KR102424942B1 - Method of channel coding for communication systems and apparatus using the same - Google Patents

Abstract

Disclosed are a channel coding/decoding method for transforming a parity check matrix and an apparatus using the same. A channel coding method according to an embodiment of the present invention includes: loading a first exponential matrix; transforming the first exponential matrix into a second exponential matrix; generating a parity check matrix corresponding to a required block size using the second exponential matrix; and performing LDPC encoding using the parity check matrix.

Description

Channel coding method for communication system and apparatus using the same

The present invention relates to a channel coding technique, and more particularly, to a data encoding and decoding technique for a communication system using a low-density parity-check (LDPC) code.

BACKGROUND Wireless communication systems are widely used to provide various types of communication content such as voice, data, and the like. These systems may be multiple-access systems capable of supporting communication with multiple users by sharing the available system resources (eg, bandwidth and transmit power). Examples of such multiple access systems are Code Division Multiple Access (CDMA) systems, Time Division Multiple Access (TDMA) systems, Frequency Division Multiple Access (FDMA) systems, Third Generation Partnership Project (3GPP) Long Term Evolution (LTE) systems. ) systems, Long Term Evolution Advanced (LTE-A) systems, and Orthogonal Frequency Division Multiple Access (OFDMA) systems.

In the modern information age, binary values (eg, ones and zeros) are used to represent and communicate various types of information such as video, audio, statistical information, and the like. Unfortunately, errors can occur during storage, transmission, and/or processing of binary data. For example, data that was originally 1 may be changed to 0, and data that was originally 0 may be changed to 1.

To check for errors and, in some cases, provide a mechanism for correcting errors, binary data can be coded to introduce carefully designed redundancy. Coding of units of data creates what are collectively referred to as code words. Because of that redundancy, the code word will contain more bits than the input unit of data from which the code word is generated. In this way, adding parity bits (redundant bits) to the information bits is called channel coding.

Redundant bits are added to the bit stream transmitted by the encoder to generate a code word. When signals originating from transmitted code words are received or processed, the redundant information contained in the code word as observed in the signal identifies and/or corrects errors in the received data to recover the original data unit. or to remove distortion from the received signal. Such error checking and/or correction may be implemented as part of the decoding process.

Communication systems often need to operate at several different rates, and in recent communication systems, a low-density parity-check (LDPC) code is actively used as a channel coding technique.

In general, a communication system is required to lower the cost for implementing an encoder/decoder in order to practically operate in devices with a wide performance range.

Accordingly, there is an urgent need for a new channel coding technique capable of lowering the encoding/decoding complexity of LDPC encoding/decoding.

An object of the present invention is to transform a parity check matrix of a given LDPC code to generate another parity check matrix having similar algebraic characteristics to perform LDPC encoding/decoding, thereby improving the efficiency of channel encoding/decoding. is to maximize

Another object of the present invention is to reduce encoding/decoding complexity by transforming parity check matrices of LDPC codes having different formats and integrating them into one unified format.

A channel coding method according to the present invention for achieving the above object includes: loading a first exponential matrix; transforming the first exponential matrix into a second exponential matrix; generating a parity check matrix corresponding to a required block size using the second exponential matrix; and performing LDPC encoding using the parity check matrix.

In this case, the converting of the first exponential matrix into the second exponential matrix includes performing circular column permutation on one column of the first exponential matrix to generate a column permuted exponential matrix. step; and generating a transform value for an element greater than 0 of the column permutated exponent matrix, and generating the second exponential matrix by using the transform value.

In this case, the one column may be a (k _b +1)-th column of the first exponential matrix (k _b is a natural number obtained by subtracting the number of rows from the number of columns of the first exponential matrix).

In this case, the first exponential matrix and the second exponential matrix are divided into two types, a first type and a second type, according to the first four elements of the (k _b +1)-th column of the first exponential matrix. can be

In this case, the first type includes only one natural number (a) in which the first four elements are greater than zero, and the second type includes two natural numbers (a) in which the first four elements are greater than zero. can

In this case, when the first exponential matrix is the first type, the second exponential matrix is the second type, and when the first exponential matrix is the second type, the second exponential matrix is the first type can

In this case, the recursive column permutation may be performed using the natural number (a) greater than 0.

In this case, the cyclic column permutation may be performed using the following equation.

[Equation]

(V' _ij is an element of the column permuted exponential matrix, V _ij is an element of the first exponential matrix, mod is a modulation operator, Z _max is the maximum block size, a is a natural number greater than 0)

In this case, the transform value may be generated by subtracting an element greater than 0 of the column permutated exponential matrix from the maximum block size.

In this case, the second exponential matrix may be generated using Equation.

[Equation]

(W _ij is an element of the second exponential matrix, V' _ij is an element of the column permuted exponential matrix, and Z _max is the maximum block size)

In addition, the channel encoder according to an embodiment of the present invention, a memory for storing data about the first exponential matrix corresponding to the existing parity check matrix; and a processor that generates a parity check matrix corresponding to a second exponential matrix generated by transforming the first exponential matrix, and performs LDPC encoding using the generated parity check matrix.

In this case, the second exponent matrix is generated using a transform value for an element greater than 0 of the column permutated exponent matrix, and the column permuted exponent matrix is generated for one column of the first exponent matrix. It may be generated by performing circular column permutation.

In this case, one column may be a (k _b +1)-th column of the first exponential matrix (k _b is a natural number obtained by subtracting the number of rows from the number of columns of the first exponential matrix).

In this case, the first exponential matrix and the second exponential matrix are divided into two types, a first type and a second type, according to the first four elements of the (k _b +1)-th column of the first exponential matrix. can be

In this case, the first type may include only one natural number in which the first four elements are greater than 0, and the second type may include two natural numbers in which the first four elements are greater than zero.

In this case, when the first exponential matrix is the first type, the second exponential matrix is the second type, and when the first exponential matrix is the second type, the second exponential matrix is the first type can

In this case, the recursive column permutation may be performed using the natural number greater than 0.

In this case, the cyclic column permutation may be performed using the following equation.

[Equation]

(V' _ij is an element of the column permuted exponential matrix, V _ij is an element of the first exponential matrix, mod is a modulation operator, Z _max is the maximum block size, a is a natural number greater than 0)

In this case, the second exponential matrix may be generated using the following equation.

[Equation]

(W _ij is an element of the second exponential matrix, V' _ij is an element of the column permuted exponential matrix, and Z _max is the maximum block size)

In addition, the channel decoder according to an embodiment of the present invention, a memory for storing data about the first exponential matrix corresponding to the existing parity check matrix; and a processor that generates a parity check matrix corresponding to a second exponential matrix generated by transforming the first exponential matrix, and performs LDPC decoding using the generated parity check matrix.

According to the present invention, LDPC encoding/decoding is performed by transforming a parity check matrix of a given LDPC code to generate another parity check matrix having similar algebraic characteristics, thereby increasing the efficiency of channel encoding/decoding. can be maximized.

In addition, the present invention can reduce encoding/decoding complexity by transforming parity check matrices of LDPC codes having different formats and integrating them into one unified format.

In addition, since the present invention generates a new parity check matrix in which most of the logarithmic characteristics and the parity check matrix before transformation are maintained, performance degradation may not be caused during channel encoding/decoding.

1 and 2 are diagrams illustrating examples of binary matrices corresponding to a basic graph.
3 and 4 are diagrams illustrating examples of exponential matrices corresponding to the basic graphs shown in FIGS. 1 and 2 , respectively.
5 is an operation flowchart illustrating a channel coding/decoding method according to an embodiment of the present invention.
6 is a block diagram illustrating a communication system according to an embodiment of the present invention.
7 is a block diagram illustrating an example of a channel encoder or a channel decoder shown in FIG. 6 .

The present invention will be described in detail with reference to the accompanying drawings as follows. Here, repeated descriptions, well-known functions that may unnecessarily obscure the gist of the present invention, and detailed descriptions of configurations will be omitted. The embodiments of the present invention are provided in order to more completely explain the present invention to those of ordinary skill in the art. Accordingly, the shapes and sizes of elements in the drawings may be exaggerated for clearer description.

Hereinafter, preferred embodiments according to the present invention will be described in detail with reference to the accompanying drawings.

An LDPC (low-density parity-check) code is a linear block code that can be generally defined as a parity-check matrix, and is typically information composed of K _ldpc bits or symbols. A codeword composed of N _ldpc bits is generated through LDPC encoding by receiving an information or information word (K _ldpc is a natural number, N _ldpc is a natural number greater than K _ldpc ).

Recently, an encoding and decoding technique based on a quasi-cyclic LDPC code has been proposed to maximize the efficiency of implementation and throughput as well as the encoding and decoding performance of the LDPC code.

The present invention provides a technique for generating an LDPC code having similar algebraic characteristics by transforming a parity check matrix of a given quasi-cyclic LDPC code. The LDPC code designed through the transformation has almost the same algebraic characteristics as the given quasi-cyclic LDPC code that is the target of the transformation. An effect of reducing encoding complexity can be obtained.

For the symbols and terms used in the description below, pp. pp. 2894-2901 or "Lifting methods for quasi-cyclic LDPC codes" by S. Myung, K. Yang and J. Kim published in June 2006, pp. 489-497 are disclosed in detail.

First, the quasi-cyclic LDPC code may be defined based on circulant permutation matrices, where P = (P _ij ), (P _ij is the i-th row, j having a size of Z x Z) element in the th column) may be defined as in Equation 1 below.

[Equation 1]

In general, the parity check matrix of the quasi-cyclic LDPC code can be expressed as in Equation 2 below.

[Equation 2]

In Equation 2, the V _ij value (i, j is a natural number) is typically an integer defined in the range {-1, 0, 1, 2, ...}, for V _ij >= 0, P ^Vij is It can be seen that it is the same as a circular permutation matrix in which each element of an identity matrix having a size of Z x Z is circularly shifted by V _ij in the right direction. In addition, in the present invention, P ^-1 means a zero matrix having a size of Z x Z.

In the present invention, for convenience of description, in Equation 2, one Z x Z sub-block corresponds to one cyclic permutation matrix, but in general, one Z x Z sub-block includes a plurality of cyclic permutation matrices. In a case corresponding to , the technical idea of the present invention can be equally applied. For reference, a Z x Z partial block composed of a plurality of cyclic permutation matrices may be generally regarded as a circulant matrix, and the parity of the LDPC code composed of the circulant matrix or the cyclic permutation matrices as shown in Equation 2 The check matrix is usually treated as a quasi-cyclic LDPC code.

Equation 2 is a parity check matrix representing a quasi-cyclic LDPC code comprising a total of m _b row blocks and n _b column blocks. Accordingly, it can be seen that the length of the total codeword is n _b Z, and if the parity check matrix has a full rank, when k _b = n _b - m _b , the length of the information word is k It can be seen that _b is Z.

In the parity check matrix of Equation 2, a binary permutation matrix having a size of Z x Z as an element '1' and a zero matrix having a size of Z x Z as an element '0' is a binary (binary) of size m _b X n _b A matrix may be referred to as a basic graph, a base matrix, or a mother matrix.

1 and 2 are diagrams illustrating examples of binary matrices corresponding to a basic graph.

1 and 2 , the matrix D may be a diagonal matrix, and the matrix Z may be a zero matrix.

In the example shown in Figure 1, the binary matrix is a 46 x 68 matrix, Z is a 4 x 42 zero matrix, D is a 42 x 42 diagonal matrix, A is a 4 x 22 matrix with elements 0 or 1, B is the elements of the first row are 1, 1, 0, 0, the elements of the second row are 1, 1, 1, 0, the elements of the third row are 0, 0, 1, 1, and the elements of the fourth row is a 4 x 4 matrix in which s are 1, 0, 0, and 1, and C may be a 42 x 26 matrix having 0 or 1 as an element. A basic graph with such a structure can be called the BG#1 type.

In the example shown in Figure 2, the binary matrix is a 42 x 52 matrix, Z is a 4 x 38 zero matrix, D is a 38 x 38 diagonal matrix, A is a 4 x 10 matrix with elements 0 or 1, B is the elements of the first row are 1, 1, 0, 0, the elements of the second row are 0, 1, 1, 0, the elements of the third row are 1, 0, 1, 1, and the elements of the fourth row are 1, 0, 0, and 1 in a 4 x 4 matrix, and C may be a 38 x 14 matrix having 0 or 1 as an element. A basic graph with such a structure can be called the BG#2 type.

The basic graph examples described with reference to FIGS. 1 and 2 may correspond to tables showing only the positions of rows and columns having '1' as an element, as shown in Table 1 below. In this case, i and j corresponding to 0 indicate the first row and the first column, respectively.

Row
index (i) Column indices (j) of every element of value 1 for BG#1 Column indices (j) of every element of value 1 for BG#2 0 0, 1, 2, 3, 5, 6, 9, 10, 11, 12, 13, 15, 16, 18, 19, 20, 21, 22, 23 0, 1, 2, 3, 6, 9, 10, 11 One 0, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 15, 16, 17, 19, 21, 22, 23, 24 0, 3, 4, 5, 6, 7, 8, 9, 11, 12 2 0, 1, 2, 4, 5, 6, 7, 8, 9, 10, 13, 14, 15, 17, 18, 19, 20, 24, 25 0, 1, 3, 4, 8, 10, 12, 13 3 0, 1, 3, 4, 6, 7, 8, 10, 11, 12, 13, 14, 16, 17, 18, 20, 21, 22, 25 1, 2, 4, 5, 6, 7, 8, 9, 10, 13 4 0, 1, 26 0, 1, 11, 14 5 0, 1, 3, 12, 16, 21, 22, 27 0, 1, 5, 7, 11, 15 6 0, 6, 10, 11, 13, 17, 18, 20, 28 0, 5, 7, 9, 11, 16 7 0, 1, 4, 7, 8, 14, 29 1, 5, 7, 11, 13, 17 8 0, 1, 3, 12, 16, 19, 21, 22, 24, 30 0, 1, 12, 18 9 0, 1, 10, 11, 13, 17, 18, 20, 31 1, 8, 10, 11, 19 10 1, 2, 4, 7, 8, 14, 32 0, 1, 6, 7, 20 11 0, 1, 12, 16, 21, 22, 23, 33 0, 7, 9, 13, 21 12 0, 1, 10, 11, 13, 18, 34 1, 3, 11, 22 13 0, 3, 7, 20, 23, 35 0, 1, 8, 13, 23 14 0, 12, 15, 16, 17, 21, 36 1, 6, 11, 13, 24 15 0, 1, 10, 13, 18, 25, 37 0, 10, 11, 25 16 1, 3, 11, 20, 22, 38 1, 9, 11, 12, 26 17 0, 14, 16, 17, 21, 39 1, 5, 11, 12, 27 18 1, 12, 13, 18, 19, 40 0, 6, 7, 28 19 0, 1, 7, 8, 10, 41 0, 1, 10, 29 20 0, 3, 9, 11, 22, 42 1, 4, 11, 30 21 1, 5, 16, 20, 21, 43 0, 8, 13, 31 22 0, 12, 13, 17, 44 1, 2, 32 23 1, 2, 10, 18, 45 0, 3, 5, 33 24 0, 3, 4, 11, 22, 46 1, 2, 9, 34 25 1, 6, 7, 14, 47 0, 5, 35 26 0, 2, 4, 15, 48 2, 7, 12, 13, 36 27 1, 6, 8, 49 0, 6, 37 28 0, 4, 19, 21, 50 1, 2, 5, 38 29 1, 14, 18, 25, 51 0, 4, 39 30 0, 10, 13, 24, 52 2, 5, 7, 9, 40 31 1, 7, 22, 25, 53 1, 13, 41 32 0, 12, 14, 24, 54 0, 5, 12, 42 33 1, 2, 11, 21, 55 2, 7, 10, 43 34 0, 7, 15, 17, 56 0, 12, 13, 44 35 1, 6, 12, 22, 57 1, 5, 11, 45 36 0, 14, 15, 18, 58 0, 2, 7, 46 37 1, 13, 23, 59 10, 13, 47 38 0, 9, 10, 12, 60 1, 5, 11, 48 39 1, 3, 7, 19, 61 0, 7, 12, 49 40 0, 8, 17, 62 2, 10, 13, 50 41 1, 3, 9, 18, 63 1, 5, 11, 51 42 0, 4, 24, 64 43 1, 16, 18, 25, 65 44 0, 7, 9, 22, 66 45 1, 6, 10, 67

In addition, in the parity check matrix of Equation 2, an integer matrix V = (V _ij ) having a size of m _b x n _b as in Equation 3 below, which consists of an exponent V _ij representing an exponent or a zero matrix of a cyclic permutation matrix, is converted to an exponential matrix (exponent matrix), shift matrix (shift matrix), or shift value matrix (shift value matrix).

[Equation 3]

In general, the parity check matrix of the LDPC code can be accurately known if the exponential matrix and the size Z value of the cyclic permutation matrix corresponding to the exponential matrix are known. In other words, if the size Z x Z of the cyclic permutation matrix is known, encoding and decoding of the LDPC code can be performed based on the exponential matrix. Hereinafter, Z is referred to as the size or block size of the cyclic permutation matrix.

As a method of storing the parity check matrix of the LDPC code, various methods as well as a method of storing an exponential matrix may be used. For example, the parity check matrix of the LDPC code can be accurately known even if only the mood matrix of the given LDPC code and the value of the element V _ij other than -1 in Equation 3 are known. As described above, in some cases, even if only the size Z of the LDPC sequence and cyclic permutation matrix corresponding to the element V _ij values corresponding to the basic matrix and the exponential matrix of the LDPC code is stored, it is the same as storing the entire parity check matrix of the LDPC code. effect can be obtained. As a result, there may be various methods for storing the parity check matrix that have the same logarithmic effect.

A lifting method may be used to generate LDPC codes of various lengths from one exponential matrix or LDPC sequence given as in Equation 3 above. For example, given the exponential matrix V = (V _ij ) as in Equation 3, each element V _ij is transformed for the block size Z as v _ij (Z) = V _ij mod Z, and then v For the _ij (Z) value, a parity check matrix based on a cyclic permutation matrix having a size of Z x Z may be defined as shown in Equation 4 below and used for LDPC encoding and decoding.

[Equation 4]

For an element V _ij of one given exponential matrix, _depending on the block size Z _{, V} = ( V _ij ) and supportable Z values are the same as storing a very diverse exponential matrix. Accordingly, it is possible to maximize the storage efficiency required for implementing LDPC encoding and decoding.

For example, as shown in Equation 5 below, block sizes may be divided into eight groups, and different exponential matrices may be applied to each block size group. All of the block sizes included in the block size group in Equation 5 below may be used in the system, or only some of them may be used.

[Equation 5]

3 and 4 are diagrams illustrating examples of exponential matrices corresponding to the basic graphs shown in FIGS. 1 and 2 , respectively.

3 and 4 , FIG. 3 shows an exponential matrix corresponding to the basic graph of FIG. 1 , and FIG. 4 shows an exponential matrix corresponding to the basic graph of FIG. 2 . '0' in the matrix shown in FIGS. 1 and 2 is changed to '-1' in the matrix shown in FIGS. 3 and 4, and '1' in the matrix shown in FIGS. 1 and 2 is shown in FIGS. 3 and 4 In the matrix shown in , it is changed to an integer defined in the range {0, 1, 2, ...}. In particular, all '1's of the diagonal matrix D of FIGS. 1 and 2 are changed to '0's of D' in the matrix shown in FIGS. 3 and 4 .

3 and 4, the matrix D' replaces element '0' of matrix D, which is a diagonal matrix, with '-1', and element '1' of matrix D, which is a diagonal matrix, replaces element It is a matrix replaced with '0'. That is, the matrix D' may be a square matrix in which diagonal elements from the upper left to the lower right are 0 and the remaining elements are -1. In the examples shown in FIGS. 3 and 4 , the matrix Z' is a matrix in which the element '0' of the zero matrix Z is replaced with '-1'. That is, the matrix Z' may be a matrix in which all elements are -1.

In the example shown in Fig. 3, the exponential matrix is a 46 x 68 matrix, Z' is a 4 x 42 matrix in which all elements are '-1', D' is a diagonal element from top left to bottom right is '0', The remaining elements are all 42 x 42 matrix with '-1', A' is a 4 x 22 matrix with integers defined in the range {-1, 0, 1, 2, ...}, and B' is A 4 x 4 matrix whose elements are integers defined in the range {-1, 0, 1, 2, ...}, where C' is defined in the range {-1, 0, 1, 2, ...} It can be a 42 x 26 matrix with integers as elements. An exponential matrix having such a structure may be referred to as a BG#1 type.

In the example shown in Fig. 4, the exponential matrix is a 42 x 52 matrix, Z' is a 4 x 38 matrix in which all elements are '-1', D' is a diagonal element from top left to bottom right is '0', The remaining elements are all 38 x 38 matrix with '-1', A' is a 4 x 10 matrix with integers defined in the range {-1, 0, 1, 2, ...}, and B' is A 4 x 4 matrix whose elements are integers defined in the range {-1, 0, 1, 2, ...}, where C' is defined in the range {-1, 0, 1, 2, ...} It may be a 38 x 14 matrix with integers as elements. An exponential matrix having such a structure can be called a BG#2 type.

Meanwhile, on the assumption that the basic graph is known, the exponential matrix of Equation 3 may store only exponential values other than -1 in order to reduce required storage memory or increase storage efficiency. At this time, exponent values other than -1 can be read and stored in column-by-column, or exponent values other than -1 can be read and stored row-by-row. may be

For example, the exponential matrix corresponding to BG#1 of Table 1 and FIGS. 1 and 3 may be expressed in the following form.

[BG#1 - Efficient storage format of Set 1 (row-by-row)]

Value of V = [250 69 226 159 100 10 59 229 110 191 9 195 23 190 35 239 31 1 0 2 239 117 124 71 222 104 173 220 102 109 132 142 155 255 28 0 0 0 106 111 185 63 117 93 229 177 95 39 142 225 225 245 205 251 117 0 0 121 89 84 20 150 131 243 136 86 246 219 211 240 76 244 144 12 1 0 157 102 0 205 236 194 231 28 123 115 0 183 22 28 67 244 11 157 211 0 220 44 159 31 167 104 0 112 4 7 211 102 164 109 241 90 0 103 182 109 21 142 14 61 216 0 98 149 167 160 49 58 0 77 41 83 182 78 252 22 0 160 42 21 32 234 7 0 177 248 151 185 62 0 206 55 206 127 16 229 0 40 96 65 63 75 179 0 64 49 49 51 154 0 7 164 59 1 144 0 42 233 8 155 147 0 60 73 72 127 224 0 151 186 217 47 160 0 249 121 109 131 171 0 64 142 188 158 0 156 147 170 152 0 112 86 236 116 222 0 23 136 116 182 0 195 243 215 61 0 25 104 194 0 128 165 181 63 0 86 236 84 6 0 216 73 120 9 0 95 177 172 61 0 221 112 199 121 0 2 187 41 211 0 127 167 164 159 0 161 197 207 103 0 37 105 51 120 0 198 220 122 0 167 151 157 163 0 173 139 149 0 0 157 137 149 0 16 7 173 139 151 0 149 157 137 0 151 163 173 139 0 139 157 163 173 0 149 151 167 0]

In addition to the above example, other exponential matrices may be stored in the above sequence form.

In order to describe the method of transforming the parity check matrix proposed by the present invention, it is assumed that the structure of the exponential matrix to be applied to each block size of Equation 5 is the same as one of four of Equations 6 to 9 below.

[Equation 6]

[Equation 7]

[Equation 8]

[Equation 9]

All of the exponential matrices of Equations 6 to 9 have the structure of FIG. 3 or FIG. 4 . That is, the elements of the (k _b +1)-th column to the (k _b +4)-th column of the first row of Equations 6 to 9, and the (k _b +1)-th column of the second row (k _b +4) )th column elements, the (k _{b +1)th to (k b +4)th columns of the third row, and the (k b +1 )} th column to the (k _b +4)th column of the fourth row A 4 x 4 matrix composed of column elements corresponds to B' in FIGS. 3 and 4 .

In Equations 6 to 9, a is an integer satisfying 1 <= a <= (Z _max -1) (Z _max is the maximum block size). In this case, Z _max may mean the size of the largest block in the block size group defined to apply the exponential matrix V = (V _ij ).

At this time, as shown in Equations 6 and 7, the exponential matrices in which the first four elements of the (k _b +1)-th column block of the exponential matrix are composed of "one a, one -1, two zeros" are type A As shown in Equations 8 and 9, the exponential matrices in which the first four elements of the (k _b +1)-th column block of the exponential matrix are composed of "two a, one -1, one 0" are type B. can be classified.

In the case of the exponential matrix corresponding to FIG. 1 shown in FIG. 3, since the third element of the first column of the B' matrix is -1, it may correspond to the exponential matrix structure of Equation 6 or Equation 8, as shown in FIG. In the case of the exponential matrix corresponding to FIG. 2, since the second element of the B' matrix is -1, it may correspond to the exponential matrix structure of Equation 7 or 9. FIG.

As a result, exponential matrices having the structures shown in FIGS. 3 and 4 may be classified into either type A or type B.

According to an embodiment of the present invention, parity check matrices of LDPC codes having different formats (types) may be converted and integrated into one format parity check matrices. In this case, the format of the parity check matrix means the structure of a partial matrix corresponding to the parity of the parity check matrix. If the structures of the partial matrix corresponding to the parity are the same, the encoding/decoding process of the LDPC code can be equally applied. have.

According to an embodiment of the present invention, exponential matrices having the format (type B) of Equation 8 or 9 are converted into exponential matrices having the format (type A) of Equation 6 or 7 above. Hereinafter, for convenience of explanation, a process of converting an exponential matrix having the format of Equation 8 into an exponential matrix having the format of Equation 6 will be described in detail as an example.

Similarly, according to the present invention, it is also possible to convert an exponential matrix having the format of Equation 6 into an exponential matrix having the format of Equation 8.

In addition, by applying a similar process, Equation 9 and Equation 7 can be mutually converted.

Since column permutation in the parity check matrix refers to the effect of rearranging only the order of codeword bits, there is no change in code performance even if this is applied. Therefore, the logarithmic characteristic of the parity check matrix does not change even if any column permutation is applied. In the present invention, since the encoding and decoding method and apparatus based on the quasi-cyclic LDPC code are considered, column permutation can also be applied using the characteristics of the quasi-cyclic LDPC code.

If -a is applied to all exponents of the (k _b +1)-th column block in Equation 8 and modulo operation is performed on Z _max , circular column permutation in the parity check matrix permutation), which can be expressed as in Equation 10 below.

[Equation 10]

In this case, V' _ij is an element of the column permuted exponential matrix, V _ij is an element of the first exponential matrix, mod is a modulation operator, Z _max is the maximum block size, and a is a natural number greater than 0.

Equation 10 is applied only to the (k _b +1)-th column block.

At this time, since V _ij =-1 means a zero matrix, the result is always a zero matrix no matter what column permutation is applied to the corresponding matrix. In other words, V _ij =-1 is always the same no matter what exponent value is added or subtracted to V _ij =-1. As a result, after applying -a to the exponent values other than -1 among the exponent values for the (k _b +1)-th column block in Equation 8, the result of applying the modulo operation to Z _max is obtained by the following equation It can be expressed as Equation 11.

[Equation 11]

In the present invention, Equation 5 and LDPC encoding and decoding for a predetermined block size group are considered. Even if the modulo operation for Z _max is applied as in Equation 10 above, the algebraic characteristic is not changed.

Thereafter, Vw = (W _ij ) is generated by applying Equation 12 below to the exponential matrix V' = (V' _ij ) transformed as in Equation 11.

[Equation 12]

In this case, W _ij is an element of the second exponential matrix, V' _ij is an element of the column permutated exponential matrix, and Z _max is the maximum block size.

Also in Equation 12, Z _max may represent the largest block size within a block size group defined to apply the exponential matrix.

The finally generated Vw = (W _ij ) may be expressed as in Equation 13 below.

[Equation 13]

Looking at the structure of Equation 13, the first four elements of the (k _b +1)-th column block of Vw = (W _ij ) are 0, a, -1, 0, and (k _b of the exponential matrix of Equation 6) +1) Same as the first 4 elements of the first column block. That is, it can be seen that the type B exponent matrix of Equation 8 is transformed into the type A exponent matrix of Equation 6 .

When one embodiment of the present invention described above is applied, the exponential matrix (type A) of Equation 6 is inter-transformed with the exponential matrix (type B) of Equation 8, and the exponential matrix (type A) of Equation 7 is It can be seen that it is inter-transformed with the exponential matrix (type B) of Equation 9.

As described above, on the assumption that the basic graph is known, the exponential matrix of Equation 13 may be stored in such a way that only exponential values other than -1 are stored in order to reduce required storage memory or increase storage efficiency. At this time, you can read and store an exponent value other than -1 in the column-by-column direction, or read an exponent value other than -1 in the row-by-row direction. You can also save it.

For example, the exponential matrix stored in row-by-row corresponding to BG#1 of Table 1 and FIGS. 1 and 3 is transformed using Equations 10 and 12 above. If the exponential matrix is stored as a column-by-column, it can be expressed in the form below.

[BG#1 - Efficient storage format of the conversion result of Set 1 (column-by-column)]

Value of V _W = [6 254 150 135 99 51 73 36 144 153 179 96 79 50 216 249 196 105 192 144 61 128 40 35 129 219 89 99 107 117 187 145 167 154 20 212 252 74 158 215 214 160 192 214 183 7 100 233 231 170 161 254 95 58 83 89 105 107 30 17 71 107 109 13 69 97 139 172 62 249 8 207 70 170 117 83 132 193 236 97 89 20 41 91 99 156 185 139 135 246 163 106 234 120 152 59 105 34 27 125 225 96 105 184 140 79 89 107 99 152 79 13 89 207 129 62 119 197 83 161 39 105 117 93 27 217 120 228 147 235 191 32 86 183 99 89 146 36 170 189 235 224 207 209 140 215 65 154 10 25 45 173 201 23 114 144 49 93 247 114 37 12 114 22 193 248 68 136 36 147 31 45 152 198 92 74 20 57 151 61 124 31 50 195 92 205 233 114 16 228 154 74 129 197 147 93 101 11 180 245 242 240 255 98 97 107 66 51 12 99 195 249 181 101 104 172 136 105 83 221 1 5 92 109 75 0 17 139 112 45 40 71 205 125 225 228 244 133 147 178 27 112 85 193 45 0 1 0 142 16 5 103 97 35 85 154 84 0 0 234 194 134 0 0 166 247 135 119 0 0 77 250 195 117 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]

Alternatively, the exponent matrix stored in row-by-row corresponding to BG#1 of Table 1 and FIGS. 1 and 3 is an exponent converted using Equations 10 and 12 above. When a matrix is stored as row-by-row, it can be expressed in the form below.

[BG#1 - Efficient storage format of the conversion result of Set 1 (row-by-row)]

Value of V _W = [6 187 30 97 156 246 197 27 146 65 247 61 233 66 221 17 225 0 0 254 17 139 132 185 34 152 83 36 154 147 124 114 101 1 228 1 0 0 150 145 71 193 139 163 27 79 161 217 114 31 31 11 51 5 139 0 0 135 167 172 236 106 125 13 120 170 10 37 45 16 180 12 112 244 0 0 99 154 0 51 20 62 25 228 133 142 0 73 234 228 189 12 245 99 45 0 36 212 97 225 89 152 0 144 252 249 45 154 92 147 16 166 0 153 74 147 235 114 242 195 40 0 158 107 89 96 207 198 0 179 215 173 74 178 5 234 0 96 214 235 224 22 249 0 79 8 105 71 194 0 50 201 50 129 240 27 0 216 160 191 193 181 77 0 192 207 207 205 103 0 249 92 197 255 112 0 214 23 248 101 109 0 196 183 184 129 32 0 105 70 39 209 97 0 7 135 147 125 85 0 192 114 68 98 0 100 109 86 104 0 144 170 20 140 35 0 233 120 140 74 0 61 13 41 195 0 231 152 62 0 128 91 75 193 0 170 20 172 250 0 40 183 136 247 0 161 79 85 195 0 35 144 57 135 0 254 69 215 45 0 129 89 92 97 0 95 59 49 154 0 219 151 205 136 0 58 36 134 0 89 105 99 93 0 83 117 107 0 0 99 119 107 0 89 83 117 105 0 107 99 119 0 105 93 83 117 0 117 99 93 84 0 107 105 89 0]

When a lifting technique according to the block size (Z) is applied to the exponential matrix of Equation 13, an appropriate parity check matrix for various block sizes can be generated and applied to LDPC encoding and decoding.

[Equation 14]

In this case, Z represents the block size.

Finally, the parity check matrix may be expressed as Equation 15 below.

[Equation 15]

In this case, P may represent a cyclic permutation matrix, I may represent an identity matrix, and O may represent a zero matrix.

5 is an operation flowchart illustrating a channel coding/decoding method according to an embodiment of the present invention.

Referring to FIG. 5 , in the channel coding/decoding method according to an embodiment of the present invention, a first exponential matrix is loaded ( S510 ).

In addition, the channel coding/decoding method according to an embodiment of the present invention converts the first exponential matrix into a second exponential matrix ( S520 ).

In this case, step S520 may include generating a column permutated exponential matrix by performing circular column permutation on one column of the first exponential matrix (Equation 10); and generating a transform value for an element greater than 0 of the column permutated exponent matrix, and generating the second exponential matrix by using the transform value (Equation 12).

In this case, one column may be a (k _b +1)-th column of the first exponential matrix (k _b is a natural number obtained by subtracting the number of rows from the number of columns of the first exponential matrix).

In this case, the first exponential matrix ( V = (V _ij )) and the second exponential matrix ( V' = (V' _ij )) are the first four elements of the (k _b +1)-th column of the first exponential matrix According to the elements (elements), it may be divided into two types: a first type (type A) and a second type (type B).

In this case, the first type includes only one natural number (a) in which the first four elements are greater than zero, and the second type includes two natural numbers (a) in which the first four elements are greater than zero. can

In this case, when the first exponential matrix is the first type, the second exponential matrix is the second type, and when the first exponential matrix is the second type, the second exponential matrix is the first type can

In this case, the recursive column permutation may be performed using the natural number (a) greater than 0.

In this case, the cyclic column permutation may be performed using Equation (10).

In this case, the transform value may be generated by subtracting an element greater than 0 of the column permutated exponential matrix from the maximum block size Z _max .

In this case, the second exponential matrix may be generated using Equation (12).

Also, in the channel coding/decoding method according to an embodiment of the present invention, a parity check matrix corresponding to a required block size is generated using the second exponential matrix ( S530 ).

In this case, in step S530, the parity check matrix may be generated using Equation 14, and the resultant parity check matrix may be the same as Equation 15 above.

Also, in the channel coding/decoding method according to an embodiment of the present invention, LDPC encoding/decoding is performed using the parity check matrix ( S540 ).

6 is a block diagram illustrating a communication system according to an embodiment of the present invention.

Referring to FIG. 6 , it can be seen that in the communication system according to an embodiment of the present invention, the transmitter 10 and the receiver 30 communicate via the physical channel 20 .

The transmitter 10 encodes k-bit information bits 11 in the channel encoder 13 to generate an n-bit codeword. The codeword is modulated by a modulator (15) and transmitted via an antenna (17). A signal transmitted through the physical channel 20 is received through the antenna 31 of the receiver 30 , and the receiver 30 undergoes a reverse process of the process that occurred in the transmitter 10 . That is, the received data may be demodulated by the demodulator 33 and decoded by the channel decoder 35 to finally recover information bits.

It is apparent to those skilled in the art that, in addition to the above-described transmission/reception process being described within the minimum range necessary to describe the characteristics of the present invention, many processes necessary for data transmission may be added.

In particular, the channel encoder and the channel decoder shown in FIG. 6 can transform the parity check matrix of a given LDPC code to generate a new parity check matrix having similar algebraic characteristics, and use such a transform to efficiently encode/decode the LDPC. can be performed.

7 is a block diagram illustrating an example of the channel encoder (or channel decoder) shown in FIG. 6 .

Referring to FIG. 7 , an example of a channel encoder (or channel decoder) may be implemented in a computer system 700 . As shown in FIG. 7 , computer system 700 includes one or more processors 710 , memory 730 , user interface input device 740 , and user interface output device 750 that communicate with each other via bus 720 . ) and storage 760 . Computer system 700 may further include a network interface 770 coupled to network 780 . Each processor 710 may be a central processing unit (CPU) or a semiconductor device for processing execution instructions stored in the memory 730 or storage 760 . Each memory 730 and storage 760 may be various types of volatile or non-volatile storage media. For example, memory 730 may include read-only memory (ROM) 731 or random access memory (RAM) 732 .

In this case, the memory 730 may store data regarding the first exponential matrix corresponding to the existing parity check matrix.

In this case, the processor 710 generates a parity check matrix corresponding to a second exponential matrix generated by transforming the first exponential matrix, and performs LDPC encoding (or LDPC decoding) using the generated parity check matrix. can do.

In this case, the second exponent matrix is generated by using a transform value for an element greater than 0 of the column permutated exponent matrix, and the column permuted exponent matrix is generated for one column of the first exponent matrix. It may be generated by performing circular column permutation.

In this case, one column may be a (k _b +1)-th column of the first exponential matrix (k _b is a natural number obtained by subtracting the number of rows from the number of columns of the first exponential matrix).

In this case, the first exponential matrix and the second exponential matrix are divided into two types, a first type and a second type, according to the first four elements of the (k _b +1)-th column of the first exponential matrix. can be

In this case, the first type includes only one natural number (a) in which the first four elements are greater than zero, and the second type includes two natural numbers (a) in which the first four elements are greater than zero. can

In this case, when the first exponential matrix is the first type, the second exponential matrix is the second type, and when the first exponential matrix is the second type, the second exponential matrix is the first may be of any type.

In this case, the recursive column permutation may be performed using the natural number (a) greater than 0.

In this case, the cyclic column permutation may be performed using Equation (10).

In this case, the second exponential matrix may be generated using Equation 12 above.

Accordingly, the embodiment of the present invention may be implemented as a non-transitory computer-readable recording medium in which a computer-implemented method is recorded or computer-executable instructions are recorded. When the computer-executable instructions are executed by a processor, the instructions may perform a method according to at least one aspect of the present invention.

Table 2 shows an example of the matrices A, B, and C shown in FIG. 1 , and Table 3 shows an example of the matrices A, B, and C shown in FIG. 2 .

That is, the matrices Z and D shown in FIG. 1 are added to the right of the matrix shown in Table 2 to become a basic graph, and the matrices Z and D shown in FIG. 2 are added to the right of the matrix shown in Table 3 to become a basic graph. have.

Tables 4 to 11 show examples of matrices A', B', and C' shown in FIG. 3 .

That is, the matrices Z' and D' shown in FIG. 3 may be added to the right side of the matrix shown in any one of Tables 4 to 11 to form an exponential matrix.

Referring to Tables 4 to 11, it can be seen that natural numbers greater than or equal to 0 are located at positions of 1 in FIG. 1 .

Table 4 corresponds to Set 1 of Equation 5, Table 5 corresponds to Set 2 of Equation 5, Table 6 corresponds to Set 3 of Equation 5, and Table 7 corresponds to Equation 5 Corresponds to Set 4, Table 8 corresponds to Set 5 of Equation 5, Table 9 corresponds to Set 6 of Equation 5, Table 10 corresponds to Set 7 of Equation 5, Table 11 may correspond to Set 8 of Equation 5 above.

Referring to the number of natural numbers (a) greater than 0 in the leftmost column of the 4 x 4 matrix at the top right of Tables 4 to 11, Table 4 is type B, Table 5 is type B, and Table 6 is type B, Table 7 is Type B, Table 8 is Type B, Table 9 is Type B, Table 10 is Type A, and Table 11 is Type B.

Tables 12 to 19 show examples of matrices A', B', and C' shown in FIG. 4 .

That is, the matrices Z' and D' shown in FIG. 4 may be added to the right side of the matrix shown in any one of Tables 12 to 19 to form an exponential matrix.

Referring to Tables 12 to 19, it can be seen that natural numbers greater than or equal to 0 are located at positions of 1 in FIG. 2 .

Table 12 corresponds to Set 1 of Equation 5, Table 13 corresponds to Set 2 of Equation 5, Table 14 corresponds to Set 3 of Equation 5, and Table 15 corresponds to Equation 5 Corresponds to Set 4, Table 16 corresponds to Set 5 of Equation 5, Table 17 corresponds to Set 6 of Equation 5, Table 18 corresponds to Set 7 of Equation 5, Table 19 may correspond to Set 8 of Equation 5 above.

Referring to the number of natural numbers (a) greater than 0 in the leftmost column of the 4 x 4 matrix at the top right of Tables 12 to 19, Table 12 is type A, Table 13 is type A, and Table 14 is type It can be seen that A, Table 15 is Type B, Table 16 is Type A, Table 17 is Type A, Table 18 is Type A, and Table 19 is Type B.

Tables 20 to 27 show matrices A', B', and C' corresponding to exponential matrices (second exponential matrices) in which the exponential matrices (first exponential matrices) corresponding to Tables 4 to 11 are transformed, respectively.

That is, the matrix Z' and D' shown in FIG. 3 may be added to the right side of the matrix shown in any one of Tables 20 to 27 to become a transformed exponential matrix (Z' and D' are maintained even after transformation).

Tables 28 to 35 show matrices A', B', and C' corresponding to exponential matrices (second exponential matrices) in which the exponential matrices (first exponential matrices) corresponding to Tables 12 to 19 are transformed, respectively.

That is, the matrix Z' and D' shown in FIG. 4 may be added to the right side of the matrix shown in any one of Tables 28 to 35 to become a transformed exponential matrix (Z' and D' are maintained even after transformation).

As described above, in the channel coding/decoding method and apparatus according to the present invention, the configuration and method of the embodiments described above are not limitedly applicable, but the embodiments are each embodiment so that various modifications can be made. All or part of them may be selectively combined and configured.

10: transmitter
20: physical channel
30: receiver

Claims (20)

delete delete loading a first exponential matrix;
transforming the first exponential matrix into a second exponential matrix;
generating a parity check matrix corresponding to a required block size using the second exponential matrix; and
performing LDPC encoding using the parity check matrix;
Transforming the first exponential matrix into the second exponential matrix includes:
generating a column permutated exponential matrix by performing circular column permutation on one column of the first exponential matrix; and
generating a transform value for an element greater than 0 of the column permutated exponent matrix, and generating the second exponent matrix by using the transform value,
The one column is
The channel coding method, characterized in that the (k _b +1)-th column of the first exponential matrix (k _b is a natural number obtained by subtracting the number of rows from the number of columns of the first exponential matrix). 4. The method of claim 3,
The first exponential matrix and the second exponential matrix are
The channel coding method, characterized in that the first type and the second type are divided into two types according to the first four elements of the (k _b +1)-th column of the first exponential matrix. 5. The method according to claim 4,
The first type includes only one natural number in which the first four elements are greater than zero, and the second type includes two natural numbers in which the first four elements are greater than zero. 6. The method of claim 5,
When the first exponential matrix is of the first type, the second exponential matrix is the second type, and when the first exponential matrix is the second type, the second exponential matrix is the first type Channel coding method characterized in that. 7. The method of claim 6,
The cyclic column permutation is
A channel coding method, characterized in that it is performed using the natural number greater than 0. 8. The method of claim 7,
The cyclic column permutation is
A channel coding method, characterized in that it is performed using the following equation.
[Equation]

(V' _ij is an element of the column permuted exponential matrix, V _ij is an element of the first exponential matrix, mod is a modulation operator, Z _max is the maximum block size, a is a natural number greater than 0) 9. The method of claim 8,
The conversion value is
and generated by subtracting an element greater than zero of the column permutated exponential matrix from the maximum block size. 10. The method of claim 9,
The second exponential matrix is
A channel coding method, characterized in that it is generated using the following equation.
[Equation]

(W _ij is an element of the second exponential matrix, V' _ij is an element of the column permuted exponential matrix, and Z _max is the maximum block size) delete delete a memory for storing data on a first exponential matrix corresponding to an existing parity check matrix; and
a processor that generates a parity check matrix corresponding to a second exponential matrix generated by transforming the first exponential matrix, and performs LDPC encoding using the generated parity check matrix,
The second exponential matrix is
It is generated using a transform value for an element greater than zero of the column permutated exponential matrix,
The column permutated exponential matrix is generated by performing circular column permutation on one column of the first exponential matrix,
The one column is
The channel encoder, characterized in that the (k _b +1)-th column of the first exponential matrix (k _b is a natural number obtained by subtracting the number of rows from the number of columns of the first exponential matrix). 14. The method of claim 13,
The first exponential matrix and the second exponential matrix are
The channel encoder according to claim 1, wherein the first type and the second type are classified according to the first four elements of the (k _b +1)-th column of the first exponential matrix. 15. The method of claim 14,
The first type includes only one natural number in which the first four elements are greater than zero, and the second type includes two natural numbers in which the first four elements are greater than zero. 16. The method of claim 15,
When the first exponential matrix is of the first type, the second exponential matrix is the second type, and when the first exponential matrix is the second type, the second exponential matrix is the first type Characterized by a channel encoder. 17. The method of claim 16,
The cyclic column permutation is
A channel encoder, characterized in that it is performed using the natural number greater than 0. 18. The method of claim 17,
The cyclic column permutation is
A channel encoder, characterized in that it is performed using the following equation.
[Equation]

(V' _ij is an element of the column permuted exponential matrix, V _ij is an element of the first exponential matrix, mod is a modulation operator, Z _max is the maximum block size, a is a natural number greater than 0) 19. The method of claim 18,
The second exponential matrix is
A channel encoder, characterized in that it is generated using the following equation.
[Equation]

(W _ij is an element of the second exponential matrix, V' _ij is an element of the column permuted exponential matrix, and Z _max is the maximum block size) a memory for storing data on a first exponential matrix corresponding to an existing parity check matrix; and
A processor that generates a parity check matrix corresponding to a second exponential matrix generated by transforming the first exponential matrix, and performs LDPC decoding using the generated parity check matrix
including,
The second exponential matrix is
It is generated using a transform value for an element greater than zero of the column permutated exponential matrix,
The column permutated exponential matrix is generated by performing circular column permutation on one column of the first exponential matrix,
The one column is
The channel decoder, characterized in that the (k _b +1)-th column of the first exponential matrix (k _b is a natural number obtained by subtracting the number of rows from the number of columns of the first exponential matrix).

Images