KR20090086744A - Method of encoding/decoding data using ldpc code and parity check matrix therefor - Google Patents

Abstract

An encoding/decoding method using a LDPC(Low Density Parity Check) code and a parity check matrix for the same are provided to minimize the number of cycles such as 4-cycle or 6-cycle by expanding a model matrix. A structure of a parity check matrix is used in case an input data row is encoded by a LDPC coding method or the encoded codeword is decoded. The structure of the parity check matrix includes at least two or more rows and a weight addition part. At least two or more rows are generated by dividing at least one or more rows of a base parity check matrix displayed into a form of a model matrix. The weight addition part is generated by replacing at least one or more sub matrixes which do not have a weight with at least one or more sub matrixes which have the weight.

Description

Method of encoding / decoding data using LDPC code and parity check matrix therefor {Method of encoding / decoding data using LDPC code and parity check matrix therefor}

The present invention relates to an encoding and decoding method, and more particularly, to an encoding / decoding method using an LDPC code and a parity check matrix therefor.

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 of low density, where most of the elements of the parity check matrix Η are zero. The LDPC code is so complex that it has been forgotten because it was impossible to implement with the hardware technology at the time of the proposal. Since it was rediscovered in 1995 and proved to have excellent performance, it has been actively studied. (Reference: [1] Robert G. Gallager, "Low-Density Parity-Check Codes", The MIT Press, September 15, 1963. [2] DJC Mackay, Good error-correcting codes based on very sparse matrices, IEEE Trans Inform.Theory, IT-45, pp. 399-431 (1999)).

Since the parity check matrix of the LDPC code is very small, it can be decoded through iterative decoding even in a very large block size. When the block size becomes very large, the performance 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 about 1000 × 2000, many operations are required in the encoding and decoding process, implementation is very complicated, and requires a lot of storage space.

In general, adding more weight to the parity check matrix H means adding more variables to the parity check equations, so it will perform better in the encoding and decoding method by LDPC code. Can be. Here, the weight means the number of '1's included in each column or row in the parity check matrix. However, if more weight is added to the parity check matrix H, 4-cycle or 6-cycle is often formed in the parity check matrix. There is also a risk of increasing the complexity of the decoding process and reducing performance.

4-cycle means the case where two rows of the parity check matrix Η have 1 at two points at the same time, and 6-cycle means the case where all two selectable combinations of any three rows have 1 at the same point. it means. The fact that the parity check matrix has many 4-cycles or 6-cycles means that the encoding or decoding performance is likely to be degraded.

As described above, in the encoding and decoding method using the LDPC code, how to distribute the weight of each row or column of the parity check matrix and how to control the cycle such as 4-cycle or 6-cycle is very important for the encoding and decoding performance. Will be affected.

The present invention has been made to solve the problems of the prior art as described above, an object of the present invention is to provide a method for improving the performance in the encoding and decoding method using the LDPC code.

Another object of the present invention is to provide a method for easily controlling the weight and the number of cycles of a row or column of a parity check matrix.

The parity check matrix in accordance with an aspect of the present invention comprises at least two or more rows generated by dividing each of at least one or more rows of the base model matrix represented in the form of a model matrix, and the weight of the information word portion of the at least two or more rows. At least one of a weight addition portion generated by replacing at least one or more sub-matrixes having no weight with at least one sub-matrix having a weight and an additional parity portion generated by adding at least one sub-matrix to the parity portion of each of the at least two or more rows. It includes one. It is desirable to consider the characteristics of cycle 4 and cycle 6 when generating the weight addition portion and the additional parity portion. That is, it is preferable to generate the weight addition part and the additional parity part so that the number of cycles 4 and 6 can be minimized in terms of the total parity check matrix generated by extending the model matrix.

According to the present invention has the following effects.

First, the weight distribution and the number of cycles such as 4-cycle or 6-cycle can be controlled when generating the parity check matrix.

Second, the coding and decoding efficiency using the LDPC code can be increased.

The construction, operation, and other features of the present invention will be readily understood by embodiments of the present invention described below with reference to the accompanying drawings.

Since embodiments of the present invention assume a structured LDPC encoding and decoding method, a structured LDPC encoding and decoding method will be described below.

To use the LDPC code, a parity check matrix is used. As described above, the parity check matrix is a binary matrix, where most elements are '0' and some are '1'. Since the size of the parity check matrix used for actual encoding or decoding is 10 ⁵ bits or more, a large memory is required to store the parity check matrix.

In the structured LDPC coding technique, the parity check matrix is stored in the form of a model matrix. The model matrix consists of a number of indexes, each pointing to a particular sub-matrix. In other words, each sub-matrix is represented by a specific index as a matrix of constant size (z × z). When encoding or decoding is performed, each index of the model matrix is replaced with a sub-matrix indicated by the index to be used as a parity check matrix.

1 illustrates an example of a model matrix. In FIG. 1, each integer means an index of a corresponding submatrix. For example, an index of '-1' means a zero matrix of a specific size, and an index of '0' means an identity matrix of a specific size. An index that is a positive integer except '-1' and '0' may mean a predetermined rule in which a corresponding submatrix is generated. For example, an index that is a positive integer represents a shift number. That is, when each sub-matrix is a permutation matrix generated by shifting each row or column of the unit matrix in a predetermined direction, the shift number may be an index of the sub-matrix. For example, when a sub-matrix is represented by an index of '1', the sub-matrix is generated by shifting each row or column of the unit matrix by one column (row or column) in a specific direction. No index may be used to indicate a submatrix that is a zero matrix in the model matrix. In the following embodiments, an index is not used to indicate a sub-matrix that is a zero matrix.

FIG. 2 is a diagram for describing a method of expressing a matrix according to the aforementioned index, that is, a shift number. When a particular parity check matrix is structured and expressed as a 4x4 matrix (that is, a submatrix), the submatrix with an index of '3' means that each column of the 4x4 unit matrix has three columns to the right. It is a permutation matrix generated by shifting by.

Memory capacity for storing parity check matrices by storing model matrices in which each sub-matrix is represented by one index according to the coded structured LDPC technique, and extending the model matrix stored at the time of encoding or decoding to the original parity check matrix. Can save.

Hereinafter, a method of generating a new model matrix by splitting at least one or more rows of the basic model matrix will be described.

3 illustrates an example of a basic model matrix, in which an index indicated in each subblock represents a number of shifts. In addition, in FIG. 3, the sub block in which the shift number is not indicated is a sub block having an index of '-1'. That is, the subblock in which the shift number is not represented represents a zero matrix.

As shown in FIG. 3, the model matrix of FIG. 3 is composed of four rows and 24 columns. The model matrix of FIG. 3 supports a code rate of 5/6. The model matrix of FIG. 3 is divided into an information word portion corresponding to an information bit and a parity portion corresponding to a parity bit. That is, in FIG. 3, the information word is a part from the column indicated by index 0 (hereinafter referred to as 'column 0') to the column indicated by index 19 (hereinafter referred to as 'column 19'). In addition, the parity portion is from the column indicated by index 20 (hereinafter referred to as 'column 20') to the column indicated by index 23 (hereinafter referred to as 'column 23').

FIG. 4 illustrates a model matrix newly generated by dividing one row of the basic model matrix of FIG. 3 into two rows. That is, row 504 of FIG. 3 is divided into rows 504A and 504B of FIG. 4. In this case, components having weights in rows 0 to 23 are exclusively separated. Here, the fact that the weighted component is exclusively separated means that the corresponding columns of the two rows after the separation are separated so as not to have weight at the same time. Also, it can be seen that the shift number of '127' is added to column 24. In this case, since the sum of the weights of column 24 is even, its effect is ignored by modulo operation. Therefore, it can be seen that the model matrix of FIG. 4 is a matrix equivalent to the model matrix of FIG. 3. Meanwhile, the matrix of FIG. 4 supports a code rate of 4/5 because the number of rows and columns is increased by one.

FIG. 5 illustrates a model matrix newly generated by dividing one row of the model matrix of FIG. 4 into two rows. Row 503 of FIG. 14 is divided into rows 503A and 503B of FIG. In this case, components having weights in rows 0 to 23 are exclusively separated. Also, it can be seen that the shift number of '119' is added to column 25. In this case, since the sum of the weights of column 25 is an even number, the influence is ignored by modulo operation. Thus, the model matrix of FIG. 5 is equivalent to the model matrix of FIG. 3 or 4. Meanwhile, the matrix of FIG. 5 supports a code rate of 20/26 since the number of rows and columns is increased by one.

FIG. 6 illustrates a model matrix newly generated by dividing one row of the model matrix of FIG. 5 into two rows. Row 501 of FIG. 5 is divided into rows 501A and 501B of FIG. In this case, components having weights in rows 0 to 23 are exclusively separated. Also, it can be seen that the shift number of '117' is added to column 26. In this case, since the sum of the weights in column 26 is an even number, the influence is ignored by modulo operation. Thus, the model matrix of FIG. 6 is equivalent to the model matrix of FIGS. 3 to 5. Meanwhile, the matrix of FIG. 6 supports a code rate of 3/4 because the number of rows and columns has increased by one.

FIG. 7 illustrates a model matrix newly generated by dividing one row of the model matrix of FIG. 6 into two rows. Row 502 of FIG. 6 is divided into rows 502A and 502B of FIG. In this case, components having weights in rows 0 to 23 are exclusively separated. Also, it can be seen that the shift number of '113' is added to column 27. In this case, since the sum of the weights of column 27 is even, its influence is ignored by modulo operation. Thus, the model matrix of FIG. 7 is equivalent to the model matrix of FIGS. 3 to 6. The matrix of FIG. 7 supports a code rate of 20/28 since the number of rows and columns has increased by one.

When rows are separated in the model matrix of FIGS. 4 to 7, non-zero components are further included such that the sum of columns is even. In this case, it is preferable that the non-zero added component takes into account the characteristics of cycle 4 and cycle-6. In other words, the non-zero component added is preferably determined such that the number of cycles 4 and 6 is minimized.

When the model matrix of FIGS. 4 to 7 is extended to the parity check matrix, it has the following cycle characteristics. Table 1 shows that each sub-matrix of the model matrix is 24 × 24 size.

Cycle-4 Cycle-6 Average VAR degree 3 (r = 5/6) 0 9672 3.08 4 (r = 4/5) 0 5832 3.04 5 (r = 10/13) 0 3384 3.00 6 (r = 3/4) 0 1944 2.96 Fig. 7 (r = 5/7) 0 1056 2.93

The non-zero component added as above has fewer cycles and fewer weights than the low code rate parity check matrix.

8 illustrates an example of a basic model matrix according to an embodiment of the present invention. The model matrix of FIG. 8 has a size of 4x12 and supports a code rate of 2/3. In addition, the model matrix of FIG. 8 is composed of an information word part and a parity part.

FIG. 9 is a diagram for describing a method of dividing one row of the basic model matrix of FIG. 8 to generate a parity check matrix in the form of a model matrix according to an embodiment of the present invention. That is, in FIG. 9, the first row of FIG. 8 is divided to generate two rows. At this time, components having a weight of heat are exclusively separated. That is, the corresponding columns of two rows after being separated are separated so as not to have weight at the same time. More specifically, the components with odd weights in the first row of FIG. 8 are located in corresponding columns of the first of the two separate rows of FIG. 9, and the components with even weights are separated rows of FIG. 9. Are separated to be located in the corresponding column of the second row. In the case where components of FIG. 8 have no weight in the first row (index '-1'), the corresponding columns of the two separate rows of FIG. 9 are separated without weight. That is, the heat corresponding to a component that does not have weight before it is separated does not have weight even after it is separated.

In addition, a new parity portion is added to the parity portion of the two separate rows. In this case, when generating a new parity check matrix by separating one or more rows, a new parity portion is added so that the number of rows and columns of the parity portion of the newly generated parity check matrix is the same. For example, when two rows are added to a new parity check matrix by row separation, an additional parity part having two columns is added to the parity part. In FIG. 9, since one row is added to the new parity check matrix by separating the first row of FIG. 8, one column including a component having a shift number (index) of '0' is added as an additional parity part.

FIG. 10 is a diagram for describing a method of dividing one row of the basic model matrix of FIG. 8 to generate a parity check matrix in a model matrix format according to another embodiment of the present invention. That is, in FIG. 10, the first row of FIG. 8 is divided to generate two rows. Even in this case, components having a weight of heat are exclusively separated. In addition, at least one sub-matrix having no weight is replaced with a weighted sub-matrix in the information word portion of the two separate rows. In FIG. 10, the number of shifts of the sub-matrix located in the first column of the two generated rows is replaced with '-1' to '2'.

FIG. 11 is a diagram for describing a method of dividing one row of the basic model matrix of FIG. 8 to generate a parity check matrix in the form of a model matrix according to another embodiment of the present invention. That is, in FIG. 11, the first row of FIG. 8 is divided to generate two rows. Even in this case, components having a weight of heat are exclusively separated. In addition, two or more sub-matrixes are added to the parity portion of each row generated separately. In FIG. 11, sub-matrixes having shift numbers '0', '1', '2', and '3' are respectively added to the parity portions of two separated rows.

FIG. 12 is a diagram for describing a method of dividing one row of the basic model matrix of FIG. 8 to generate a parity check matrix in a model matrix format according to another embodiment of the present invention. The example of FIG. 12 combines the example of FIG. 10 and FIG. That is, in FIG. 12, when the first row of FIG. 8 is divided to generate two rows, at least one sub-matrix having no weight in the information word portion of the two separated rows is replaced with the weighted sub-matrix. In addition, two or more sub-matrixes are added to the parity portion of each generated row. In FIG. 12, the sub-matrix corresponding to the first column of the two separated rows is replaced with a sub-block having a shift number of '11', and the shift numbers '0', '1', '2' and '3' in the parity portion are respectively. Submatrices were added.

The model matrix generated by the embodiment of FIG. 12 includes at least two or more rows generated by dividing each of at least one or more rows of the base model matrix, and at least one or more that do not have the weight of the information word portion of the at least two or more rows. A weight addition portion generated by replacing the sub-matrix with at least one sub-matrix with weights, and an additional parity portion generated by adding at least one sub-matrix to the parity portion of each of the at least two or more rows. It is desirable to consider the characteristics of cycle 4 and cycle 6 when generating the weight addition portion and the additional parity portion. That is, it is preferable to generate the weight addition part and the additional parity part so that the number of cycles 4 and 6 can be minimized in terms of the total parity check matrix generated by extending the model matrix.

When encoding is performed using the parity check matrix generated by the embodiments of the present invention, input source data may be encoded using a generator matrix. That is, k bits of input source data s _{1 x k} are encoded into a generation matrix to be n bits of codeword x _{1 x k} . Codeword x has a configuration of x = [sp] = [s ₀ , s ₁ , ..., s _{k -1} , p ₀ , p ₁ , ..., p _{m -1} ] (where (p ₀ , p ₁ , ..., p _{m -1} ) are parity check bits, and (s ₀ , s ₁ , ..., s _{k -1} ) are system bits. ).

However, the coding method using the generation matrix is very complicated. Therefore, in order to reduce such a complexity, it is preferable to directly code input source data using the parity check matrix H instead of the generation matrix. That is, since x = [sp] , using the characteristic of Hx = 0, Hx = H · sp [ = 0 ] , the parity check bit p can be obtained from this equation, resulting in codeword x. = [sp] can be obtained.

A method of performing decoding by using the parity check matrix generated by the embodiments of the present invention will be described. The decoder must obtain the information bit (x) from the codeword (c) which is the encoding result, and finds it using the property of cH ^T = 0. That is, for example, when the codeword received at the receiving side is c ', the value of c'H ^T is calculated, and if the result is 0, the preceding k bits of c' are determined as decoded information bits. If the value of c'H ^T is not 0, the value of c'H ^T satisfies 0, using a sum-product algorithm, a reliability propagation algorithm, and the like according to the graph according to the prior art. Find c 'and recover x.

The terminology used herein may be replaced with other terms having the same meaning. For example, the model matrix may be replaced by the term 'base matrix', and the sub matrix may be replaced by terms such as 'sub block' or 'permutation matrix'.

It is apparent to those skilled in the art that the present invention can be embodied in other specific forms without departing from the spirit and essential features of the present invention. 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.

1 illustrates an example of a model matrix.

FIG. 2 is a diagram for describing a method of representing a matrix according to shift numbers.

3 shows an example of a basic model matrix.

FIG. 4 illustrates a model matrix newly generated by dividing one row of the basic model matrix of FIG. 3 into two rows.

FIG. 5 illustrates a model matrix newly generated by dividing one row of the model matrix of FIG. 4 into two rows.

FIG. 6 illustrates a model matrix newly generated by dividing one row of the model matrix of FIG. 5 into two rows.

FIG. 7 illustrates a model matrix newly generated by dividing one row of the model matrix of FIG. 6 into two rows.

8 illustrates an example of a basic model matrix according to an embodiment of the present invention.

FIG. 9 is a diagram for describing a method of dividing one row of the basic model matrix of FIG. 8 to generate a parity check matrix in the form of a model matrix according to an embodiment of the present invention.

FIG. 10 is a diagram for describing a method of dividing one row of the basic model matrix of FIG. 8 to generate a parity check matrix in a model matrix format according to another embodiment of the present invention.

FIG. 11 is a diagram for describing a method of dividing one row of the basic model matrix of FIG. 8 to generate a parity check matrix in the form of a model matrix according to another embodiment of the present invention.

FIG. 12 is a diagram for describing a method of dividing one row of the basic model matrix of FIG. 8 to generate a parity check matrix in a model matrix format according to another embodiment of the present invention.

Claims (7)

In the structure of the parity check matrix used when the input data string is encoded or decoded by a low density parity check (LDPC) coding scheme, At least two rows generated by dividing each of at least one or more rows of the basic parity check matrix represented in the form of a model matrix; And And a weight addition portion generated by replacing at least one or more sub matrices not having a weight of the information word portion of each of the at least two rows with at least one or more sub matrices having a weight. The method of claim 1, And an additional parity portion generated by adding at least one sub-matrix to the parity portion of each of the at least two or more rows. The method according to claim 1 or 2, And minimizing the number of cycles 4 and 6 for the parity check matrix when generating the weight addition portion or the additional parity portion. In the method of encoding the input data string by the LDPC coding technique, Providing an input data sequence; And Encoding the input data string using a parity check matrix; The parity check matrix is at least two or more rows generated by dividing each of at least one or more rows of the basic parity check matrix represented in the form of a model matrix, and at least not having the weight of the information word portion of each of the at least two or more rows. And a weight addition portion generated by replacing one or more sub-matrices with at least one or more sub-matrices having weights. The method of claim 4, wherein And the parity check matrix further comprises an additional parity portion generated by adding at least one sub-matrix to a parity portion of each of the at least two or more rows. In the method for decoding the coded codeword by LDPC coding method, Providing the codeword; And Decoding the codeword using a parity check matrix; The parity check matrix is at least two or more rows generated by dividing each of at least one or more rows of the basic parity check matrix represented in the form of a model matrix, and at least not having the weight of the information word portion of each of the at least two or more rows. And a weight addition portion generated by replacing one or more sub-matrices with at least one or more sub-matrices having weights. The method of claim 6, And the parity check matrix further comprises an additional parity portion generated by adding at least one sub-matrix to a parity portion of each of the at least two or more rows.

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