement corresponding relation information pair I 'output by the column replacement unit'_tReverse substitution to generate I_t(ii) a According to the relation G_ldgct(0:L-1，0:L-1)×I_t＝s_tGeneration of s_tAnd from s_tD known bits are deleted, and then an information sequence of K bits is output;

g above_ldgctIs a matrix with N + L-K rows and L columns.

In addition, the a generated by the column permutation unit through column permutation is an M-th lower triangular square matrix, and M is L-X_L，X_LThe number of bits erased by the channel in the first L symbols of R.

Further, let Xset_LA set of serial numbers of deleted code character numbers in the first L code character symbols of R after the d known bits are filled, wherein the number of the serial numbers in the set is X_L；

The column replacement unit is configured to replace G_eThe middle column sequence number belongs to Xset_LIs shifted to G_eThe position vacated by the corresponding column does not belong to the Xset by the sequence number of the subsequent column_LIs sequentially filled in columns to generate the G_a。

Furthermore, the Gaussian elimination unit adopts the following sub-step pairs G_aPerforming Gaussian elimination:

s31: for the G_aA and D in (1) are subjected to Gaussian elimination, so that A becomes M-order unit array E_MWhile changing D to elements all 0 (N-K- (X)_T-X_L) Row M column matrix, i.e.:

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

s32: for G_a' B-DA of^-1C, Gaussian elimination is carried out, the square matrix corresponding to the front L-M lines is taken as a unit matrix, and A is added^-1C is eliminated as a matrix of M rows and L-M columns with all 0 elements, i.e.:

<math> <mrow> <msub> <mi>G</mi> <mi>b</mi> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>E</mi> <mi>M</mi> </msub> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <msubsup> <mi>E</mi> <mrow> <mi>L</mi> <mo>-</mo> <mi>M</mi> </mrow> <mo>&prime;</mo> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mo>.</mo> </mrow> </math>

in addition, the Gaussian elimination unit judges whether the x-th row and y-th column elements H [ x, y ] in A and D are non-zero elements or not by the following method, and performs the Gaussian elimination on A and D according to the positions of the non-zero elements:

s311: according to the padding of d known bitsThe sequence number set Xset of deleted code character numbers in R obtains the H [ x, y [ ]]At G_ldgctRow position in (2): x ', y';

s312: if it is not $G_{\mathrm{bt}}^{\mathrm{uniform}}[x_z,y_z]=0,$ Then H [ x, y]If the element is zero, the flow is finished, otherwise, the next step is executed;

s313: if ix_z＝mod(iy_z+ offset, z), then A [ x, y)]Is a non-zero element; otherwise, A [ x, y]Is a zero element;

wherein: z is a spreading factor, z_maxIs the maximum spreading factor;

x_z＝floor(x’/z)，y_z＝floor(y’/z)；

ix_z＝mod(x’，z)，iy_z＝mod(y’，z)；

<math> <mrow> <mi>offset</mi> <mo>=</mo> <mi>floor</mi> <mrow> <mo>(</mo> <msubsup> <mi>G</mi> <mi>bt</mi> <mi>uniform</mi> </msubsup> <mo>[</mo> <msub> <mi>x</mi> <mi>z</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>z</mi> </msub> <mo>]</mo> <mo>&CenterDot;</mo> <mi>z</mi> <mo>/</mo> <msub> <mi>z</mi> <mi>max</mi> </msub> <mo>)</mo> </mrow> <mo>.</mo> </mrow> </math>

the LDGC decoding method can fully utilize the diagonalization characteristic of the structured LDGC coding matrix, and can greatly reduce the decoding complexity and accelerate the decoding speed compared with a decoding method directly adopting a Gaussian elimination method, so that the LDGC can be applied to a high-speed communication system.

Drawings

FIG. 1 is a transposed LDGC generator matrix G_ldgctA schematic diagram of (a);

FIG. 2 is a flowchart of a decoding method for low density generator matrix codes according to an embodiment of the present invention;

FIG. 3 is a schematic diagram of an erasure process performed on a generator matrix according to an erasure condition of a received codeword sequence R;

FIG. 4 is a block diagram of an embodiment of a method for generating a matrix G for erase_eSchematic representation of performing column permutation;

FIG. 5 shows an embodiment of the present invention, pair G_aSchematic representation of performing gaussian elimination;

FIG. 6 is a flowchart of a method for zero element discrimination according to an embodiment of the present invention;

fig. 7 is a schematic diagram of a decoding apparatus for low density generator matrix codes according to an embodiment of the present invention.

Detailed Description

For the description, the receiving code word sequence R (containing filling bits) with length of N + d is firstly erased by the channel_TA code word symbol, this X_TThe set of the character number position indexes of the erased codes is Xset; in particular, the set of all position index elements in Xset smaller than L is XSet_L，XSet_LThe number of elements of (2) is X_LI.e. XSet_LIt is shown that X is erased by the channel in the first L symbols in R_LA codeword symbol; if M is equal to L-X_L。

Since the basic elements in all the objects in the LDGC decoding are from the finite field GF (2), the operations between the objects are also operations defined by the finite field GF (2).

The basic idea of the invention is that the diagonalization characteristic of the structured LDGC generator matrix is utilized to firstly perform column permutation on the LDGC generator matrix subjected to the erasing processing, so that the LDGC generator matrix has $\left[\begin{array}{cc}A& C\\ D& B\end{array}\right]$ Wherein the matrix A is an M-order square matrix and has the characteristic of strict lower triangle. Then, the characteristic that A is a strict lower triangular matrix and the structural characteristics of A and D are utilized to simplify decoding.

The present invention will be described in detail below with reference to the drawings and examples.

Fig. 2 is a flowchart of a decoding method of a low density generator matrix code according to an embodiment of the present invention. As shown in fig. 2, the method comprises the following steps:

201: filling known bit sequences with length d ═ L-K at corresponding positions of the received codeword sequence R, for example: 1, 1, …, 1, and deleting the code character number erased by the channel to obtain R_e。

Where K is the length of the original information bits and L is the length of the original information bits after padding and encoding.

202: generating a matrix G for LDGC according to the condition that the received code word sequence R is erased_ldgctPerforming row erasure (deletion) to obtain an erasure generation matrix G_e。

Fig. 3 is a schematic diagram of erasing the generator matrix according to the erasure of the received codeword sequence R. As shown in fig. 3, after being wipedGeneration matrix G of division processing_eThe first L rows of (a) are no longer the lower triangular square matrix.

Let R (R) after filling the known bit sequence be assumed₀，r₁，……r_N+d-1) X in (1)_TThe symbol: { r_i，r_j’…，r_p…r_xIs erased by channel erasure, where X in the preceding L symbols_LA symbol r_i，r_j，…，r_pIs erased by the channel; then Xset ═ i, j, …, p, …, x }; xset_LI, j, … p. Accordingly G_ldgctRow { i, j, …, p, …, x } in (a) needs to be erased, resulting in G_eAt this time G_eThe above matrix is not strictly diagonalized already because of the erasure of several rows, as shown in fig. 3 (c).

203: generating a matrix G for the erasures_ePerforming column replacement to G_eTaking M-order square matrix with (0, 0) as vertex as lower triangular matrix, and taking G as lower triangular matrix_eThe permutated matrix is recorded as the permutation generator matrix G_a(ii) a Simultaneous recording G_eAnd G_aFor the subsequent pair I_tPerforming corresponding replacement operation to generate I'_t；

FIG. 4 is a diagram of generating a matrix G for erasures_eSchematic representation of column permutation.

Specifically, to obtain the lower triangular matrix, G_eThe middle column sequence number belongs to Xset_LIs shifted to G_eThe position vacated by the corresponding column does not belong to the Xset by the sequence number of the subsequent column_LThe columns are filled in sequence to obtain a permutation generator matrix:

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

the matrix A is an M-order square matrix and has the characteristic of strictly lower triangular; matrix C is a matrix of size M x (L-M); the matrix D is (N-K- (X)_T-X_L) X M); the matrix B is (N-K- (X)_T-X_L) Matrix of (L-M).

According to the pair G_ldgctColumn replacement case of (1), simultaneously for I_tPerforming a corresponding replacement operation, setting I_tIs changed to I 'after substitution'_t；I_tTo l'_tThe permutation relationship of (a) may be recorded by an array for use in the subsequent inversion permutation process.

204: generating matrix G for pair permutation_aPerforming Gaussian elimination to G_aThe L-order square matrix formed by the first L rows becomes an L-order unit matrix (if G_aFull rank), the matrix after elimination is denoted as G_bI.e. by $G_b=\left[\begin{array}{c}{\mathrm{<figure-callout\; id="0"\; label="E\; L"\; filenames="A20081009664400191.png,A20081009664400201.png"\; state="\{\{state\}\}">E</figure-callout>}}_L\\ 0\end{array}\right];$ At the same time to R_ePerforming substitution and addition operations of corresponding elements, setting R_eAfter conversion to R_e’；

Above E_LIndicating an L-order unit matrix.

Due to G_aHas the following characteristics:

1) the diagonal lines of A are provided with non-zero elements, and A has the characteristic of strict downward triangle;

2) the non-zero elements in A and D can be directly calculated by the formula defined by constructing the generator matrix during encoding, so A and D do not need to be stored actually.

Thus, for G_aThe gaussian elimination process of (a) can be seen as comprising the following three sub-processes:

204a) and (3) Gaussian elimination is carried out by utilizing the characteristics of A: transforming A into M-order unit matrix E_M；

When Gaussian elimination is carried out on the A, the positions of all the nonzero elements in the A can be directly calculated, and row addition operation is carried out on the A according to the positions of all the nonzero elements, so that an actual storage matrix A is not needed.

The specific method of calculating the positions of the non-zero elements in a (or the method of determining whether the elements in a are 0) is described in detail below.

By performing Gaussian elimination (row addition) on A, A can be converted into M-order unit array E_M(ii) a The row add operation described above will act on C simultaneously, with the end result being equivalent to a simultaneous left multiplication of A and C by A^-1Namely:

204b) using unit arrays E_MPerforming Gaussian elimination on the D, and changing the D into a full 0 matrix; accordingly, B needs to subtract D to multiply A^-1The result of C, here the subtraction of the inter-matrix elements corresponds to the modulo-2 addition of the inter-matrix elements, the final result corresponding to:

similarly, when performing gaussian elimination on D, the positions of the non-zero elements in D can be directly calculated, and the row addition operation is performed on D according to the positions of the non-zero elements, so that the actual storage matrix D is not needed. The specific method for calculating the positions of the non-zero elements in D (or determining whether the elements in D are 0) is described in detail below.

The above process is shown in fig. 5(a) and 5 (b).

For simplicity of description, let S be B-DA^-1C。

204c) Performing Gaussian elimination on the S;

if G is_aIs full-rank, S can be transformed into a matrix containing (L-M) order unit matrix (namely, the matrix corresponding to the first L-M rows is the unit matrix) by Gaussian elimination, and the upper A can be completely eliminated^-1C. I.e. G_aFinally, the method can be changed into the following form through Gaussian elimination:

e 'mentioned above'_L-MThe first L-M rows form an L-M order unit array, and the following rows are all zero rows. As shown in fig. 5 (c).

If G is_aIf the rank is not full, the decoding fails, and the method ends.

Also, according to the pair G_aLine permutation and line addition operations performed with Gaussian elimination for R_ePerforming substitution and addition operations of corresponding elements, setting R_eAfter conversion to R_e’。

205: according to the equation set G_b×I′_t＝R_e' equation I ' can be obtained '_t＝R_e' (1: L); i 'can be directly obtained from the formula'_t(ii) a Then through the pair I_tTo l'_tA permutation of (i.e. G)_eTo G_aColumn replacement relation of (1) by reverse replacement to obtain'_tTo find out I_t。

206: according to the relation between the information bits s (containing the padding bits) and the intermediate variable I:

G_ldgct(0:L-1，0:L-1)×I_t＝s_tdetermining an information bit s_tRemoving s_tThe d known padding bits in (a) result in the K bits of information sequence m.

A method of determining whether each of a and D is a non-zero element will be described below by taking a as an example. The judgment of the elements in D is the same as that of A.

FIG. 6 is a flowchart of a method for zero element discrimination according to an embodiment of the present invention.

First, each symbol used in the discrimination method will be explained:

G_b ^uniform: is LDGC basic matrix defined in CMMB standard; g_b ^nuniformHas a size of k_b×n_b12 × 40, the transposed basis matrix G_b ^uniformSize n_b×k_b＝40×12；

Spreading factor z-ceil (L/k)_b) (ii) a ceil (·) denotes round down;

maximum spreading factor z_max＝683。

As shown in FIG. 6, the method determines whether A [ x, y ] is 0 by the following steps:

601: deriving A [ x, y ] from the deleted row index Xset]G before erasing_ldgctRow position in (2): x ', y'; i.e. A [ x, y ]]Is G_ldgctRow x ', column y' elements;

602: calculating x_z＝floor(x’/z)，y_z＝floor(y’/z)；

floor (. cndot.) indicates rounding up.

603: according to G_bt ^uniformMiddle (x)_zLine, y_zElements of columns, i.e. G_bt ^uniform[x_z，y_z]Whether A [ x, y ] is zero or not is judged]Whether it is zero:

if it is not $G_{\mathrm{bt}}^{\mathrm{uniform}}[x_z,y_z]=0,$ Then A [ x, y]＝0；

If it is not $G_{\mathrm{bt}}^{\mathrm{uniform}}[x_z,y_z]>0,$ Then A [ x, y]Possibly non-zero, and subsequent decision making operations need to be performed.

604: calculate ix_z＝mod(x’，z)，iy_z＝mod(y’，z)；

605: calculating offset according to a correction formula defined by CMMB standard;

the correction formula is as follows: floor (z. (g)_i，j ^b)_uniform/z_max)；(g_i，j ^b)_uniformIs exactly G_b ^uniform[i，j]Or G_bt ^uniform[j，i]；

<math> <mrow> <mi>offset</mi> <mo>=</mo> <mi>floor</mi> <mrow> <mo>(</mo> <msubsup> <mi>G</mi> <mi>bt</mi> <mi>uniform</mi> </msubsup> <mo>[</mo> <msub> <mi>x</mi> <mi>z</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>z</mi> </msub> <mo>]</mo> <mo>&CenterDot;</mo> <mi>z</mi> <mo>/</mo> <msub> <mi>z</mi> <mi>max</mi> </msub> <mo>)</mo> </mrow> <mo>.</mo> </mrow> </math>

606: according to ix_zWhether or not it is equal to mod (iy)_z+ offset, z) is determined for A [ x, y]Whether or not it is 0:

if ix_z＝mod(iy_z+ offset, z), then A [ x, y)]Is a non-zero element;

otherwise, A [ x, y ] is zero element.

The method for judging whether the element D [ x, y ] in D is zero is the same as the steps.

Fig. 7 is a schematic diagram of a decoding apparatus for low density generator matrix codes according to an embodiment of the present invention. As shown in fig. 7, the apparatus includes: the device comprises a filling erasing unit, a column replacing unit, a Gaussian elimination unit and an information sequence generating unit. Wherein,

a filling and erasing unit for filling d known bits in the received code word sequence R and deleting the code word number erased by the channel, generating and outputting R_e(ii) a And generating a transposed matrix G of the matrix from the LDGC by the row corresponding to the code character number erased by the channel_ldgctDelete, generate and output G_e；

A column replacement unit for replacing G output from the filling and erasing unit_ePerforming column replacement to G_eTaking M-order square matrix A with 0 th row and 0 th column elements as vertexes as a lower triangular matrix, generating and outputting $G_a=\left[\begin{array}{cc}A& C\\ D& B\end{array}\right],$ And output G_eAnd G_aThe column replacement correspondence information of (1);

said M ═ L-X_L，X_LThe number of bits erased by the channel in the first L symbols of R.

The column replacement unit can replace G_eThe middle column sequence number belongs to Xset_LIs shifted to G_eThe position vacated by the corresponding column does not belong to the Xset by the sequence number of the subsequent column_LIs sequentially filled to obtain the G_a。

A Gaussian elimination unit for G output from the column replacement unit_aPerforming Gaussian elimination (the specific steps are as described above), generating and outputting G_bSo that G is_bThe square matrix formed by the first L rows is an L-order unit matrix; simultaneously, according to the row replacement and row addition operation in the Gaussian elimination process, the R output by the filling and erasing unit is subjected to_eCarrying out replacement and addition operation on corresponding elements to generate and output Re';

in the gaussian elimination process, the gaussian elimination unit further determines whether the elements in a and D are non-zero elements according to a formula, and the specific determination method is as described above.

An information sequence generation unit for generating an information sequence according to the relation G_b×I′_tRe 'produces I'_t(ii) a According to the column replacement corresponding relation information pair I 'output by the column replacement unit'_tReverse substitution to generate I_t(ii) a According to the relation G_ldgct(0:L-1，0:L-1)×I_t＝s_tGeneration of s_tAnd from s_tAfter deleting d known bits, the bit information sequence is output.

From the above, by using the decoding method and apparatus of the present invention for the LDGC generator matrix, the processing speed of gaussian elimination can be increased.

The above-described embodiments may also be varied in many ways according to the basic principles of the invention:

for LDGC generation matrices of other shapes, for example, the first L row is an upper triangular matrix, which can be transformed into a lower triangular matrix and then the decoding method of the present invention is adopted.

The above description is only an example of the present invention, and is not intended to limit the present invention, and it is obvious to those skilled in the art that various modifications and variations can be made in the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.

Claims (10)

1. A decoding method of low density generator matrix code decodes the bit information sequence transmitted after the received LDGC code, which is characterized in that the method comprises the following steps:

s1: filling L-K known bits in the received code word sequence R and deleting the code character number erased by the channel in R to obtain R_e(ii) a And generating a transposed matrix G of the matrix from the LDGC by the row corresponding to the code character number erased by the channel_ldgctIs deleted to obtain G_e；

S2: for G_ePerforming column replacement to generate $G_a=\left[\begin{array}{cc}A& C\\ D& B\end{array}\right],$ Where A is a lower triangular square matrix of order M and records G_eAnd G_aThe column permutation correspondence of (1);

s3: for G_aPerforming Gaussian elimination to generate G_bSo that G is_bThe square matrix formed by the first L rows is a unit matrix; simultaneously, R is subjected to line replacement and line addition operation in the Gaussian elimination process_eCarrying out replacement and addition operation on corresponding elements to generate Re';

s4: according to the relation G_b×I′_tRe 'solution to obtain I'_tAnd is paired according to the column substitution correspondence relationship'_tReverse substitution to give I_t；

S5: according to the relation G_ldgct(0:L-1，0:L-1)×I_t＝s_tFind s_tAnd from s_tDeleting the filled L-K known bits to obtain an information sequence of K bits;

g above_ldgctIs a matrix with N + L-K rows and L columns.

2. The method of claim 1,

said M ═ L-X_L，X_LThe number of bits erased by the channel in the first L codeword symbols of R.

3. The method of claim 2,

let Xset_LFor filling the first L code words of R after the d known bitsIn the symbol, the number of deleted code character number is X_L；

In step S2, the G_eThe middle column sequence number belongs to Xset_LIs shifted to G_eThe position vacated by the corresponding column does not belong to the Xset by the sequence number of the subsequent column_LIs sequentially filled to obtain the G_a。

4. The method of claim 2,

in step S3, for G_aThe gaussian elimination specifically comprises the following sub-steps:

s31: for the G_aA and D in (1) are subjected to Gaussian elimination, so that A becomes M-order unit array E_MWhile changing D to elements all 0 (N-K- (X)_T-X_L) Row M column matrix, i.e.:

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

s32: for G_a' B-DA of^-1C is highThe elimination element takes the square matrix corresponding to the front L-M lines as a unit matrix, and A is added^-1C is eliminated as a matrix of M rows and L-M columns with all 0 elements, i.e.:

<math> <mrow> <msub> <mi>G</mi> <mi>b</mi> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>E</mi> <mi>M</mi> </msub> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <msubsup> <mi>E</mi> <mrow> <mi>L</mi> <mo>-</mo> <mi>M</mi> </mrow> <mo>&prime;</mo> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mo>.</mo> </mrow> </math>

5. the method of claim 4,

in step S31, it is determined whether the xth row and yth column element H [ x, y ] in a and D is a non-zero element by the following method, and the gaussian elimination is performed on a and D according to the position of the non-zero element:

s311: obtaining the H [ x, y ] according to the sequence number set Xset of deleted code character numbers in R after filling d known bits]At G_ldgctRow position in (2): x ', y';

s312: if it is not $G_{\mathrm{bt}}^{\mathrm{uniform}}[x_z,y_z]=0,$ Then H [ x, y]Is zero element, the process endsOtherwise, executing the next step;

s313: if ix_z＝mod(iy_z+ offset, z), then A [ x, y)]Is a non-zero element; otherwise, A [ x, y]Is a zero element;

wherein: z is a spreading factor, z_maxIs the maximum spreading factor;

x_z＝floor(x’/z)，y_z＝floor(y’/z)；

ix_z＝mod(x’，z)，iy_z＝mod(y’，z)；

<math> <mrow> <mi>offset</mi> <mo>=</mo> <mi>floor</mi> <mrow> <mo>(</mo> <msubsup> <mi>G</mi> <mi>bt</mi> <mi>uniform</mi> </msubsup> <mo>[</mo> <msub> <mi>x</mi> <mi>z</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>z</mi> </msub> <mo>]</mo> <mo>&CenterDot;</mo> <mi>z</mi> <mo>/</mo> <msub> <mi>z</mi> <mi>max</mi> </msub> <mo>)</mo> </mrow> <mo>.</mo> </mrow> </math>

6. a decoding apparatus for decoding a received bit information sequence transmitted after LDGC encoding, the apparatus comprising: the device comprises a filling erasing unit, a column replacing unit, a Gaussian elimination unit and an information sequence generating unit; wherein:

a filling and erasing unit for filling d known bits in the received code word sequence R and deleting the code word number erased by the channel, generating and outputting R_e(ii) a And generating a transposed matrix G of the matrix from the LDGC by the row corresponding to the code character number erased by the channel_ldgctDelete, generate and output G_e；

A column replacement unit for replacing G output from the filling and erasing unit_ePerforming column permutation, generating and outputting $G_a=\left[\begin{array}{cc}A& C\\ D& B\end{array}\right],$ Wherein A is a lower triangular square matrix of order M and outputs G_eAnd G_aThe column replacement correspondence information of (1);

a Gaussian elimination unit for G output from the column replacement unit_aPerforming Gaussian elimination, generating and outputting G_bSo that G is_bThe square matrix formed by the first L rows is a unit matrix; simultaneously, according to the row replacement and row addition operation in the Gaussian elimination process, the R output by the filling and erasing unit is subjected to_eCarrying out replacement and addition operation on corresponding elements to generate and output Re';

an information sequence generation unit for generating an information sequence according to the relation G_b ×I′_tRe 'produces I'_t(ii) a According to the column replacement corresponding relation information pair I 'output by the column replacement unit'_tReverse substitution to generate I_t(ii) a According to the relation G_ldgct(0:L-1，0:L-1)×I_t＝s_tGeneration of s_tAnd from s_tD known bits are deleted, and then an information sequence of K bits is output;

g above_ldgctIs a matrix with N + L-K rows and L columns.

7. The apparatus of claim 6,

the A generated by the column replacement unit through column replacement is an M-order lower triangular square matrix, and M is L-X_L，X_LThe number of bits erased by the channel in the first L symbols of R.

8. The apparatus of claim 7,

let Xset_LA set of serial numbers of deleted code character numbers in the first L code character symbols of R after the d known bits are filled, wherein the number of the serial numbers in the set is X_L；

The column replacement unit is configured to replace G_eThe middle column sequence number belongs to Xset_LIs shifted to G_eThe position vacated by the corresponding column does not belong to the Xset by the sequence number of the subsequent column_LIs sequentially filled in columns to generate the G_a。

9. The apparatus of claim 7,

the Gaussian elimination unit adopts the following substep pairs G_aPerforming Gaussian elimination:

s31: for the G_aA and D in (1) are subjected to Gaussian elimination, so that A becomes M-order unit array E_MWhile changing D to elements all 0 (N-K- (X)_T-X_L) Row M column matrix, i.e.:

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

s32: for G_a' B-DA of^-1C, Gaussian elimination is carried out, the square matrix corresponding to the front L-M lines is taken as a unit matrix, and A is added^-1C is eliminated as a matrix of M rows and L-M columns with all 0 elements, i.e.:

<math> <mrow> <msub> <mi>G</mi> <mi>b</mi> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>E</mi> <mi>M</mi> </msub> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <msubsup> <mi>E</mi> <mrow> <mi>L</mi> <mo>-</mo> <mi>M</mi> </mrow> <mo>&prime;</mo> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mo>.</mo> </mrow> </math>

10. the apparatus of claim 9,

the Gaussian elimination unit judges whether the x-th row and y-th column elements H [ x, y ] in A and D are non-zero elements or not by the following method, and performs Gaussian elimination on A and D according to the positions of the non-zero elements:

s311: obtaining the H [ x, y ] according to the deleted code character number sequence number set Xset in R after filling d known bits]At G_ldgctRow position in (2): x ', y';

s312: if it is not $G_{\mathrm{bt}}^{\mathrm{uniform}}[x_z,y_z]=0,$ Then H [ x, y]If the element is zero, the flow is finished, otherwise, the next step is executed;

s313: if ix_z＝mod(iy_z+ offset, z), then A [ x, y)]Is a non-zero element; otherwise, A [ x, y]Is a zero element;

wherein: z is a spreading factor, z_maxIs the maximum spreading factor;

x_z＝floor(x’/z)，y_z＝floor(y’/z)；

ix_z＝mod(x’，z)，iy_z＝mod(y’，z)；

<math> <mrow> <mi>offset</mi> <mo>=</mo> <mi>floor</mi> <mrow> <mo>(</mo> <msubsup> <mi>G</mi> <mi>bt</mi> <mi>uniform</mi> </msubsup> <mo>[</mo> <msub> <mi>x</mi> <mi>z</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>z</mi> </msub> <mo>]</mo> <mo>&CenterDot;</mo> <mi>z</mi> <mo>/</mo> <msub> <mi>z</mi> <mi>max</mi> </msub> <mo>)</mo> </mrow> <mo>.</mo> </mrow> </math>

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