KR101073907B1 - Encoding method by using LDPC code and computer-readable medium for the same - Google Patents

Abstract

In the encoding method using a Low Density Parity Check (LDPC) code according to the present invention, a u vector that is k-bit source input data is represented by the following equation, c = [I | (H _p ^-1 H _d ) ^t ] ^t ㆍ u (Where c is an n-bit codeword, I is an identity matrix, H _p and H _d are part of the parity check matrix H, where H = [H _d | H _p ] (H _d is (nk) × k , H _p is the m when divided by (nk) × (nk) dimension Im) between Im) doedoe encoded by, of m having the H _d (nk) / m × k-dimensional sub-matrix of The j th row of a particular submatrix of one of the submatrices is W _j (j = 1, 2, ..., under the condition that the column weight of all columns of the particular submatrix is 1). (nk) / m) consecutive 1s, and any two rows as a whole of H _d are characterized by not having 1 at two or more points at the same time.

LDPC code, encoding, decoding, parity check, matrix

Description

Encoding method by using LDPC code and computer-readable medium for the same}

1 is a configuration of a communication system for explaining an embodiment of the present invention.

2 is an exemplary diagram for explaining a relationship of Η = [H _d | H _p ].

3 shows an example of a double diagonal matrix.

4 is a view for explaining a specific sub-matrix of H _d according to an embodiment of the present invention.

5 is a view for explaining a specific sub-matrix of H _d according to another preferred embodiment of the present invention.

6 is a procedure flowchart for explaining a process of generating a parity check matrix H.

The present invention relates to an encoding method. More specifically, the amount of memory for storing the parity check matrix required for encoding using a low density parity check (LDPC) code, and the amount of computation and complexity required for encoding are determined. And a computer readable recording medium for encoding.

In general, encoding means that the receiver can restore the original data in spite of an error caused by distortion or loss of the signal generated in the process of transmitting the data transmitted from the transmitter through the communication channel. In order to do so, it means a process of data processing at the transmitting side. Decoding is a process of restoring the encoded and transmitted signal to the original data at the receiving side.

Recently, a coding method using an LDPC code has emerged. The LDPC code was proposed by Gallagher in 1962 as a linear block code in which most of the elements of the parity check matrix Η are zero and low density. Since the LDPC code is so complex that it was impossible to implement with the technology at the time of the proposal, it has been forgotten and rediscovered in 1995.

Since the parity check matrix of the LDPC code is very small, it is possible to decode by iterative decoding even in a very large block size. When the block size becomes very large, it shows performance that is close to Shannon's channel capacity limit like a turbo code.

The LDPC code can be described by the (n-k) × n parity check matrix Η. The generator matrix 하는 corresponding to the parity check matrix ƒ can be obtained from Equation 1 below.

Η · Ｇ = 0

In the encoding and decoding method using the LDPC code, the transmitting side encodes the input data by the following equation (2) by using the generation matrix 에 in the relation between the parity check matrix ƒ and equation (1).

c = u and u (where c is a codeword and u is a data frame)

As described above, in the coding method using the LDPC code, the parity check matrix ƒ is the most important factor. Since the parity check matrix ƒ has a size of at least 1000 × 2000, many operations are required in the encoding and decoding process, implementation is very complicated, and requires a lot of storage space.

The present invention has been made to solve the problems of the prior art as described above, an object of the present invention is the amount of memory and the amount of complexity and complexity required for storing the parity check matrix required for the encoding method using the LDPC code It is to provide an encoding method that can reduce the complexity.

Another object of the present invention is to provide a computer readable recording medium having recorded thereon a data structure necessary for providing the encoding method.

Summary of the Invention

In the encoding method using a Low Density Parity Check (LDPC) code according to the present invention, the source input data is encoded using a parity check matrix H having a configuration of [H _d | H _p ], wherein a portion of the H _d matrix is encoded. It is characterized by consisting of a structure having a certain regularity.

More specifically, the u vector, which is k-bit source input data, is represented by the following equation, c = [I | (H _p ^-1 H _d ) ^t ] ^t ㆍ u (where c is an n-bit codeword) Where I is the unit matrix, H _p and H _d are part of the parity check matrix H, where H = [H _d | H _p ] (H _d is (nk) × k, H _p is (nk) × (nk)). ) relationship Im) doedoe encoded by, the H _d to (nk) / m × in the case where divided into m number of sub-matrices having k dimensions, j-th of the m sub-matrices of a certain sub-matrix of A row has W _j (j = 1, 2, ..., (nk) / m) consecutive 1s, provided that the column weight of all columns of the particular submatrix is 1, In any case, any two rows of the H _{d as a} whole do not have 1 at two or more points at the same time.

The computer-readable recording medium according to the present invention has a relationship between a parity check matrix H and H = [H _d | H _p ] used in a coding method using a low density parity check (LDPC) code. A computer-readable recording medium storing a data structure of H _d having, wherein when H _d is divided into m sub matrices having a (nk) / m × k dimension, among the m submatrices. The j th row of one particular submatrix is W _j (j = 1, 2, ..., (nk) / m under the condition that the column weight of all columns of the particular submatrix is 1). ) of having a continuous 1, characterized in that as a whole the H _d H _d in storing the data structure having the features two lines (rows) of any one that does not have a 1 at the same time to more than one point.

Example

Hereinafter, preferred embodiments of a coding method using a Low Density Parity Check (LDPC) code according to the present invention will be described with reference to the accompanying drawings. 1 is a view for explaining a preferred embodiment of the present invention, an example of the technical features of the present invention applied to a wireless communication system. Embodiments described below are merely examples for explaining the features of the present invention, and it is apparent to those skilled in the art that the technical features of the present invention may be applied to all fields requiring encoding.

In FIG. 1, the transmitter 10 and the receiver 30 perform communication via a radio channel 20. In the transmitter 10, the k-bit source data u output from the data source 11 becomes an n-bit codeword c by LDPC encoding in the LDPC encoding module 13. The codeword c is wirelessly modulated by the modulation module 15 and transmitted through the antenna 17 and received by the antenna 31 of the receiver 30 through the radio channel 20. The receiver 30 undergoes an inverse process of the process that occurred in the transmitter 10, which is demodulated by the demodulation module 33 and decoded by the LDPC decoding module 35 to finally obtain source data u. Can be.

It will be readily understood by those skilled in the art that the above-described data transmission / reception processes are described within the minimum range necessary to describe the features of the present invention, and there are many other processes necessary for data transmission.

In the above Equation 1, the parity check matrix Η is represented by Η = [H _d | H _p ] (H _d is (nk) × k and H _p is (nk) × (nk).) Can be expressed. FIG. 2 is a diagram illustrating the relationship of ƒ = [H _d | H _p ] to be easily understood, and is not related to the technical features of the present invention. K denotes the length (bit unit) of the source data input to the LDPC encoding module 13, and n denotes the length (bit unit) of the coded codeword c.

It can be seen from the relationship between Equation 1 and Η = [H _d | H _p ] that Ｇ = [I | (H _p ^-1 H _d ) ^t ] ^t . Accordingly, the LDPC encoding module 13 encodes the input data u by multiplying the input data u by Ｇ = [I | (H _p- ¹ H _d ) ^t ] ^t by Equation (2). As a result, Equation 2 is equal to Equation 3 below.

c = [I | (H _p ^-1 H _d ) ^t ] ^t

In the present embodiment, a dual diagonal matrix having a dimension of (nk) × (nk) is used as H _p . The double diagonal matrix refers to a matrix in which the main diagonal and the diagonal just below the main diagonal are 1 and the rest are all 0, and FIG. 3 is an example to help the understanding of the double diagonal matrix.

Features of the present invention to provide a data structure of the H _d. That is, when the H _d is divided into m submatrices having (nk) / m × k dimensions, the j th row of one particular submatrices of the m submatrices is determined by the specific subquery. Under the condition that the column weight of every column of the matrix is 1, it has W _j (j = 1, 2, ..., (nk) / m) consecutive 1s, and any two rows as a whole as H _d (rows) also has the feature of not having 1 at more than one point at the same time. W _j may be the same for all rows of the specific sub-matrix. In addition, the W _j may be increased or decreased irregularly for all rows of the specific sub-matrix.

Figure 4 illustrates an example of the specific sub-matrix contained in the H _d. The specific sub-matrix shown in Fig. 4 is a matrix having a 7x28 dimension, and the matrix used for the actual LDPC encoding is a much larger matrix than this. In Figure 4, each row of the particular submatrix has four consecutive 1s and the rest have a value of zero (i.e. the weight of each row is four). Also, the weight of each column in the particular submatrix is one.

FIG. 5 illustrates another example of the specific sub-matrix included in the H _d , wherein each row of the specific sub-matrix has W _j consecutively 1 and the remainder 0, where W _j is irregular for each row. This is an example of change. Even in this case, the weight of each column in the specific sub-matrix is one.

In addition, the H _d is characterized in that any two rows as a whole do not have 1 at two or more points at the same time. The fact that any two rows in H _d does not have 1 at two or more points at the same time means that two or more points where 1 exists when the two rows are compared with respect to the entire H _d may not overlap. to be.

6 is a flowchart illustrating a process of generating a parity check matrix H. The method described below is just one example, and H having the above characteristics may be obtained by various methods.

First, with respect to a particular sub-matrix of H _d (first sub-matrix), the j-th row of the particular sub-matrix is W, provided that the column weights of all columns of the particular sub-matrix are 1. _j (j = 1, 2, ..., (nk) / m) are configured to have one consecutive [S51].

Second, column permutation so that any two rows of the remaining submatrices of H _d have no 1 at the same time at more than one point for the other submatrices (second submatrix). [S52].

Third, the second process is sequentially applied to the remaining submatrices to form all submatrices up to the last submatrice (m sub-matrix) [S53].

Fourth, the submatrices are combined to generate H _d [S54].

Fifth, by combining the H _d and H _p generates a H [S55].

In FIG. 1, the receiver 30 uses Equation 4 below to receive and decode the data encoded by the method described above.

Η · c = 0

That is, if the coded data c is multiplied by the parity check matrix Η and becomes 0, it means that there is no transmission error. If not, it means that there is a transmission error. Can be.

In Equation 3 and Equation 4, it can be seen that in the encoding and decoding method according to the present invention, only the data structure of H _{d needs} to be stored in the memory. That is, since H _p and H _p ^-1 are structured data structures, there is no need to store them, and only the H _d data structure can be encoded and decoded, thereby saving memory.

The technical idea of the present invention is a recording medium readable by a CPU (Control Process Unit) such as a CD-ROM, a floppy disk, a computer memory, or a memory of a mobile communication terminal, on which a data structure such as H _d having the above characteristics is recorded. It should be understood that it can also extend.

It will be apparent to those skilled in the art that the present invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. Accordingly, the above detailed description should not be construed as limiting in all aspects and should be considered as illustrative. The scope of the invention should be determined by reasonable interpretation of the appended claims, and all changes within the equivalent scope of the invention are included in the scope of the invention.

According to the encoding method using the LDPC code and the computer-readable recording medium for encoding according to the present invention, a portion of the parity check matrix required for LDPC encoding is structured in a structured form. For this reason, there is no need to store the memory in memory, and thus the memory can be saved and the calculation process for encoding and decoding can be simplified.

Claims (9)

In the encoding method using a low density parity check (LDPC) code, Encoding the source input data using the parity check matrix H having a configuration of [H _d | H _p ], When the H _d is divided into m submatrices having (nk) / m × k dimensions, the column weight of all columns of one particular submatrix of the m submatrices is 1, and the specific The jth row of the submatrix has W _j (j = 1, 2, ..., (nk) / m) consecutive 1s, and any two rows throughout the H _d Does not have 1 at more than one point at the same time, The W _j coding method using an LDPC code, characterized in that for increasing or decreasing irregularly for all the rows of the particular sub-matrix. The method of claim 1, The u vector, which is the k-bit source input data, is c = [I | (H _p ^-1 H _d ) ^t ] ^t ㆍ u (where c is an n-bit codeword, I is a unit matrix of k × k dimension, H _p and H _d are parity checks) Is encoded according to H = [H _d | H _p ] (where H _d is (nk) × k and H _p is (nk) × (nk)) as part of the matrix H). , Coding method using LDPC code. delete delete The method of claim 1, The H _p is an encoding method using an LDPC code, characterized in that the dual diagonal matrix. delete delete delete delete

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