KR101187070B1 - Method for encoding using parity check matrix - Google Patents

Abstract

The present invention relates to LDPC (Low Density Parity Check) encoding and decoding, and more particularly, an apparatus for transmitting / receiving data using a parity check matrix for converting an information word into a code word through a simple process and encoding / decoding using the same. It is about a method.

The encoding method according to the present invention includes encoding information bits to be transmitted to a receiver using a parity check matrix including an information word portion and a parity portion; And transmitting the encoded signal to a receiving side, wherein the parity portion is designed according to a lower triangle type.

LDPC, parity check matrix, model matrix, parity part, coding

Description

Method for encoding using parity check matrix

1 is a view showing the structure of a mobile communication channel to which the present invention and the prior art are applied.

2 is a diagram for explaining structured LDPC.

3 is a view showing a model matrix according to the prior art.

4 is a diagram illustrating a method of expressing a matrix according to a shift number.

5 is a diagram illustrating an LDPC decoding method.

6 shows the structure of a general model matrix according to the present embodiment.

7A to 7J show the structure of the model matrix according to the present embodiment.

8 shows an example in which encoding is performed by a parity check matrix of a lower triangle type according to the present embodiment.

9A and 9B are diagrams illustrating the encoding method according to the present embodiment.

FIG. 10 is a diagram illustrating an example of a model matrix composed of various subblocks _{Pi and j} according to the present embodiment.

The present invention relates to LDPC (Low Density Parity Check) encoding and decoding, and more particularly, an apparatus for transmitting / receiving data using a parity check matrix for converting an information word into a code word through a simple process and encoding / decoding using the same. It is about a method.

1 is a view showing the structure of a mobile communication channel to which the present invention and the prior art are applied. Hereinafter, the structure of a mobile communication channel will be described with reference to FIG. 1. In order to transmit the data to be transmitted from the transmitter without loss or distortion in the radio channel, a channel coding procedure is performed. As the channel coding technique, there are various techniques such as convolutional coding, turbo coding, and LDPC coding. Data that has undergone the channel coding procedure may be transmitted as a single symbol by collecting a plurality of bits when transmitted through a wireless channel. In this case, a procedure in which several bits are mapped to one symbol is called modulation.

The modulated data is converted into a signal for multiplex transmission through a multiplexing process or a multiple access method. As the multiplexing method, various methods such as CDM, TDM, and FDM exist. In FIG. 1, an example of orthogonal frequency division multiplexing (OFDM) is illustrated. The signal that has passed through the multiplexing block is changed into a structure suitable for transmission to one or more multiple antennas and transmitted to a receiver through a radio channel. Data transmitted in the course of passing through the wireless channel may experience fading and thermal noise, which may cause distortion of the data.

The modulated data is transmitted to a receiver through a wireless channel. In this process, the transmitted data may experience fading and thermal noise, which may cause distortion of the data. After receiving the distorted data, the receiving end performs a series of procedures in the reverse order. A demodulation operation of converting the data mapped to the symbol into a bit string is performed, and the distorted data is restored to the original data through a channel decoding process.

The apparatus for performing channel coding generates a parity check derived from an H matrix or an H matrix, which is a parity check matrix used to generate parity bits to be added to input data (Systematic Bits). It stores G matrix, which is a parity check generate matrix. That is, the transmitting end includes an encoder for generating parity bits through the H or G matrix and the input data. The apparatus for performing channel decoding checks whether the inputted data (Systematic Bits) are properly recovered through the H matrix and the operation of the received data (distorted Systematic Bits + Parity Bits). Rerun

The modulation includes Binary Phase Shift Keying (BPSK), Quadrature Phase Shift Keying (QPSK), Quadrature Amplitude Modulation (16-QAM), 64-QAM, 256-QAM, and the like. For example, 16-QAM maps a sequence of data that has undergone a channel encoding procedure to one symbol in units of 4 bits during modulation. In demodulation, 16-QAM demaps one symbol of data received through a wireless channel into four bits.

The LDPC code will be described below. The concept of the LDPC code is as follows.

을 만족하도록 부호가 구성된다는 점이다. 이 선형 부호의 일종으로서, 최근에 주목받는 LDPC 부호는 1962년 Gallager에 의하여 처음 제안되었다. 이 부호의 특징으로는 패리티 체크 행렬의 성분이 대부분 0으로 이루어지고, 0이 아닌 성분의 개수는 부호 길이에 비하여 적은 수를 가지도록 하여 확률을 기반으로 한 반복적 복호가 가능한 점이다. 처음 제안된 LDPC 부호는 패리티 체크 행렬을 비체계적인(non-systematic) 형태로 정의하였고, 그것의 행과 열에 균일하게 적은 무게(weight)를 갖도록 설계되었다. The linear code can be described by the generation matrix G or parity check matrix H. The characteristic of linear code is that for all codewords c,

The sign is constructed to satisfy. As a form of this linear code, a recent notable LDPC code was first proposed by Gallager in 1962. The characteristic of this code is that the components of the parity check matrix are mostly 0, and the number of non-zero components has a smaller number than the code length so that iterative decoding based on probability is possible. The first proposed LDPC code defines the parity check matrix in a non-systematic form and is designed to have a uniformly low weight in its rows and columns.

Here, the weight means the number of 1s included in a column or a row in the matrix.

Since the density of nonzero components on the parity check matrix H of the LDPC code is small, the decoding complexity is low. In addition, the decoding performance is also better than the existing codes, showing a good performance close to Shannon's theoretical limit. The LDPC code, however, was a hardware technology that was difficult to implement at the time and has not attracted much attention for more than 30 years. In the early 1980s, a method of iterative decoding using a graph was developed, and various algorithms were developed to actually decode the LDPC code using the graph. The sum-product algorithm can be extracted as the representative algorithm.

Hereinafter, the features of the LDPC code will be described. LDPC codes have high error correction performance, which allows for improvements in communication speed and capacity. The LDPC code may be applied to a high speed wireless LAN capable of transmitting hundreds of Mbit / s in combination with a multiple input multiple output (MIMO) system, and may be applied to high speed mobile communication having a transmission speed of 1 Mbit / s or more at 250 km / h. It can also be applied to optical communication of 40Gbits / s or more. In addition, the high error correction performance of the LDPC code may improve the transmission quality, thereby enabling quantum encrypted communication that reduces the number of retransmissions in a low quality communication path. In addition, due to the low complexity and excellent loss compensation of the LDPC code, lost packets can be easily recovered, which makes it possible to transmit content of the same quality as TV quality through the Internet and mobile communication. Due to the wide coverage and large capacity of LDPC, 10GBASE-T transmissions up to the 100m range, previously considered impossible, are possible with LDPC codes. At the same time, the transmission capacity of a single satellite transmitter in the 36MHz band can be increased by 1.3 times to 80Mbit / s. These advantages are being adopted as the next generation channel coding method in IEEE802.16 system and IEEE802.11 system for high frequency efficiency.

The structured LDPC is described below.

In order to use the LDPC code includes a matrix H to use, uses a parity check matrix H is most 0 and part of one of the components (elemnet), the H matrix, since the size of the H matrix size by more than 10 ⁵ bits It requires a large amount of memory to represent. The structured LDPC technique is a method of expressing components of the H matrix used for LDPC encoding and decoding into sub-blocks having a constant size as shown in FIG. 2. In IEEE802.16e, the subblock is represented by one integer index to reduce the size of memory required to store the H matrix. The subblock may be various matrices, for example, a permutation matrix of a constant size.

In the structured LDPC technique, instead of storing a matrix of 1 or 0 in a specific memory, only one integer (that is, an index) needs to be stored. Can be reduced.

For example, when the size of the codeword reflected in the IEEE802.16e standard is 2304 and the code rate is 2/3, the model matrix used for LDPC encoding / decoding is shown in FIG. Same as 3.

As shown in Fig. 3, the structured LDPC matrix of IEEE802.16e consists of -1, 0 and positive integer components. -1 is a zero matrix of all elements 0 and 0 represents an identity matrix. Positive integer components other than -1 and 0 are permutation matrices in which the identity matrix is shifted to the right by a positive integer. That is, if the component of the matrix is 3, the permutation matrix is expressed by shifting the unit matrix three times to the right.

4 is a diagram illustrating a method of expressing a matrix according to the aforementioned positive integer, that is, a shift number. When a specific H matrix is structured and expressed as a matrix having a size of 4 * 4 (that is, a sub block), if the specific sub block is denoted as 3, the sub block becomes the matrix of FIG.

Hereinafter, the LDPC encoding method will be described.

In the general LDPC encoding method, a generation matrix G is derived from an LDPC parity check matrix H to encode an information bit. In order to derive the generation matrix G, the inspection matrix H is configured in the form of [P ^T : I] through a Gaussian Reduction method. When the number of information bits is k and the size of an encoded codeword is n, the P matrix is a matrix in which the number of rows is k and the number of columns is nk, and I is K is the identity matrix whose k column size is k.

The generation matrix G becomes a [I: P] matrix when the check matrix H is expressed as [P ^T : I]. If the encoded information bits of k-bit size are represented in a matrix, the number of rows is 1 and the number of columns is k. In this case, the code word c is described as follows.

In the above equation, x denotes a systematic part and xP denotes a parity part.

)을 이용하여, 상기 수학식 1에서 H^T을 곱하면, 하기 수학식 2 같은 수학식을 얻을 수 있다. 하기 수학식 2에 부합하는 패리티 비트를 정보 비트(x) 뒤에 추가하여 코드워드 c를 얻을 수 있다. On the other hand, in the case of encoding by the Gaussian Reduction method as described above, a large amount of calculation is performed, and a method of directly encoding the H matrix without inducing the G matrix by designing the shape of the H matrix into a special structure. Use That is, H ^{T in the} form of a transpose of the G matrix and the H matrix. The product of 0 (that is,

By multiplying H ^T by Equation 1, Equation 2 can be obtained. A codeword c may be obtained by adding a parity bit corresponding to Equation 2 after the information bit x.

Hereinafter, the LDPC decoding method will be described.

The coded data in the communication system includes noise in the process of passing through the wireless channel of FIG. 1, and the receiving end performs decoding of the data through the procedure of FIG. 5. The decoded block of the receiving end to obtain the information bits from the noise to the encoded code word (c) adding the received signal (c ') (x), find using the cH ^T = 0 in nature. That is, when the received codeword is c ', the value of c'H ^T is calculated, and if the result is 0, the first k bits in c' are determined as the information bits x. If the value of c'H ^T is not 0, a decoding technique such as a sum-product algorithm through a graph is used to find c 'whose value of c'H ^T satisfies 0. recover (x)

Hereinafter, the code rate of the LDPC code will be described.

In general, a code rate (R) is as follows when the size of the information bit is k and the size of the codeword actually transmitted is n.

R = k / n

The code rate is as follows when the row size of the H matrix required for LDPC encoding and decoding is m and the size of the column is n.

R = 1-m / n

As described above, the conventional LDPC code is encoded and decoded by the H matrix, and thus the structure of the H matrix is very important. That is, the design of the H matrix is more important than anything, since the performance of encoding and decoding is greatly affected by the structure of the H matrix.

It is proposed to improve the above-mentioned prior art of the present invention, and an object of the present invention is to propose a parity check matrix of improved performance compared to the prior art.

Another object of the present invention is to propose a parity check matrix with improved complexity due to coding.

The present invention is characterized by modifying the structure of the parity part of the parity check matrix in order to improve performance compared to the prior art. More specifically, the parity check matrix H according to the present invention is characterized in that the parity portion has a dual diagonal component and a parity portion of a lower triangle type. The parity check matrix according to the present invention has an advantageous effect of reducing the complexity due to coding compared to the prior art.

The encoding method according to the present invention includes encoding information bits to be transmitted to a receiver using a parity check matrix including an information word portion and a parity portion; And transmitting the encoded signal to a receiving side, wherein the parity portion is designed according to a lower triangle type.

The decoding method according to the present invention comprises the steps of: receiving a signal transmitted from a transmitting side; And decoding the received signal using a parity check matrix composed of an information word part and a parity part, wherein the parity part is designed according to a lower triangle type.

The construction, operation and effects of the present invention will be embodied by one embodiment of the present invention described below. Hereinafter, an embodiment of the present invention will be described with reference to the accompanying drawings.

Hereinafter, a matrix representing a parity check matrix in a subblock of a specific z * z size according to the structured LDPC technique described above is referred to as a model matrix. Each subblock of the model matrix can be extended to various kinds of matrices by a specific index, and the model matrix makes the index an element of the model matrix. Each sub block of the model matrix may be determined in various ways according to the index. Hereinafter, it is assumed that the index is a shift number for a unit matrix of a specific size z * z. In addition, when the index is -1, the sub block having the index of -1 is a zero matrix of a specific size z * z.

The model matrix is extended to a specific parity check matrix according to the index, so that encoding and decoding are performed by the model matrix, and that encoding and decoding is performed by a specific parity check matrix generated by the model matrix. it means.

6 illustrates a structure of a model matrix according to an embodiment of the present invention. Each integer indicated in FIG. 6 represents an index, and an unmarked portion has an index of -1. The model matrix of FIG. 6 is largely comprised of an information part and a parity part. That is, the model matrix of FIG. 6 has a structure of [H _d : H _p ], where H _d is an information word portion corresponding to an information bit encoded by the model matrix in a 1: 1 ratio. H _p (p1, p2, p3, p4) is a parity portion that generates a parity bit included in an encoded codeword.

As shown, the model matrix of FIG. 6 has a dual diagonal component in the parity portion. However, the double diagonal component of the model matrix of FIG. 6 includes one diagonal component and a component adjacent to the diagonal component. The adjacent component is also located at the upper of the diagonal component. In other words, the adjacent component is located to the right of the diagonal component. The up, down, left, and right sides of the components of the matrix are variable according to the direction of viewing the matrix. The matrix of FIG.

The model matrix is called [H _d : H _p ], the row of sub blocks in the parity portion of FIG. 6 is r, the column is indexed by c, and the shift number for a particular sub block is A _{r , c} . In this case, the indexes A _{r and c} have 0 when r = c and when c = r + 1. In other cases, the indexes A _{r and c} have −1. For example, when the parity portion of the model matrix of FIG. 6 has 16 subblocks, the parity portion is determined as shown in Equation 5 below.

The parity portion of the model matrix or parity check matrix can be divided into various types according to the design method of the double diagonal component. The parity portion designed in the same manner as the model matrix of FIG. 6 is an 'upper triangle type'. Expressed as designed according to

When encoding is performed by a model matrix designed according to the upper triangle type, the parity bits included in the codeword are determined by the following method.

When the model matrix is referred to as H _b , the model matrix may be summarized by the following equation.

K _b represents the number of sub-blocks located in the row direction in the information word portion of the specific model matrix. In addition, m _b represents the number of sub-blocks located in the column direction in the model matrix. That is, the information word portion of the model matrix has a size of m _b * k _b when expressed in units of sub-blocks. In addition, the parity portion of the model matrix has a size of m _b * m _b when expressed in units of sub-blocks.

The codeword x generated by H _b includes an information bit s and a parity bit p, and is represented by the following formula.

As described above, the model matrix is composed of subblocks of size z * z. For encoding, the model matrix may be divided into k _b groups by z-bit information bits. Although the information bits are conventionally processed in units of 1 bit, for convenience of description, it is assumed that the information bits s are grouped by z bits and divided into k _b groups. Information bits s grouped into k _b groups may be represented as vectors, as shown in Equation 8.

In Equation 8, u (i) is a column vector of size z * 1.

The parity bits are expressed by the same grouping method as the method used in Equation 8 as follows.

In Equation 9, v (i) is a column vector of size z * 1.

A process of encoding the z * z unit using the upper triangle type model matrix may be represented by Equations 10 to 12 below.

As can be seen from Equation 10, in order to obtain the first z bits of all parity bits, the entire operation of the information word portion of the model matrix must be performed.

Equation 11 shows a process of obtaining a parity of a next z bit by using a first z bit value among all parity bits.

Equation 12 recursively expresses an encoding process using a model matrix based on the contents of Equations 10 and 11 below.

The characteristics of the encoding process according to the above-described general model matrix (matrix consisting of sub-blocks of a specific size) are summarized as follows.

First, when a parity bit is generated by the model matrix, an operation on the entire information word portion of the model matrix should be performed to calculate a parity bit of the first part of all parity bits.

In general, when a model matrix having a parity portion having a dual diagonal form is used, a parity bit can be easily calculated through an encoding device operating in an accumulator form. However, when the first bits of the parity bits have already been obtained, the parity bits can be simply obtained through the accumulator. However, when the parity portion is in the upper triangle form, in order to obtain the first bits of the parity portion, it is necessary to perform an operation on the entire information word portion. Since the amount of computation for the entire information word portion is about the same as the amount of computation for obtaining the parity bits except for the first bits, the model matrix of the upper triangular form increases the complexity of decoding.

Second, when the retransmission scheme such as H-ARQ is performed using the model matrix, complexity increases.

When data is retransmitted at different code rates according to a retransmission scheme such as H-ARQ, the code rate can be adjusted by controlling the length of the parity bits. When additional parity bits need to be generated using the model matrix, the entire calculation of the information word portion is performed again to calculate only the parity portion corresponding to the additionally generated parity bits. As a result, the complexity increases when the retransmission scheme is performed using the model matrix.

Hereinafter, a model matrix according to an embodiment of the present invention will be described.

7A shows the structure of the model matrix according to the present embodiment. The model matrix of FIG. 7A is largely comprised of a systematic part and a parity part. That is, the model matrix of FIG. 7A has a structure of [H _d : H _p ], where H _d is an information word portion corresponding to an information bit encoded by the model matrix in a 1: 1 ratio. , H _p is a parity portion for generating a parity bit included in the coded codeword.

As shown, the model matrix according to the present embodiment has a dual diagonal component in the parity portion. However, the double diagonal component according to the present exemplary embodiment includes one diagonal component and a component adjacent to the diagonal component as shown. The adjacent component is also located at the lower end of the diagonal component. That is, the adjacent component is located to the left of the diagonal component. The up, down, left, and right sides of the components of the matrix are variable depending on the direction of viewing the matrix. The model matrix according to the present embodiment is described in another method as follows.

The model matrix is called [H _d : H _p ], the row of sub blocks in the parity portion of FIG. 7A is r, the column is indexed by c, and the shift number for a particular sub block is A _{r , c} . In this case, the index A _{r , c} has any integer that is not -1 when r = c and r = c + 1. That is, when the parity portion of the model matrix of FIG. 7A has 16 subblocks, the parity portion is determined as shown in Equation 13 below.

In the above formula, x _i and y _i represent an arbitrary integer. The parity portion of the model matrix or parity check matrix can be divided into various types according to the design method of the double diagonal component. The parity portion designed by the method of the model matrix of FIG. 7A has a 'lower triangle type'. Expressed as designed accordingly.

7B to 7J illustrate various model matrices according to the present embodiment. In the model matrix of FIGS. 7B-7J, x_1 to x_21, y_1 to y45, and z_1 to z_55 represent arbitrary shift numbers. Since x_1 to x_21 are double diagonal components, they may have various shift numbers except '-1' which means a zero matrix.

In addition, since the information word portion Hd-part of the model matrices of FIGS. 7B to 7J may have various shift numbers, a description of the specific shift number is omitted.

As shown in FIG. 7B, the double diagonal component of the model matrix and the remaining components except for the double diagonal component may have the same or different various values.

In addition, as illustrated in FIG. 7C, the double diagonal component of the model matrix designed according to the lower triangle type may be a shift number of '0'.

As shown in FIGS. 7D and 7E, the components positioned on the double diagonal component of the model matrix designed according to the lower triangle type may be a shift number of '-1' corresponding to a zero matrix. . However, as shown in FIG. 7E, the model matrices designed according to the lower triangle type may include components z_1, z_2, and z_3 that are not a certain number of '-1'.

7F shows another example of a model matrix designed according to the lower triangle type. As shown, the components located below the model matrix may be shift numbers of '-1' corresponding to a zero matrix. Also, as shown in FIGS. 7G and 7H, some of the components located below the model matrix may be components y_1 and y_2 that are not '-1'.

7I and 7J show another example of a model matrix designed according to the lower triangle type. As shown, the x_1 component of the model matrix designed according to the lower triangle type may be any component other than '0' and '-1', and is located in the same column as the arbitrary component. The number of components can be any component other than '-1'. The position and number of non--1 components positioned in the same column as the double diagonal component other than '0' may be determined in various ways. That is, it may have various values depending on the encoding device for generating parity bits or the structure of the information word portion of the model matrix.

When encoding is performed by a model matrix designed according to the lower triangle type, the parity bits included in the codeword are determined by the following method.

8 shows an example in which encoding is performed by a parity check matrix of a lower triangle type according to the present embodiment. 8 illustrates an encoding step based on a parity check matrix operating in units of bits for convenience of description, but the encoding method according to the present invention can be applied to both a model matrix and a parity check matrix. It may also be performed in units of bits or sub-blocks. Hereinafter, the encoding method according to the present embodiment will be described with reference to FIG. 8.

) 만을 통해 계산될 수 있다. 또한, p₁은 도 8의 두 번째 행에 대한 연산(

) 만을 통해 계산될 수 있다. 상기 p₁을 구하는 도중에 p₀ 값이 필요하지만, 이미 p₀는 산출되어 있는바 새롭게 구할 필요가 없다. 동일한 방법으로, p₂, p₃를 구할 수 있는바, 본 실시예에 따라 하위 삼각형 구조의 패리티 검사 행렬을 사용하는 경우, 정보어 부분 중 일부에 대한 연산을 통하여 패리티 비트를 구할 수 있다. The information bits are a ₀ , a ₁ , a ₂ , a ₃ , and the parity bits p ₀ , p ₁ , p ₂ , p ₃ are added by the parity check matrix of FIG. 8, and the codeword c (a ₀ , a ₁ , a ₂ , a ₃ , p ₀ , p ₁ , p ₂ , p ₃ ) are generated. As shown, the first parity bit p ₀ of the parity bits is calculated through operations on some of the information word portions of FIG. 8. That is, p ₀ is an operation on the first row of FIG.

) Can be calculated only. In addition, p ₁ is the operation for the second row of FIG.

) Can be calculated only. While the value of p ₀ is required during the calculation of p ₁ , p ₀ has already been calculated and there is no need to obtain a new value. In the same manner, p ₂ and p ₃ can be obtained. In the case of using the parity check matrix having a lower triangular structure according to the present embodiment, the parity bit can be obtained by calculating a part of the information word part.

9A and 9B are diagrams illustrating the encoding method according to the present embodiment. Hereinafter, the features of the encoding method according to the present embodiment will be described with reference to FIGS. 8 and 9. In order to obtain p ₀ in FIG. 9A, operations on information bits should be performed according to the structure of the parity check matrix. That is, in order to obtain a parity value for the region 901, an operation for the region 902 must be performed. If encoding is performed using a general parity check matrix, the operation on the 903 region must be performed first to complete the operation on the 901 region. However, the present embodiment includes the parity portion of the lower triangle type, so that the parity value for the region 901 can be obtained only by calculating the region 902.

9B illustrates an operation for obtaining p ₁ . In order to obtain p ₁ in FIG. 9B, an operation on information bits should be performed according to the structure of the parity check matrix. That is, to obtain a parity value for the region 904, an operation for the region 905 must be performed. If encoding is performed using a general parity check matrix, the operation on the 903 region must be performed first to complete the operation on the 904 region.

In conclusion, in the case of using the parity check matrix of the lower triangular type according to the present embodiment, the information word part is used to obtain the first bit of the parity bit (if the bits correspond to the size of the sub-block when the sub-block is calculated). There is no need to perform the calculation on the whole, but only on the information word portion corresponding to the parity bit to be generated.

Hereinafter, a method of encoding is performed by a model matrix consisting of subblocks having a specific size.

When the model matrix is referred to as H _b , the H _b is composed of an information word, that is, an information word part H _b1 corresponding to an information bit one-to-one and a parity part H _b2 . The model matrix is summarized as follows.

FIG. 10 is a diagram illustrating an example of a model matrix composed of various subblocks _{Pi and j} according to the present embodiment. The double diagonal component of the parity portion of the model matrix according to the present invention may have various shift numbers. Hereinafter, the operation on the model matrix composed of the double diagonal component having the shift number '0' will be described.

The codeword x generated by H _b includes an information bit s and a parity bit p, and is represented by the following formula.

As described above, the model matrix is composed of subblocks of size z * z. For encoding, the model matrix may be divided into k _b groups by grouping the information bits s by z bits. Hereinafter, a method of processing the information bits s by z bits and separating them into k _b groups will be described. Information bits s grouped into k _b groups are represented by column vectors as shown in Equation 16 below.

In Equation 16, u (i) is a column vector of size z * 1.

The parity bits are expressed by the same grouping method as the method used in Equation 16 as follows.

In Equation 17, v (i) is a column vector of size z * 1.

A process of encoding the z * z unit according to the lower triangle type model matrix may be represented by Equations 18 to 20 below.

는 패리티 부분에 위치하는 서브 블록으로부터 확장되어 생성되는 행렬을 나타낸다. 예를 들어,

이라면, 특정한 모델 행렬의 첫 번째 행과 첫 번째 열에 위치하는 서브 블록을 나타내는 것이다. 상기 수학식 18a에서도 알 수 있듯이, 전체 패리티 비트 중 처음 z 비트는 처음 z비트에 상응하는 정보어 부분에 대한 연산 결과이다. 다음 z 비트는, 처음 z 비트에 대한 패리티 부분에 대한 연산과 다음 z비트에 상응하는 정보어 부분에 대한 연산 결과를 이용하여 계산되는바, 패리티 비트를 계산하는 과정은 상기 수학식 18b와 같은 재귀적 방법으로 표현될 수 있다. In the above equation,

Denotes a matrix generated by extending from a subblock located in the parity portion. E.g,

, The subblock at the first row and first column of a particular model matrix. As can be seen from Equation 18a, the first z bits of all the parity bits are the operation result of the information word portion corresponding to the first z bits. The next z bits are calculated using the operation on the parity portion for the first z bits and the operation result on the information word portion corresponding to the next z bits. The process of calculating the parity bits is recursive as shown in Equation 18b. Can be expressed in an enemy way.

As can be seen from the above equation, when encoding is performed using a lower triangular matrix according to the present embodiment, there is an advantage in that the encoding is completed through a smaller amount of calculation.

The receiving side receiving the encoded signal according to the present embodiment may receive desired data by performing decoding using the matrix of the lower triangular form.

Those skilled in the art through the above description can be seen that various changes and modifications can be made without departing from the spirit of the present invention. Therefore, the technical scope of the present invention should not be limited to the contents described in the detailed description of the specification but should be defined by the claims.

Hereinafter, the effect of the present invention will be described.

In the encoding method according to the present invention, encoding is performed using a model matrix or a parity check matrix having a lower triangular feature. In the matrix having the lower triangular feature, first parity bits are quickly calculated by the structure of a parity part. In other words, there is an advantageous effect of reducing complexity due to decoding.

In addition, in the case of performing the encoding method according to the present invention, when the parity bit is additionally calculated by a specific need, the additional parity bit may be calculated by calculating only an information word portion corresponding to the added parity bit. There is.

Claims (9)

Encoding the information bits to be transmitted to the receiver using a parity check matrix including an information word portion and a parity portion; And Transmitting the encoded signal to the receiving side , ≪ / RTI > The parity check matrix is generated by extending from a model matrix consisting of a plurality of sub blocks of a specific size, wherein the parity portion of the parity check matrix is designed according to a lower triangle type, Encoding method. The method of claim 1, A dual diagonal component included in the parity portion of the model matrix is a subblock corresponding to an identity matrix. Encoding method. The method of claim 1, Wherein the model matrix has a specific shift number as a component of the matrix, each representing the plurality of subblocks, Encoding method. The method of claim 1, The information bit is characterized in that one-to-one corresponding to the information word portion, Encoding method. Receiving a signal transmitted from a transmitting side; And Decoding the received signal using a parity check matrix including an information word portion and a parity portion , ≪ / RTI > The parity check matrix is generated by extending from a model matrix consisting of a plurality of sub blocks of a specific size, wherein the parity portion of the parity check matrix is designed according to a lower triangle type, Decryption method. The method of claim 5, The double diagonal component included in the parity portion of the model matrix is a subblock corresponding to the unit matrix. Decryption method. The method of claim 5, The model matrix has a specific number of shifts, each of the plurality of subblocks, as a component of a matrix, Decryption method. delete delete

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