JP5749784B2 - Error correction code method - Google Patents

Description

  The present invention relates to an error correction code method and system, and in particular, a method for generating a check matrix of an error correction code in a transmission system using the error correction code and a method for sharing a check matrix of an error correction code in the transmission system And a transmission system.

● Puncture LDGM (Low Density Generator Matrix) overview:
FIG. 1 shows a configuration example of a transmission system using an error correction code.

  This communication system has an error correction code function. The transmission side error correction encoder 2 receives transmission data, applies an error correction code, is transmitted from the transmitter 3 via the binary erasure communication path 4, and is received. The error correction decoder 6 on the side performs error correction decoding and outputs transmission data.

  The LDPC (Low Density Parity Check) code is a linear block code defined by a check matrix H (hereinafter referred to as “H matrix”) in which the number of nonzero elements is sparse with respect to the code length (block length: N). It is. The LDPC code is encoded using a generator matrix G (hereinafter referred to as “G matrix”) that can be converted from the H matrix. Therefore, when it is actually used as an error correction technique for a transmission apparatus, it is necessary to share the G matrix or the H matrix on the transmitter side and the receiver side. For example, as shown in FIG. 1, it is necessary to generate an H matrix (check matrix information) and a G matrix (generation matrix information) by the check matrix generator 1 and arrange them on the respective transmitter / receiver sides. In order to generate the H matrix, in addition to the code length N, the number of source packets K is required. At this time, the parity packet number M is given by M = (N−K), and the coding rate R is given by R = K / N.

  The LDGM code is a kind of LDPC code, and an H matrix is composed of a combination of a sparse matrix and a step matrix H2 as shown in FIG. For example, FIG. 3 shows an LDGM code (H = [H1 | H2]) with N = 16, K = 8, and R = 0.5. In general, the H matrix of the LDPC code is a sparse matrix, but the corresponding G matrix is not a sparse matrix, but the LDGM code has a characteristic that the G matrix also becomes a sparse matrix.

  When an LDGM code is used in a transmission system such as that shown in FIG. 1, the desired number of source packets K and the number of parity packets M vary depending on the transmission data. Therefore, in order to generate the H matrix, it is necessary to provide these pieces of information at the time of generation, but this is not always possible. For example, there is a case where the number of parity packets M is changed after encoding using LDGM codes and generating parity packets. At this time, a puncture method has been proposed as means for changing the number M of parity packets without re-encoding (see Non-Patent Document 1, for example).

  FIG. 4 shows a state where the H matrix is converted into an H ′ matrix (H ′ = [H1 | H2 ′]) in which the number M of parity packets is reduced by one by the puncturing method. By adding and merging the c1 row of the H matrix to the c2 row and merging, the parity packet p1 becomes theoretically unrelated to the H ′ matrix. This gives H 'substantially an LDGM code with K = 8 and M = 7. Further, by repeating this operation, the number of parity packets M can be reduced as shown in FIG.

  FIG. 6 shows a flowchart of an LDPC code decoding process in a conventional binary erasure channel. The binary lost channel 4 performs lost packet recovery processing based on the reception status of the H matrix packet. Each row of the H matrix corresponds to one parity check equation, and it is possible to recover at most one packet loss. Therefore, it is assumed that one lost packet is recovered for the H matrix or a row that does not include any lost packet is “invalid” because there is no possibility of further recovery processing (step 4, Yes). Step 5, Yes). Conversely, when one or more lost packets are included (step 4, Yes, step 5, No, step 6, No), the state before the recovery process is assumed to be “valid”. In the initial state, all rows of the H matrix are set to “valid” (step 2), and if there is only one lost packet for each row that is “valid” (step 4, Yes, step 5, No, (Step 6, Yes) Recovery processing is performed (Step 7), and then the corresponding line is made "invalid" (Step 8).

  If a line that does not contain any lost packets is found (step 4, Yes, step 5, Yes), the line is set to “invalid” (step 9).

  The above process is repeated, and when there is no “valid” row or the number of “invalid” rows does not change (step 11, Yes), the processing is terminated.

Guosen Yue; Xiaodong Wang; Madihian, M., "Design of Rate-Compatible Irregular Repeat Accumulate codes," Communications IEEE Transactions on, vol.55, no.6, pp.1153,1163, June 2007.

  However, the method for generating the error correction code parity check matrix requires too much time to create the LDPC code parity check matrix from scratch after specifying the coding rate for each transmission, and has low latency as in video transmission. There is a problem that it is particularly difficult when required.

  If the error correction code matrix exchange method and system simply share a check matrix file, the file size increases as the size (code length) of the check matrix increases. In particular, in the case of changing every transmission, in order to share the error correction code check matrix, a method of sharing matrix information at the lowest possible transmission cost is required.

  The present invention has been made in view of the above points, and provides an error correction coding method capable of reducing transmission cost for sharing matrix information and time for creating a check matrix between an encoder and a decoder. The purpose is to do.

  An error correction coding method capable of sharing only information that is necessary and sufficient for exchanging matrices in an error correction encoder and an error correction decoder and minimizing the capacity, and that can suppress overhead related to matrix exchange, and The purpose is to provide a system.

According to one aspect, in a transmission system using an error correction code, an error correction code method for generating a check matrix of an error correction code,
On the storage means of the device that performs error correction coding,
The initial value that expands the size of a given H matrix (hereinafter referred to as “root matrix H”) and sets all the elements of the newly added region (hereinafter referred to as “extended region”) to zero. Step,
Using the minimum loop local maximization algorithm as the density of non-zero elements is uniform in the expansion area, have rows, and root matrix extension step of moving a non-zero element in the extended area of the root matrix,
In the initialization step,
The number of rows m1 of the sparse matrix H1 included in the root matrix H is expanded to (m0 + m1) (where m0 is the number of parity of H1 and m1 is the number of added parity), and all the elements of the extension region are expanded. Set to zero,
A step matrix H2 ′ is generated by expanding the size of the step matrix H2 included in the root matrix H to (m0 + m1) × (m0 + m1);
H '= [H1' | H2 '] (where H1' is an expanded matrix)
In the root matrix expansion step,
Extracting the column number of the non-zero element having the girth which is the minimum distance from the path returning to the original starting from the non-zero element in the root matrix, and the girth value at this time is min_girth,
The line number of the elements that make up the smallest girth is i,
There is provided an error correction coding method for moving a non-zero element of i-th row and D-column to the extension region so as to maximize the girth within the D-th column belonging to the extension region added to H1 ′ .

  According to one aspect, the generation of the H matrix (check matrix) that determines the code performance of the code by the error correction coding method, without reducing the code characteristics of the root matrix and generating the H matrix from scratch It is also possible to obtain a desired H matrix at high speed. This enables error correction using an H matrix suitable for the situation in a transmission system in which the bit rate is variable and real-time performance is required, such as moving image distribution.

It is a structural example of the transmission system using an error stop code. It is an example of a staircase matrix. This is an example of an LDGM code with N = 16, K = 8, and R = 0.5. In this example, the H matrix is converted into an H ′ matrix by the puncture method. This is an example in which the puncturing operation is repeated. It is a flowchart of the decoding process of the LDPC code in the conventional binary erasure channel. It is a flowchart of the root matrix expansion in the 1st Embodiment of this invention. It is a flowchart of the initialization process in the 1st Embodiment of this invention. It is the minimum loop local maximization algorithm in the 1st Embodiment of this invention. It is an example of the original H matrix in the 1st Embodiment of this invention. It is an example of the H 'matrix at the time of completion | finish of the initialization process in the 1st Embodiment of this invention. It is an example of the H matrix newly generated in the 1st embodiment of the present invention. It is a structural example of the communication system using the matrix exchange method in the 2nd Embodiment of this invention. It is an example of the matrix exchange packet of the production | generation system by the file reading and puncture process in the 2nd Embodiment of this invention. It is an example of the matrix exchange packet of the production | generation system by the algorithm production | generation and puncture process in the 2nd Embodiment of this invention. It is an example of the matrix exchange packet of the production | generation system (scratch type) only by the algorithm production | generation in the 2nd Embodiment of this invention. It is an example of the matrix exchange packet of the production | generation system (root matrix expansion type) only by the algorithm production | generation in the 2nd Embodiment of this invention. It is a flowchart of the matrix exchange method in the 2nd Embodiment of this invention. It is a flowchart of the puncturing process of the check matrix in the second embodiment of the present invention. It is a flowchart of the algorithm production | generation of a check matrix (scratch type) in the 2nd Embodiment of this invention. It is an example of the check matrix produced | generated based on the matrix exchange information in the 2nd Embodiment of this invention.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings.

[First embodiment]
The present embodiment relates to a parity check matrix between an encoder and a decoder, and adds and merges a plurality of rows of a single parity check matrix H shared between the encoder side and the decoder side. To reduce the number of rows, add rows with elements set to zero, move non-zero elements to maximize the girth in the column, and increase the matrix, thereby reducing the coding performance. The parity check matrix H ′ having an arbitrary code length (the size of the parity check matrix) is generated from the single parity check matrix H, and the transmission cost for sharing the matrix information and the time for creating the parity check matrix is reduced.

  In the present embodiment, the parity check matrix generator 1 in the transmission system shown in FIG. 1 can generate a matrix having an arbitrary parity amount (coding rate) from a matrix (root matrix) as a seed. It can be configured in a shorter time than making.

  This embodiment is effective in the case where transmission is performed by changing the packet size to be transmitted and the error correction coding rate for each transmission.

  FIG. 7 shows a flowchart of root matrix expansion in the first embodiment of the present invention. The process of the flowchart expands the size of the region by initialization processing for the given H matrix (root matrix), and then minimizes the non-zero element density in the expanded region so that the density is uniform. Move non-zero elements of J = floor [(E) / (m0 + m1)] using a local maximization algorithm. Here, floor is a floor function, and the fractional part is truncated. E is the total number of non-zero elements in the matrix (the number of “1” s standing in the matrix). The range of m1 is 100 to 5000, and the range of m0 is 1 to 4 × m1.

  Step 110) The total number of non-zero elements of the check matrix H1 is E, the parity number of H1 is m0, and the H matrix is punctured, and the parity number added by the H 'matrix obtained by reducing the parity packet number M by 1 is m1. .

  Step 120) An initialization process is performed on the given H matrix (root matrix) to expand the size. Details are shown in FIG.

  Step 130) J = floor [(E) / (m0 + m1)].

  Step 140) Let j = 1.

  Step 150) Move non-zero elements to extended region by minimum loop local maximization algorithm. Details are shown in FIG.

  Step 160) Set j = j + 1.

  Step 170) If j is larger than J obtained in Step 130, the process is terminated; otherwise, the process returns to Step 150.

  Next, the initialization process in step 120 will be described with reference to FIG.

  In the initialization process, for a given root matrix H, the number of parities of the sparse matrix H1 included therein is m0, the number of added parities is m1 (step 121), and the size of (m0 + m1) is A staircase matrix H2 ′ is generated (step 122). The number of rows m0 of the sparse matrix H1 included in the matrix is expanded to (m0 + m1) rows, and all the elements of the newly added area are set to zero (step 123). Similarly, for the staircase matrix H2 included in the H matrix, a staircase matrix H2 ′ in which the size of the matrix is expanded to (m0 + m1) × (m0 + m1) is generated (step 122). Using these matrices, the H matrix is set as H ′ = [H1 ′ | H2 ′].

  Next, the minimum loop local maximization algorithm in step 150 of FIG. 7 will be described.

  FIG. 9 shows a minimum loop local maximization algorithm in the first embodiment of the present invention.

  In the given H1 matrix, the column number of the non-zero element having the smallest girth is checked, and it is set as D, and the girth is set in min_girth (step 161). "Girth" is the minimum distance in the path starting from the non-zero element and following the relevant rows and columns back. The line number of the element constituting the minimum girth is set to i (step 162). Subsequently, the non-zero element in the i-th row and D-column is moved so as to maximize the girth within the D-th column belonging to the new region added to H1 ′ in step 123 (step 163). In this process, the girth is examined for all elements of the matrix H1 ′, and the smallest one is moved. Temporarily move a non-zero element to the destination candidate, and then check the girth of the moved element again. In this way, all the girths in the movement destination candidates are examined, and the non-zero element is moved using the place where the girth is the maximum as the movement destination.

  A specific example of this embodiment will be shown below.

  FIG. 10 is an example of a given original H matrix in the first embodiment of the present invention. The original H matrix is K = 8, M = m0 = 4, N = 12, and R = 0.67. An H matrix H ′ of K = 8, M = 6, N = 14, and R = 0.57 is generated by newly adding a column of m1 = 2. The example of FIG. 11 shows a state at the stage where the initialization process is completed. Here, the element with J = 4 is moved to the newly added region based on the minimum loop local maximization algorithm. FIG. 12 shows a newly generated H matrix.

  The code performance of an LDPC code depends on the position of the non-zero elements and their girth values (it is better that the girth is large). Considering this, it takes time to create an H matrix with good code characteristics from zero each time. Take it. Therefore, in the present embodiment, an approach is taken in which an H matrix having a certain size is prepared in advance, and the matrix is expanded using the matrix as a root, instead of creating from zero. In the case of expansion, in order to maximize the minimum girth included in the matrix, the element having a small girth is preferentially moved to increase the girth as a whole. In addition, when an element with a small girth is moved preferentially, the number of elements to be moved is determined based on the target matrix size (how much to extend), not based on the girth (for example, the value of J in FIG. 7). Equivalent).

  According to the method of the present embodiment, for example, when generating a parity check matrix from a matrix of code length n = 1125 and parity length m = 125, it takes time equivalent to extending from code length n = 0 to 1125 Compared to the prior art, the girth calculation is reduced to 1/2 hour.

[Second Embodiment]
In this embodiment, when an error correction code is applied in transmission in which various services such as voice, video, and data transmission are assumed, the amount of transmission information generated for matrix exchange according to the usage, A method and system for shortening the matrix generation calculation time in the system will be described.

  FIG. 13 shows a configuration example of a communication system using the matrix exchange method according to the second embodiment of the present invention. This communication system has an error correction code function. The transmission side error correction encoder 2 inputs transmission data, applies an error correction code, communicates via the binary erasure channel 4, and receives the error correction. The decoder 6 performs error correction decoding and outputs transmission data.

  The transmission side of the communication system includes an error correction encoder 2, a check matrix generator 10 A, a check matrix pool 20 A, and a transmitter 3. The error correction encoder 2 receives the generation matrix information after transmitting the code length and the coding rate to the check matrix generator 10A based on the input transmission data. After that, error correction code processing is performed based on the generation matrix information obtained here, and the data is transmitted to the binary erasure channel 4 using the transmitter 3.

  The receiving side of this system includes an error correction decoder 6, a check matrix generator 10B, a check matrix pool 20B, and a receiver 5. The check matrix generator 10B receives the matrix exchange packet from the check matrix generator 10A on the transmission side, generates a check matrix corresponding to the generation matrix generated on the transmission side based on this packet, and notifies the error correction decoder 6 of the check matrix. The error correction decoder 6 uses this check matrix and the transmission data received by the receiver 5 to perform recovery processing for lost packets included in the transmission data. Thereafter, the transmission data is transmitted.

  The check matrix pools 20A and 20B are storage devices that store a previously shared H matrix.

In this embodiment, as a matrix exchange method
a. Generation by puncturing after reading a file [matrix type 0]
b. Generation by puncturing after algorithm generation [Matrix type 1]
c. Generation only by algorithm generation (scratch type) [Matrix type 2]
d. Generation by algorithm generation only (root matrix expansion type) [Matrix type 3]
There are four types.

  The selection criteria for each matrix exchange are shown below.

a. Generation by puncturing after reading the file:
The method is
・ When processing time limit of error correction code is fixed;
・ When the transmitter / receiver is fixed in advance;
・ When the storage area can be secured by the transceiver;
・ When there is little change in packet size and bit rate to be transmitted;
And is suitable for compressed video transmission at a stable bit rate.

b. Generation by puncturing after algorithm generation:
The method is
・ When processing time limit of error correction code is fixed;
-If the transceiver is not fixed in advance;
・ When the storage area cannot be secured by the transceiver;
・ When there are large changes in the packet size and bit rate to be transmitted;
And is suitable for video multicast distribution using a variable bit rate and a scalable code.

c. Generation only by algorithm generation (scratch type):
The method is
・ When the time limit of error correction code processing is not decided;
Suitable for file data transmission.

  Processing for each matrix type is as follows.

[Matrix type = 0]
d. Generation by algorithm generation only (extended root matrix)
The method is
・ When processing time limit of error correction code is fixed;
・ When better error correction capability than method a and method b is required;
-If the processing time constraint is more relaxed than method a and method b;
-When processing performance on the receiving terminal is higher than method a and method b;
Suitable for video reception based on hardware implementation.

  FIG. 14 shows an example of a matrix exchange packet of a generation method by puncturing after reading a file in the second embodiment of the present invention. This matrix exchange packet includes a matrix type for identifying “a generation method by puncturing after reading a file”, a parent matrix ID for uniquely designating a check matrix stored in the check matrix pool 20B, and actually error correction code processing. It consists of the number of rows and the number of columns of the parity check matrix used (hereinafter referred to as “child matrix”). The number of columns of the parent matrix is obtained from information read from the parent matrix ID, which is the same as the number of packets including padding in the H matrix, that is, the value of (number of child matrices + number of padding packets). Here, the parent matrix ID is an ID (such as a file name) for specifying the parent matrix. When the parent matrix ID is designated, the parent matrix information is read from the check matrix pools 20A and 20B, and read. The relationship between the number of columns of the parent matrix and the number of columns of the child matrix included in the parent matrix information is the value of “number of child matrices + number of padding packets”.

[Matrix type = 1]
FIG. 15 shows an example of a matrix exchange packet of a generation method by puncture processing after algorithm generation according to the second embodiment of the present invention. This matrix exchange packet is a matrix type that identifies "a generation method by puncturing after algorithm generation", the number of rows and columns of a check matrix (called a parent matrix) that is generated by an algorithm, and a check matrix that is actually used in error correction code processing. It consists of the number of rows and columns of (child matrix), the column weights of two types of check matrices given as parameters in algorithm generation, and the ratio of these column weights. These parameters are arbitrarily specified and given by the user. For example, weight 1 = 3, weight 2 = 7, number of columns of weight 1: number of columns of weight 2 = 0.8: 0.2.

[Matrix type = 2]
FIG. 16 shows an example of a matrix exchange packet of a generation method (scratch type) based only on algorithm generation according to the second embodiment of the present invention. This matrix exchange packet is a matrix type that identifies the `` generation method using only algorithm generation (scratch type) '', the number of columns of the check matrix (parent matrix) at the time of algorithm generation, and the check matrix actually used in error correction code processing (child Matrix), the column weights of two types of check matrices given as parameters in algorithm generation, and the ratio of the column weights. The method of giving parameters is the same as in FIG.

[Matrix type = 3]
FIG. 17 shows an example of a matrix exchange packet of a generation method (root matrix expansion type) based only on algorithm generation according to the second embodiment of the present invention. This matrix exchange packet is a matrix type that identifies "a generation method using only algorithm generation (root matrix expansion type)", the number of columns of the check matrix (parent matrix) at the time of algorithm generation, and the check matrix that is actually used in error correction code processing It consists of the number of rows and columns of (child matrix), the column weights of two types of check matrices given as parameters in algorithm generation, and the ratio of these column weights. The method of giving parameters is the same as in FIG.

  Next, matrix conversion will be described.

  FIG. 18 is a flowchart of the matrix exchange method according to the second embodiment of the present invention.

  The check matrix generator 10B selects a method for generating a check symbol sequence based on the matrix type of the matrix exchange packet received from the check matrix generator 10A.

  The parity check matrix generator 10B on the receiving side performs matrix exchange from the parity check matrix pool 20B connected to the parity check matrix generator 10B when the matrix type corresponds to the generation method by puncture processing after reading the file (matrix type = 0). A check matrix corresponding to the parent matrix ID in the packet is read (step 502, Yes, step 503). Note that this parity check matrix pool 20B is synchronized in advance on the transmitting and receiving sides and shares the same parity check matrix data. Thereafter, the number of rows of the read check matrix is compared with the number of rows of the child matrix of the matrix exchange packet, and puncture processing is performed by the method shown in FIG. 19 (step 506). Since the former is basically large from the difference between the number of rows of the parity check matrix read and the number of child matrix rows of the matrix exchange packet, the number of rows of the child matrix is adjusted by performing the puncturing process. The check matrix thus obtained is notified to the error correction decoder 6 (step 510).

  When the matrix type corresponds to the generation method by the puncture process after generating the algorithm (matrix type = 1) (step 504, Yes), based on the information of the matrix exchange packet, the algorithm generation of the check matrix is performed as shown in FIG. Perform (step 505). Here, a staircase matrix H2 that satisfies the number of rows and columns of the parity check matrix to be generated and a matrix H1 in which all elements are zero are prepared. For H1, non-zero elements are randomly arranged so as to satisfy two types of column weights and their ratio for each column.

  FIG. 21 shows an example in which this method is applied when the number of parent matrix columns N = 16, the number of child matrix rows M = 8, column weight 1 = 2, column weight 2 = 3, and column weight ratio = 0.625. Yes. Thereafter, the number of rows of the check matrix generated in this way is compared with the number of rows of the child matrix of the matrix exchange packet, and puncturing is performed by the method shown in FIG. 19 (step 506). The check matrix thus obtained is notified to the error correction decoder 6 (step 510).

  When the matrix type corresponds to a generation method (scratch type) based only on algorithm generation (matrix type = 2) (Yes in step 507), a check matrix algorithm is generated by the existing H matrix generation method, and the process proceeds to step 512. (Step 508). If the generation method (root matrix expansion type) is based only on algorithm generation (matrix type = 3) (step 509, Yes), the above-described processing of FIG. 7 is performed (step 510). Finally, the check matrix data is notified to the error correction decoder 6 and the process is terminated (step 512). If it does not correspond to any matrix type (step 509, No), error processing is performed (step 511), and the processing is terminated.

  Here, the check matrix puncturing process of FIG. 19 will be described.

  The parity check matrix generator 10B sets j0 = 1, cnt = 0, and step = 2 (step 601). Here, Step = 2 is set to substantially reduce the number of rows of the H matrix and the number of columns of the parity part in the puncturing process. In order to perform puncturing, there is a sequence of rows / columns to be erased. The first one is as shown in FIG. 4, and the first parity packet is erased because puncturing is performed based on the second parity packet. It depends. j = j0 is set (step 602).

  The jth parity packet is punctured (step 603), and cnt is set to cnt = cnt + 1 (step 604). It is determined whether or not the number of columns of the current matrix matches the number of columns of the child matrix. If they match (step 605, Yes), the process ends. If they do not match (step 605, No), j is predetermined. (J> m) (step 606, Yes), j0 = j0 × 2 (step 608), step = step × 2 (step 609), and the process returns to step 602. In this process, when the second parity packet is punctured as a reference, the first parity packet disappears, and then punctured in order of 2, 4, 6,. When the puncturing is completed, the even-numbered packets from the top among the remaining parity packets are punctured. That is, 2,4,6,8, ... is punctured in the first stage, and 4,8,16, ... is punctured in the second stage. If j ≦ m (step 606, No), j = j + step is set (step 607), and the process proceeds to step 603.

  Next, a process for generating a check matrix algorithm (scratch type) based on information of the matrix exchange packet will be described with reference to FIG.

  First, N is the number of columns in the parent matrix and M is the number of columns in the child matrix (step 701). num_deg1 = floor [N × (column weight ratio)], deg1 = column weight 1, and deg2 = column weight 2 (step 702). j = 0 is set (step 703), and the check matrix H1 = N × (N−M) matrix in which all elements are examples is obtained (step 704). Further, a step matrix of a check matrix H2 = M × M is obtained (step 705). If j is equal to or greater than the number of rows M of the child matrix (step 706, No), the check matrix is set to [H1 | H2] (step 707), and the process is terminated. If j is smaller than M (step 706, Yes), it is determined whether j <num_deg1. If so (step 708, Yes), deg1 columns are randomly selected from the jth column of the check matrix H1. Are set to non-zero elements (step 709), j = j + 1 is set (step 711), and the process proceeds to step 706. If j ≧ num_deg1 (step 708, No), randomly select deg2 columns from the jth column of H1, set them as non-zero elements (step 710), and set j = j + 1 (step 711), the process proceeds to step 706.

  In the present embodiment, it is possible to apply to a wide range of scenes by integrally dealing with a plurality of H matrix exchange methods. Furthermore, because it assumes a transmission method that controls the coding rate by puncture processing, optimal error correction depending on the network conditions and transmission data bandwidth (a matrix with the minimum coding rate that can recover packet loss on the communication path) (Error correction using) is possible. In addition, the same matrix is configured on the transmission side and the reception side, and only the information necessary for exchanging and the minimum capacity (information necessary for configuring the same matrix on the transmitter and the receiver) is shared, It is possible to minimize the overhead associated with matrix exchange.

  For example, in the alit format, which is a matrix file format commonly used in LDPC, the matrix data with a code length of n = 1125 and the number of parity m = 125 is 30 kilobytes. By using, it can be reduced to 13 bytes.

  The check matrix generator that performs the processes of FIGS. 7 to 9 and the check matrix generator processes shown in FIGS. 18 to 20 are constructed as a program and installed in a computer that is used as the check matrix generator. It can be executed or distributed via a network.

  The present invention is not limited to the above-described embodiments, and various modifications and applications are possible within the scope of the claims.

DESCRIPTION OF SYMBOLS 1 Check matrix generator 2 Error correction encoder 3 Transmitter 4 Dual erasure channel 5 Receiver 6 Error correction decoder 10A, 10B Check matrix generator 20A, 20B Check matrix pool

Claims (1)

An error correction code method for generating a parity check matrix of an error correction code in a transmission system using an error correction code,
On the storage means of the device that performs error correction coding,
The initial value that expands the size of a given H matrix (hereinafter referred to as “root matrix H”) and sets all the elements of the newly added region (hereinafter referred to as “extended region”) to zero. Step,
A root matrix expansion step of moving non-zero elements of the root matrix to the extension region using a minimum loop local maximization algorithm so that the density of non-zero elements in the extension region is uniform;
The stomach line,
In the initialization step,
The number of rows m1 of the sparse matrix H1 included in the root matrix H is expanded to (m0 + m1) (where m0 is the number of parity of H1 and m1 is the number of added parity), and all the elements of the extension region are expanded. Set to zero,
A step matrix H2 ′ is generated by expanding the size of the step matrix H2 included in the root matrix H to (m0 + m1) × (m0 + m1);
H '= [H1' | H2 '] (where H1' is an expanded matrix)
In the root matrix expansion step,
Extracting the column number of the non-zero element having the girth which is the minimum distance from the path returning to the original starting from the non-zero element in the root matrix, and the girth value at this time is min_girth,
The line number of the elements that make up the smallest girth is i,
An error correction coding method , wherein a non-zero element of i rows and D columns is moved to the extension region so as to maximize the girth within the D-th column belonging to the extension region added to H1 ′ .

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