KR101043558B1 - Flexible Code Rate Fast LDPC Encoder based on Jacket Pattern - Google Patents

Abstract

The present invention relates to a fast LDC coder based on a jacket pattern having a variety of code rates,

It is configured to generate additional parity bits for the codeword obtained by the Richardson Low Density Parity Check (LDPC) coder based on the jacket pattern, and to configure a fast coder supporting various code rates by using the same.

According to the present invention, it is possible to solve the problem of not supporting various code rates in a Richardson type LDPC coder based on a jacket pattern having excellent characteristics in terms of coding complexity. There is an advantage that can be easily realized.

In addition, the fast encoder according to the present invention is capable of fast encoding of various code rates for both normal and irregular LDPC codes, and has a very simple hardware structure.

 LFPC, jacket pattern, lower triangular matrix, RA code, IRA code.

Description

Flexible Code Rate Fast LDPC Encoder based on Jacket Pattern}

1 is a structural diagram of a Richardson type LDPC encoder,

2 is a Tanner graph for an extended jacket LDPC encoder (type 1) according to the present invention;

3 is a structural diagram of an LDPC encoder of an extended jacket pattern according to the present invention;

4 is a Tanner graph for an extended jacket LDPC encoder (type 2) according to the present invention;

5 shows an expanded jacket pattern H matrix (type 1),

6 shows an expanded jacket pattern H matrix (type 2),

7 is a graph showing the BER performance of the extended jacket pattern LDPC code according to the present invention.

8 is a graph showing the BER performance of an extended jacket pattern LDPC code according to the present invention.

9 is a graph showing the BER performance of the extended jacket pattern LDPC code according to the present invention.

10 is a graph showing the BER performance of the extended jacket pattern LDPC code according to the present invention.

Description of the Related Art

200: codeword output unit of LDPC encoder 230: adder

210: codeword of LDPC encoder 240: delay unit

220: data selector 250: additional parity

The present invention relates to a fast LCD encoder based on a jacket pattern having various code rates.

The channel encoding technique can be modified in various forms according to the characteristics of the channel, but an error-correcting code is used as a basic method. The ultimate goal of error correction code is to present a way to achieve reliable communication on an unreliable channel. In other words, the encoder extracts information such as original information from the channel output after encoding using channel codes before transmitting on the channel. The basic characteristic of such a system is based on Shannon's channel coding theory that there is a limit in reducing the error caused by a noisy channel as much as possible without proper loss of information rate when proper encoding of information is performed. . Sign theory, which systematically studies these codes, has undergone remarkable developments over the last few decades.

Among these codes, the turbo code released in 1993 concatenates and encodes a recursive systematic convolutional (RSC) code in parallel, and performs a decoding operation through iterative decoding, which is a quasi-optimal decoding method. In addition, the turbo code shows an excellent performance approaching the limit of Shannon in terms of bit error rate (BER) when the interleaver is large in size and repeated decoding is sufficiently performed.

However, when using the turbo code, there are problems such as increased complexity due to a large amount of computation, delay due to interleaver and iterative decoding, and difficulty in real time processing.

As an alternative, low density parity check (LDPC) codes, which show better code characteristics in terms of complexity and performance than conventional turbo codes, have attracted much attention. This LDPC code was first proposed by Gallager in 1962, and has been forgotten for a long time because of the complexity of decoding, which is a linear block code in which most of the elements of the parity check matrix H are zero. . Mackay and Neal, however, have rediscovered this and have shown very good performance using Gallager's simple probabilistic decoding method.

The LDPC code is defined by a sparse parity check matrix of 1 in the matrix, and is divided into a random LDPC code, a deterministic LDPC code, and the like according to a pattern of the parity check matrix.

Although the random LDPC code has a slightly superior characteristic compared to the deterministic LDPC code, the implementation of the complex LDPC code has attracted attention in recent years because of its complicated implementation. LDPC codes are considered significant competitors in comparison to turbo codes in terms of complexity and performance, and both are based on a similar philosophy of limited random code collections and iterative decoding algorithms. In particular, the LDPC code shows progressively better performance than the turbo code. And it accepts a wide trade-off between performance and decoding complexity. The main problem associated with LDPC codes is their apparently high coding complexity. Recently Richardson introduced a general efficient coding algorithm based on the approximate lower triangulation of LDPC codes [T.J. Richardson and R.L. Urbanke: "Efficient Encoding of Low Density Parity Check Codes," IEEE Trans. IT, vol. 47, pp. 638-856, Feb. 2001.]. However, the Richardson type of calculation is based on several submatrix operations. Therefore, if the parity check matrix H is not selected properly, the complexity of the transformation and matrix processing becomes higher.

Therefore, a simple H parity check matrix has been proposed from the jacket pattern and CPM, which easily avoids cycle-4 and provides access to flexible code rates and code lengths. However, due to the nature of the jacket pattern, the selection of the code rate is not free.

SUMMARY OF THE INVENTION The present invention has been made to solve the above problems, and an object thereof is to add additional parity bits to a codeword obtained by a Richardson low density parity check (LDPC) encoder based on a jacket pattern having excellent characteristics in terms of coding complexity. It is configured to generate and use a high speed coder that supports a variety of code rates.

Jacket pattern-based high speed LDPC coder having various code rates according to the present invention for achieving the above object,

It is configured to generate additional parity bits for the codeword obtained by the Richardson Low Density Parity Check (LDPC) coder based on the jacket pattern, and to configure a fast coder supporting various code rates by using the same.

Hereinafter, an LDP encoder based on a jacket pattern having various code rates according to the present invention will be described with reference to the drawings.

1 is a general configuration diagram of a Richardson type LDPC coder.

패리티 검사 행렬 H에 의하여 정의된 LDPC 부호의 부호어 x는 다음을 만족한다. The efficient coding technique proposed by Richardson and Urbanke is a technique that enables encoding using only the parity check matrix by reconstructing the parity check matrix without generating a matrix [TJ Richardson and RL Urbanke: "Efficient Encoding of Low Density Parity Check". Codes, "IEEE Trans. IT, vol. 47, pp. 638-856, Feb. 2001.]. Generally

The codeword x of the LDPC code defined by the parity check matrix H satisfies the following.

In order to generate codewords using this property, Gaussian elimination can be used to form a lower triangular matrix structure as follows.

라 할 때

길이의 정보 비트

를 패리티 검사 행렬의 앞부분에 곱하고 나머지 패리티 비트

은 아래의 식을 이용하여 순차적으로 구할 수 있다.When constructing an encoder using this structure,

When

Information bits of length

Multiply by the beginning of the parity check matrix and the remaining parity bits

Can be obtained sequentially using the following equation.

이 된다. 부호기의 복잡도를 줄이기 위하여 Richardson은 가우스 소거법을 사용하는 대신 행렬 H의 행과 열을 치환하는 것만을 허용하여 1이 적은 성질이 그대로 유지되도록 하였다. 치환만을 이용하여 행렬 H를 재구성하는 경우 완벽한 하삼각 구조가 아닌 근사 하삼각(ALT; approximate lower triangular) 행렬 구조를 가지게 된다. 이러한 구조를 가진 행렬 H를 부호화를 위하여 다음과 같은 6개의 부분으로 나눌 수 있다.In this case, the complexity of the matrix H is reduced by Gaussian elimination.

Becomes To reduce the complexity of the encoder, Richardson allowed only replacing rows and columns of the matrix H, instead of using Gaussian elimination, so that the property of one less than one would remain. When reconstructing the matrix H using only substitution, it has an approximate lower triangular (ALT) matrix structure, not a perfect lower triangular structure. Matrix H having such a structure can be divided into six parts as follows.

 To make the E part of this matrix zero, we can multiply the matrix by

라 할 때 부호어는 다음의 두 식을 만족한다.Codeword for the new matrix

In this case, the codeword satisfies the following two expressions.

라고 정의하면 다음의 수식을 이용하여 패리티 비트를 얻을 수 있다. here

In this case, the parity bit can be obtained using the following equation.

이 되어

의 크기를 최대한 작게 할 경우 거의

에 가까운 복잡도를 얻을 수 있다.If you use this coding scheme, the complexity

This

If you try to make the size as small as possible

You can get the complexity closer to.

Each block of Figure 1 is associated with a respective submatrix operation.

와 부행렬 A 및 C 간의 이진 곱셈을 수행한다. 부행렬 연산 블록 A (100)의 계산 결과는 부행렬 연산 블록 ET^-1 (120)에서 부행렬 ET^{- 1}와 이진 곱셈된 후 부행렬 연산 블록 C (110)의 결과와 EXOR 게이트 (130)에 의해 이진 가산된다. 이는 다시 부행렬 연산 블록

(140)에서 부행렬

과 이진 곱셈된 후 첫 번째 패리티 벡터인

를 출력한다. 첫 번째 패리티 벡터인

은 부행렬 연산 블록 B (150)에서 부행렬 B와 이진 곱셈된 후 EXOR 게이트 (160)에 의해 부행렬 연산 블록 A (100)의 계산 결과와 이진 가산된다. 이는 다시 부행렬 연산 블록

에서 부행렬 B와 이진 곱셈된 후 두 번째 패리티 벡터인

를 출력한다.First, the submatrix operation block A 100 and the submatrix operation block C 110 are input information data vectors, respectively.

Performs binary multiplication between and submatrices A and C. The calculation result of the submatrix operation block A (100) is binary multiplied by the submatrix ET ^{- 1} in the submatrix operation block ET- ¹ (120), and then the result of the submatrix operation block C (110) and the EXOR gate 130. By binary addition. This is again a submatrix operation block

Sub-matrix at 140

And binary multiplication then the first parity vector

. The first parity vector

Is binary multiplied with sub-matrix B in sub-matrix block B 150 and then binaryly added to the result of calculation of sub-matrix block A 100 by EXOR gate 160. This is again a submatrix operation block

Is the second parity vector after binary multiplication with B

.

2 is a Tanner graph for an extended jacket LDPC encoder (Type 1) according to the present invention.

In general, the Sylvester Hadamard matrix consists of +1 or 1 elements. Therefore, the calculation of these matrices is performed only by addition and subtraction. Recently, a jacket matrix has been introduced that generalizes the median weighted Hadamard matrix [M.H. Lee, "A New Reverse Jacket Transform and Its Fast Algorithm," IEEE, Trans. on Circuit and System, vol. 47. no. 1, pp. 39-47, Jan. 2000.].

이다. 여기서 k는 정수, j는 허수 단위(imagination unit),

, 아다마르 행렬의 중앙부에 위치한다. 또한,

,

인 재킷 행렬

은 대칭적(symmetric)이다[참조문헌: M. H. Lee, B.S. Rajan, and J. Y. Park, "A Generalized Reverse Jacket Transform," IEEE Trans. Circuits Syst. II, vol.48, no.7, pp.684-690, July 2001.]. The name jacket matrix derives from the geometric structure of the reversible jacket. This includes the conventional general Hadamard matrix [95-96] but with a weight ω, where ω is j or

to be. Where k is an integer, j is an imagination unit,

, Located in the center of the Adama matrix. Also,

,

Jacket jacket

Is symmetric [MH Lee, BS Rajan, and JY Park, "A Generalized Reverse Jacket Transform," IEEE Trans. Circuits Syst. II, vol. 48, no. 7, pp. 684-690, July 2001.].

  The position of the weighted elements of the forward matrix can be replaced by the non-weighted elements of its inverse, but their signs do not change in the forward and inverse matrices.

This means a very interesting complementary matrix relationship, the jacket matrix being defined as follows (H. Lee, "A simple element inverse Jacket transform coding", IEEE ITW 2005.).

<Definition 1>

의 행렬

에 대해The size of non-zero elements

Matrix

About

Its inverse is

This is called the jacket matrix.

과 이의 역 행렬은 행렬의 원소 단위의 역으로 정의되며,

,

을 엘레멘트 인버스(element inverse)라 한다. Square matrix in general definition

And its inverse matrix are defined as the inverse of the element units of the matrix,

,

Is called element inverse.

에 대해 이의 역행렬은 단지 각 성분들의 역, 즉

이 성립하는 경우에 이를 재킷(Jacket)이라 부르기로 한다. 흥미로운 행렬들, Hadamard 행렬, DFT(discrete Fourier transform) 행렬 등의 대다수의 유용한 행렬 역시 재킷 계열에 포함된다[참조문헌: Jia Hou, M.H. Lee, and J.Y. Park, "New Polynomial Construction of Jacket Transform," IEICE Trans. Fund. vol.E86A, no.3, pp.652-660, March 2003.]. 본 발명에서는 복소수 필드 상에서 재킷 행렬의 부류를 이용한다.

를 홀수 소수(odd prime), 원시 원소를

라 하자. 따라서

이고

연산을 하는

는 유한체이고 여기서Square matrix

Its inverse is for only the inverse of each component,

In this case, it will be called a jacket. Many useful matrices, such as interesting matrices, Hadamard matrices, and discrete Fourier transform (DFT) matrices, are also included in the jacket series [Jia Hou, MH Lee, and JY Park, "New Polynomial Construction of Jacket Transform," IEICE. Trans. Fund. vol. E86A, no. 3, pp. 652-660, March 2003.]. The present invention utilizes a class of jacket matrices on complex fields.

For odd prime, for primitive elements

Let's do it. therefore

ego

Arithmetic

Is a finite field where

.

.

라고 하고, 다음과 같은 함수를 정의하면

If you define a function like

는 벡터이고 여기서

이다.

Is a vector where

to be.

Now define the following vector:

.

.

재킷 행렬은 [참조문헌: M.H. Lee, "A New Reverse Jacket Transform and Its Fast Algorithm," IEEE, Trans. on Circuit and System, vol.47. no.1, pp.39-47, Jan. 2000.]에 의해 구해질 수 있다.therefore

Jacket matrices are described in MH Lee, "A New Reverse Jacket Transform and Its Fast Algorithm," IEEE, Trans. on Circuit and System, vol. 47. no. 1, pp. 39-47, Jan. 2000.].

라 하면 E.g

If

,

,

And

,

,

.

.

This represents a form of binary low density matrix based on jacket pattern.

재킷 행렬이 주어진 경우 LDPC 부호의 부호 길이 N은

으로 주어지며, 여기서 p는 CPM의 크기를 결정하는 소수(prime number)이다.

Given a jacket matrix, the code length N of the LDPC code is

Where p is the prime number that determines the size of the CPM.

과 같으며, 여기서 M은 정보 데이터 벡터의 길이를 나타낸다. 또한, 행 무게(row weight) j는

를 만족하도록 결정된다.The rate R of the LDPC code is

Where M represents the length of the information data vector. Also, the row weight j is

Is determined to satisfy.

The CPM insertion for the low density matrix on the jacket pattern is according to the following definition, and in this way an LDPC code that extends from the CPM is obtained.

<Definition 2>

을 갖는 재킷 행렬을

라고 하고 각 성분

를 순환 치환 행렬(CPM)

로 바꾸면 결과 행렬은 재킷 패턴의 저밀도 행렬의 한 형태이다.

Having a jacket matrix

Each ingredient

Is a cyclic substitution matrix (CPM)

In this case, the resulting matrix is a form of low density matrix of jacket patterns.

는 소수이며,

Is a prime number,

,

,

Let's do it. here

,

,

,

를 나타낸다.

,

Indicates.

,

는 CPM으로서 참조된다.

가 기존의 행렬 곱과

를 갖는 아벨 군(Abelian group)을 형성한다는 것을 알 수 있다. 또한 CPM의 전치(transpose)는 이의 역이 된다. procession

,

Is referred to as the CPM.

Is equal to the conventional matrix product

It can be seen that it forms an Abelian group with. Also, the transpose of CPM is the inverse of it.

The following describes the coding form of the LDPC code extended from the CPM using the definition of the low density matrix on the jacket pattern.

라 하고

를 크기

의 CPM

로 교체하면 저밀도 재킷 행렬을 얻을 수 있다. 예를 들어 행렬

는 다음과 같이 바꿀 수 있다. Jacket procession

And

Size

CPM of

Replace with to get a low density jacket matrix. E.g. matrix

Can be changed to

인

균일 LDPC 부호는

패턴의 저밀도 행렬에 의해 설계되어지고

이면 다음과 같이 나타낼 수 있다. Cycle-4 in the low density jacket matrix series by Equation 20 is described in Y. Kou, S. Lin, and M. Fossorier, "Low density parity check codes based on finite geometries: A rediscovery," Proc. of ISIT 2000, Sorrento, Italy, June 22-30, 2000.]. But it is a square matrix. The nonsquare parity check matrix H can be easily obtained by the rowing of the columns and rows. Example size

sign

Uniform LDPC code is

Is designed by a low density matrix of patterns

Can be expressed as follows.

 Also, to get a better sign, the zero padding method can be applied as follows.

Clearly, the LDPC code sequence based on this jacket pattern can easily generate the following Richardson type codes.

,

,

이며,

는 하삼각 분해가 되어야 한다. 특히, 재킷 패턴

H 행렬은 도 5와 같이 나타낼 수 있다. 여기서

는

단위행렬(identity matrix)이고, 나머지

는 좀 더 간단한 연산의 여러 CPM에 의해서 구해진다. Where the parity check matrix is

Is,

Should be the lower triangular decomposition. Especially, jacket pattern

The H matrix may be represented as shown in FIG. 5. here

Is

Identity matrix, the rest

Is obtained by several CPMs of simpler operations.

For example, Richardson's ALT LDPC code is obtained from the reversing form of Equation 20 in the following manner.

그리고

라는 것을 쉽게 알 수 있다. In this case

And

It is easy to see that.

와 체계적인 부분인

에 의해 얻어지고, 그 함수들은 다음과 같이 계산되어 진다. Parity check bits

And the systematic part

Is obtained by, and the functions are computed as

이고 재킷 패턴의 저밀도 부호들이 사용될 경우 이는 분명히 non-singular이다. 재킷 패턴에 의해 구성된 Richardson의 ALT LDPC 부호의 경우 [수학식 22]에서 보여진 것처럼 역순 형태를 사용해서

이 되도록 할 수 있으며, 크기

의

를 얻을 수 있다. 결국 [수학식 23], [수학식 24]는 다음과 같이 단순화된다. here

And if low density codes in the jacket pattern are used, this is clearly non-singular. For Richardson's ALT LDPC code constructed by a jacket pattern, we use the reverse form as shown in Equation 22.

Can be as large as

of

Can be obtained. As a result, Equation 23 and Equation 24 are simplified as follows.

,

이며,

는

순환 행렬이다

. here

,

Is,

Is

Is a circular matrix

.

It is clear that the approximate lower triangular LDPC code using a jacket pattern with a matrix structure similar to Richardson's ALT LDPC code can be simply encoded by using CPM and their multiplication. The computational complexity of such a series of LDPC codes is very low, and high speed encoding can be realized.

의 형태로 구성된다. 물론 열의 무게를 증가시키도록 E의 형태가

(여기서 α은 자연수)로 만들 수도 있다. 이러한 경우에는 영행렬을 삽입하여

의 연산을 쉽게 할 수 있다. 어떠한 경우라도 n-k의 경우가 p의 배수이어야 함은 분명하다. 이러한 점에서 재킷 패턴 LDPC 부호의 부호율은 자유롭지 못하다.By the jacket pattern coding method, it was possible to easily code from an H matrix. However, the code rate is not very free due to the characteristics of the H matrix. In the process of encoding, T and E form are important for calculating p1 and p2.

It is configured in the form of Of course, the shape of E increases the weight of the heat.

(Where α is a natural number). In this case, you can insert a zero matrix

The operation of can be made easy. In any case, it is clear that the case of nk must be a multiple of p. In this respect, the code rate of the jacket pattern LDPC code is not free.

Hereinafter, a method of expanding the jacket pattern LDPC will be described.

The basic structure of an H matrix is

는 임의의 자연수를 의미하고 최대 열의 무게를 결정하는 요인이다. 임의의 k 가 정보 길이로 볼 수 있는지 알아보기 위해 다음 행렬 크기로서 전개해 볼 수 있다. 앞에서 보인 바와 같이 패리티 비트는 다음과 같이 구해진다.Where n means code length and k means information length. P is the size of the base matrix constituting the H matrix and is also a prime number.

Means any natural number and is the factor that determines the maximum heat weight. To see if any k can be seen as the length of the information, we can expand it as the next matrix size. As shown above, the parity bit is obtained as follows.

Since T = I and modulo 2 operation, it can be expressed as follows.

Based on this, considering only the size of the matrix to see if the coding is performed by arbitrary k, the following is considered.

Therefore, the following holds true.

이 성립해야 한다. 따라서 영행렬을 삽입하지 않았을 경우

이어야 하므로

이어야하고, 영행렬을 삽입하였을 경우

이므로

이어야 한다. Therefore, it can be seen that coding can be performed on any k. At this time,

This must hold. So if you don't insert zero matrix

Should be

Should be inserted and zero matrix is inserted

Because of

Should be

이다. 여기서 n을 줄이면 앞의 행렬 계산은 더 이상 성립하지 않게 되므로 부호화가 불가능하게 된다. 하지만 [수학식31]과 같이 만들 수 있다면 부호율의 변경이 가능하다고 할 수 있 다. Assuming that k is given, the code rate is

to be. In this case, if n is reduced, the previous matrix calculation is no longer true, so coding is impossible. However, if it can be made as shown in [Equation 31], it can be said that the code rate can be changed.

이다. 여기서 s는 정보 비트이고 p1과 p2는 부호화로 얻어진 패리티 비트이다. 이를 바탕으로 새로운 패리티 비트 p3 및 패리티 비트 p3이 포함된 부호어를 간단한 RA(repeat accumulate) 부호기로 생성할 수 있다. The codeword obtained from the previous encoding is

to be. Where s is information bits and p1 and p2 are parity bits obtained by encoding. Based on this, a codeword including the new parity bit p3 and parity bit p3 can be generated by a simple repeat accumulate (RA) coder.

이 될 것이다. 이때의 새로운 부호어는 다음과 같이 구성된다.Suppose that ε bits are extracted directly from the previous codeword at uniform intervals.

Will be The new codeword at this time is composed as follows.

In this case, the recursive formula can be expressed as Equation 33.

로 정의할 때, 다음이 성립한다.The position of the sample of the previous codeword

When defined as, the following holds true.

의 범위에 존재한다. Where α is

Exists in the range of.

를

의 위치에 존재하는 샘플의 값이라고 정의한다면, 다음 식이 성립한다. And

To

If we define it as the value of the sample at the position of, then

단

only

3 is a block diagram of an extended jacket pattern LDPC encoder according to the present invention,

A codeword output unit 200 of the LDPC coder, a codeword 210 of the LDPC coder, a data selector 220, an adder 230, a delayer 240, and an additional parity 250 are included.

The codeword output unit 200 of the LDPC coder represents a codeword 210 output from an existing jacket pattern LDPC coder. Like the Richardson type LDPC coder, one codeword 210 is represented by (s, p1, p2). Has a structure.

The data selector 220 sequentially selects and outputs 1 bit of the codeword 210.

The adder 230 binaryly adds an output bit of the data selector 220 and a bit fed back by the delay unit 240 to generate an additional parity 250 p3.

4 shows a Tanner graph for an extended jacket LDPC encoder (Type 2).

개의 샘플을 추출하는 대신 모든 부호어를 전부 표본으로 이용하는 방법으로 IRA(iterative RA) 부호를 생각해볼 수 있다.From previous codeword

Instead of extracting two samples, it is possible to think of an IRA (iterative RA) code by using all codewords as samples.

인 부호어와

개의 패리티 비트를 보여주고 있다. 그리고 세 번째의 패리티 비트는

가 될 것이다. 패리티 비트의 값은 모듈로 2 연산에 의해 결정된다. 이러한 경우 다음과 같은 순환 공식이 성립하게 된다.Tanner graph

Codeword and

Parity bits. And the third parity bit

Will be. The value of the parity bit is determined by modulo 2 operation. In this case, the following circular formula is established.

5 and 6 show the expanded jacket pattern H matrix (type 1) and the expanded jacket pattern H matrix (type 2), respectively.

개의 비트를 부호어로부터 추출할 때, 재킷 패턴 행렬의 하단은 [수학식 37]과 같이 구성되어진다. 이러한 형태는 인터리버를 무시하고, 패리티 검사 비트 사이의 간격을 동일하게 했을 경우의 형태이다.If you analyze Type 1,

When two bits are extracted from the codeword, the lower end of the jacket pattern matrix is configured as shown in [Equation 37]. This type is a case where the interleaver is ignored and the intervals between parity check bits are equalized.

은 [수학식 38]과 같이 구성되어진다.When targeting type 2,

Is constructed as shown in Equation 38.

의 행렬 크기는

이다. 재킷 패턴 행렬의 오른쪽 부분은 영행렬로 구성된다. 행렬 크기는

가 된다. H 행렬을 살펴보면,

관계식을 쉽게 얻을 수 있고, H 행렬의 열의 길이는

이다. 여기서 k는 정보어의 길이이다. 일반적으로 열의 길이와 행의 길이의 차이가 정보어의 길이이다. 따라서 확장된 재킷 행렬의 정보어의 길이를 구하면

으로 정보어의 길이가 확장 전과 동일함을 알 수 있다. here

The matrix size of

to be. The right part of the jacket pattern matrix consists of zero matrices. Matrix size

Becomes Looking at the H matrix,

You can easily get a relation, and the length of the columns of the H matrix

to be. Where k is the length of the information word. In general, the difference between the length of a column and the length of a row is the length of the information word. Therefore, if you find the length of the information word of the expanded jacket matrix

It can be seen that the length of the information word is the same as before expansion.

In FIG. 6 and FIG. 7, the diagonally marked portion at the bottom right is composed of a dual diagonal matrix as shown in [Equation 39].

7 to 10 is a view showing the BER performance of the Richardson type jacket LDPC code according to the present invention.

The random design LDPC is referred to as R-LDPC, which is called a (3, k) uniform LDPC code. Let jacket pattern LDPC be J-LDPC. In the same way, the expanded jacket LDPC is referred to as EJ-LDPC. All experiments resulted in 5000 frames. Also tried for various code rates R = 2 / 3,5 / 6,1 / 2,3 / 4. EJ-LDPC was used because pure J-LDPC could not complete the desired code rate.

7 is a diagram showing the BER performance of the Richardson type jacket LDPC code according to the present invention, the performance of approximately 0.1 ~ 0.2dB when the matrix size (288 * 864), (192 * 576) and the code rate is 2/3 Seems to improve.

8 is a diagram showing the BER performance of the Richardson type jacket LDPC code according to the present invention. If the matrix sizes are (192 * 1152) and (240 * 1440) and the code rate is 5/6, the performance improvement is about 0.25dB at BER = 10-5.

9 is a diagram showing the BER performance of the Richardson type jacket LDPC code according to the present invention. If the matrix sizes are (528 * 1056), (672 * 1344) and the code rate is 1/2, the performance degradation is about 0.3dB at 10-3.

10 is a diagram showing the BER performance of the Richardson type jacket LDPC code according to the present invention. An interesting result is obtained when the matrix sizes are (432 * 1728), (504 * 2016) and the code rate is 3/4. At BER 10-5, the former shows a 0.5dB performance improvement and the latter shows a 0.3dB performance degradation.

According to the jacket pattern-based LDPC encoder having various code rates according to the present invention described above,

의 모든 열을 순환 시프트시킨 구조만으로 구성되므로 부행렬과 정보 벡터간의 연산은 단지 순환 시프트 과정만으로 처리될 수 있으며, 재킷 패턴을 이용한 Richardson 유형 LDPC 부호는 CPM과 이들의 곱셈을 사용함으로써 간단히 부호화 되어질 수 있다. 이러한 계열의 LDPC 부호에 대한 계산 복잡도는 매우 낮아지게 되어 보다 간단한 하드웨어로 부호기를 구성할 수 있는 장점이 있지만 다양한 부호율을 지원하지 못하는 단점이 있다. 이러한 문제를 해결하기 위해 재킷 패턴 기반의 리차드슨 LDPC(low density parity check) 부호기에 의해 얻어진 부호어에 대해 추가의 패리티 비트들을 생성하도록 구성하고 이를 이용하는 방법으로 다양한 부호율을 지원하는 고속 부호기의 구성이 가능하다. 부호화의 복잡도 측면에서 우수한 특성을 갖는 재킷 패턴 기반의 리차드슨 유형 LDPC 부호기에서 다양한 부호율을 지원하지 못하는 문제점을 RA 또는 IRA 부호화 방법을 적용하여 해결함으로써 다양한 부호율을 지원하는 고속 부호화기의 구현이 간단한 하드웨어를 이용하여 용이하게 실 현될 수 있는 이점이 있다.Each submatrix of the parity check matrix is a null matrix, an identity matrix, and an identity matrix.

Since only the structure of cyclic shift of all columns of is composed, the operation between submatrix and information vector can be processed by cyclic shift only. Richardson type LDPC code using jacket pattern can be simply encoded by using CPM and their multiplication. have. The computational complexity of this series of LDPC codes is very low, which makes it possible to configure an encoder with simpler hardware. However, it does not support various code rates. In order to solve this problem, a scheme for generating additional parity bits for a codeword obtained by a Richardson LDPC (Low Density Parity Check) coder based on a jacket pattern is used. It is possible. Simple hardware implementation of fast coder that supports various code rates by applying RA or IRA coding method to solve the problem that various code rates are not supported in Richardson type LDPC coder based on jacket pattern having excellent characteristics in coding complexity. There is an advantage that can be easily implemented using.

Claims (5)

A codeword output unit configured to output a codeword by a Richardson type LDPC (Low Density Parity Check) encoder based on a jacket pattern; A data selector for sequentially selecting and outputting 1 bit of the codeword; And And an adder configured to binaryly add the bits output by the data selector and the bits fed back by the delay unit to generate additional parity. The addition unit, The additional parity (

A fast, fast LD codec encoder based on a jacket pattern that supports various code rates.

only

Is a sample of previous codeword The method according to claim 1, The addition unit, A jacket pattern based fast LFPC encoder supporting various code rates for generating the additional parity by a Reapeat accumulate (RA) encoder. delete A codeword output unit configured to output a codeword by a Richardson type LDPC (Low Density Parity Check) encoder based on a jacket pattern; And And an adder configured to generate additional parity by using an IRA (Interative Reapeat accumulate) coder as a sample of the output codeword. The addition unit, The additional parity (

A fast, fast LD codec encoder based on a jacket pattern that supports various code rates.

only

Is a sample of previous codeword delete

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