阅读说明：本技术 基于有限域傅里叶变换的qc-ldpc码构造方法、系统及设备 (Finite field Fourier transform-based QC-LDPC code construction method, system and equipment ) 是由 穆锡金 董琦 尚晓舟 孙凤松 于 2021-07-21 设计创作，主要内容包括：本发明公开了一种基于有限域傅里叶变换的QC-LDPC码构造方法、系统及设备,基于有限域傅里叶变换的QC-LDPC码构造方法,包括：对满足特定约束条件的二元向量进行有限域傅里叶变换,以获得频域对角矩阵,其中,二元向量中元素取值为0或1,特定约束条件包括：二元向量的长度n满足：n+1为一个素数,且所有元素取值为1的元素下标向量中所有元素之间的差值在模n运算下不同；对频域对角矩阵依次进行矩阵分块和元素变换,以获得频域置换矩阵；对频域置换矩阵依次进行有限域傅里叶逆变换和循环子矩阵处理,以获得时域矩阵阵列；对时域矩阵阵列依次进行裁取和掩模,以获得QC-LDPC码对应的校验矩阵。采用本发明,可以实现较低的构造复杂度和较大的构造灵活度。(The invention discloses a method, a system and equipment for constructing a QC-LDPC code based on finite field Fourier transform, wherein the method for constructing the QC-LDPC code based on the finite field Fourier transform comprises the following steps: performing finite field Fourier transform on the binary vector meeting specific constraint conditions to obtain a frequency domain diagonal matrix, wherein the values of elements in the binary vector are 0 or 1, and the specific constraint conditions comprise: the length n of the binary vector satisfies: n +1 is a prime number, and the difference values between all elements in the element subscript vector with all elements taking the value of 1 are different under the modulo n operation; sequentially carrying out matrix blocking and element transformation on the frequency domain diagonal matrix to obtain a frequency domain permutation matrix; sequentially carrying out finite field inverse Fourier transform and cyclic sub-matrix processing on the frequency domain permutation matrix to obtain a time domain matrix array; and sequentially cutting and masking the time domain matrix array to obtain a check matrix corresponding to the QC-LDPC code. By adopting the invention, lower construction complexity and larger construction flexibility can be realized.)

1. A QC-LDPC code construction method based on finite field Fourier transform is characterized by comprising the following steps:

performing finite field Fourier transform on a binary vector meeting a specific constraint condition to obtain a frequency domain diagonal matrix, wherein the value of an element in the binary vector is 0 or 1, and the specific constraint condition comprises: the length n of the binary vector satisfies: n +1 is a prime number, and the difference values between all elements in the element subscript vector with all elements taking the value of 1 are different under the modulo n operation;

sequentially carrying out matrix blocking and element transformation on the frequency domain diagonal matrix to obtain a frequency domain permutation matrix;

sequentially carrying out finite field inverse Fourier transform and cyclic sub-matrix processing on the frequency domain permutation matrix to obtain a time domain matrix array;

and sequentially cutting and masking the time domain matrix array to obtain a check matrix corresponding to the QC-LDPC code.

2. The method of claim 1, wherein the matrix blocking and element transforming the frequency-domain diagonal matrix in sequence comprises:

dividing an n × n frequency domain diagonal matrix into an e × e matrix array, wherein the size of each sub-matrix in the matrix array is L × L, and n, e and L satisfy: e × L ═ n;

determining elements of each sub-matrix in the matrix array based on the frequency domain diagonal matrix by adopting replication and multiplication/addition operation on a finite field, wherein the sub-matrices are all diagonal matrices or all-zero matrices, and the sub-matrices on the diagonal of the matrix array are the same.

3. The method of claim 2, wherein the performing inverse finite field fourier transform and cyclic sub-matrix processing on the frequency domain permutation matrix in sequence to obtain a time domain matrix array comprises:

for each of the sub-matrices, determining a corresponding first vector of length n, u ═ n (u ═ n)₀,u₁,…u_n-1) The first L elements in the first vector are diagonal elements of the sub-matrix, and the other elements are conjugate vectors of the first L elements;

performing a finite field inverse Fourier transform on the first vector to obtain a second vector of length n, w ═ w (w ═ w)₀,w₁,…w_n-1) The value of the element in the second vector is 0 or 1;

taking the first L elements of the second vector to form a binary vector with the length of e, and taking the binary vector as a first row to perform cyclic shift to obtain an L multiplied by L binary cyclic sub-matrix;

and constructing a time domain matrix array based on the binary cycle submatrices corresponding to all the submatrices.

4. The method of claim 3, wherein the sequentially clipping and masking the time domain matrix array comprises:

cutting the time domain matrix array according to the requirements of code length and code rate;

and replacing partial submatrices in the cut time domain matrix array with all-zero submatrices.

5. A QC-LDPC code construction system based on finite field fourier transform, comprising:

the device comprises a frequency domain diagonal matrix construction unit, a frequency domain diagonal matrix calculation unit and a frequency domain diagonal matrix calculation unit, wherein the frequency domain diagonal matrix construction unit is used for performing finite field Fourier transform on binary vectors meeting specific constraint conditions to obtain a frequency domain diagonal matrix, the values of elements in the binary vectors are 0 or 1, and the specific constraint conditions comprise: the length n of the binary vector satisfies: n +1 is a prime number, and the difference values between all elements in the element subscript vector with all elements taking the value of 1 are different under the modulo n operation;

the frequency domain permutation matrix construction unit is used for sequentially carrying out matrix blocking and element transformation on the frequency domain diagonal matrix so as to obtain a frequency domain permutation matrix;

the time domain matrix array construction unit is used for sequentially carrying out finite field inverse Fourier transform and cyclic sub-matrix processing on the frequency domain permutation matrix so as to obtain a time domain matrix array;

and the check matrix construction unit is used for sequentially cutting and masking the time domain matrix array so as to obtain a check matrix corresponding to the QC-LDPC code.

6. The system of claim 5, wherein the frequency domain permutation matrix constructing unit is configured to:

dividing an n × n frequency domain diagonal matrix into an e × e matrix array, wherein the size of each sub-matrix in the matrix array is L × L, and n, e and L satisfy: e × L ═ n;

determining elements of each sub-matrix in the matrix array based on the frequency domain diagonal matrix by adopting replication and multiplication/addition operation on a finite field, wherein the sub-matrices are all diagonal matrices or all-zero matrices, and the sub-matrices on the diagonal of the matrix array are the same.

7. The system of claim 6, wherein the time domain matrix array construction unit is to:

for each of the sub-matrices, determining a corresponding first vector of length n, u ═ n (u ═ n)₀,u₁,…u_n-1) The first L elements in the first vector are diagonal elements of the sub-matrix, and the other elements are conjugate vectors of the first L elements;

subjecting the first vector toInverse domain-limited fourier transform to obtain a second vector of length n w ═ w (w)₀,w₁,…w_n-1) The value of the element in the second vector is 0 or 1;

taking the first L elements of the second vector to form a binary vector with the length of e, and taking the binary vector as a first row to perform cyclic shift to obtain an L multiplied by L binary cyclic sub-matrix;

and constructing a time domain matrix array based on the binary cycle submatrices corresponding to all the submatrices.

8. The system of claim 7, wherein the check matrix construction unit is to:

cutting the time domain matrix array according to the requirements of code length and code rate;

and replacing partial submatrices in the cut time domain matrix array with all-zero submatrices.

9. A QC-LDPC code construction apparatus based on finite field fourier transform, comprising: memory, a processor and a computer program stored on the memory and executable on the processor, the computer program, when executed by the processor, implementing the steps of the finite field fourier transform-based QC-LDPC code construction method according to any one of claims 1 to 4.

10. A computer-readable storage medium, having stored thereon an information transfer-enabling program which, when executed by a processor, enables the steps of the finite field fourier transform-based QC-LDPC code construction method according to any one of claims 1 to 4.

Technical Field

The invention relates to the field of communication, in particular to a method, a system and equipment for constructing a QC-LDPC code based on finite field Fourier transform.

Background

For current wireless communication scenarios, such as: for data chain communication, satellite communication, ground cellular communication, underwater communication and the like of an unmanned platform, a transmitting and receiving end needs to adopt channel coding to ensure the reliability of transmission. Quasi-Cyclic Low-density parity-check (QC-LDPC) code is a channel coding scheme with strong error control capability and Low codec complexity, and has been used in many practical communication systems. Current methods of constructing QC-LDPC codes include graph-based methods and algebraic construction methods. The main process of the graph construction method is as follows: some measurement parameters (such as decoding threshold, minimum distance, etc.) capable of reflecting the code performance are selected, and then codes with better measurement parameters are searched based on a computer within a certain code set range. This method can obtain good QC-LDPC codes, but the construction complexity is high because of the large number of computations and searches required. The algebraic construction method is to construct the QC-LDPC code by using mathematical algebraic tools (such as finite field, finite geometry, combined design and other mathematical tools), and the method is systematic and can directly generate a check matrix of the QC-LDPC code through some simple matrix transformations and operations, so the construction complexity is low. But on one hand, the method is restricted by stronger mathematical relation, so that the flexibility of code parameter change is smaller.

Disclosure of Invention

The embodiment of the invention provides a method, a system and equipment for constructing a QC-LDPC code based on finite field Fourier transform, which are used for solving the problems of higher construction complexity and inflexible code parameter change of the QC-LDPC code constructing method in the prior art.

The QC-LDPC code construction method based on finite field Fourier transform comprises the following steps:

performing finite field Fourier transform on a binary vector meeting a specific constraint condition to obtain a frequency domain diagonal matrix, wherein the value of an element in the binary vector is 0 or 1, and the specific constraint condition comprises: the length n of the binary vector satisfies: n +1 is a prime number, and the difference values between all elements in the element subscript vector with all elements taking the value of 1 are different under the modulo n operation;

sequentially carrying out matrix blocking and element transformation on the frequency domain diagonal matrix to obtain a frequency domain permutation matrix;

sequentially carrying out finite field inverse Fourier transform and cyclic sub-matrix processing on the frequency domain permutation matrix to obtain a time domain matrix array;

and sequentially cutting and masking the time domain matrix array to obtain a check matrix corresponding to the QC-LDPC code.

According to some embodiments of the invention, the sequentially performing matrix blocking and element transformation on the frequency domain diagonal matrix comprises:

dividing an n × n frequency domain diagonal matrix into an e × e matrix array, wherein the size of each sub-matrix in the matrix array is L × L, and n, e and L satisfy: e × L ═ n;

determining elements of each sub-matrix in the matrix array based on the frequency domain diagonal matrix by adopting replication and multiplication/addition operation on a finite field, wherein the sub-matrices are all diagonal matrices or all-zero matrices, and the sub-matrices on the diagonal of the matrix array are the same.

According to some embodiments of the present invention, the sequentially performing inverse finite field fourier transform and cyclic sub-matrix processing on the frequency domain permutation matrix to obtain a time domain matrix array includes:

for each of the sub-matrices, determining a corresponding first vector of length n, u ═ n (u ═ n)₀,u₁,…u_n-1) The first L elements in the first vector are diagonal elements of the sub-matrix, and the other elements are conjugate vectors of the first L elements;

performing a finite field inverse Fourier transform on the first vector to obtain a second vector of length n, w ═ w (w ═ w)₀,w₁,…w_n-1) The value of the element in the second vector is 0 or 1;

taking the first L elements of the second vector to form a binary vector with the length of e, and taking the binary vector as a first row to perform cyclic shift to obtain an L multiplied by L binary cyclic sub-matrix;

and constructing a time domain matrix array based on the binary cycle submatrices corresponding to all the submatrices.

According to some embodiments of the invention, said sequentially clipping and masking the time domain matrix array comprises:

cutting the time domain matrix array according to the requirements of code length and code rate;

and replacing partial submatrices in the cut time domain matrix array with all-zero submatrices.

The QC-LDPC code construction system based on finite field Fourier transform comprises the following steps:

the device comprises a frequency domain diagonal matrix construction unit, a frequency domain diagonal matrix calculation unit and a frequency domain diagonal matrix calculation unit, wherein the frequency domain diagonal matrix construction unit is used for performing finite field Fourier transform on binary vectors meeting specific constraint conditions to obtain a frequency domain diagonal matrix, the values of elements in the binary vectors are 0 or 1, and the specific constraint conditions comprise: the length n of the binary vector satisfies: n +1 is a prime number, and the difference values between all elements in the element subscript vector with all elements taking the value of 1 are different under the modulo n operation;

the frequency domain permutation matrix construction unit is used for sequentially carrying out matrix blocking and element transformation on the frequency domain diagonal matrix so as to obtain a frequency domain permutation matrix;

the time domain matrix array construction unit is used for sequentially carrying out finite field inverse Fourier transform and cyclic sub-matrix processing on the frequency domain permutation matrix so as to obtain a time domain matrix array;

and the check matrix construction unit is used for sequentially cutting and masking the time domain matrix array so as to obtain a check matrix corresponding to the QC-LDPC code.

According to some embodiments of the invention, the frequency domain permutation matrix construction unit is configured to:

dividing an n × n frequency domain diagonal matrix into an e × e matrix array, wherein the size of each sub-matrix in the matrix array is L × L, and n, e and L satisfy: e × L ═ n;

determining elements of each sub-matrix in the matrix array based on the frequency domain diagonal matrix by adopting replication and multiplication/addition operation on a finite field, wherein the sub-matrices are all diagonal matrices or all-zero matrices, and the sub-matrices on the diagonal of the matrix array are the same.

According to some embodiments of the invention, the time domain matrix array construction unit is configured to:

for each of the sub-matrices, determining a corresponding first vector of length n, u ═ n (u ═ n)₀,u₁,…u_n-1) The first L elements in the first vector are diagonal elements of the sub-matrix, and the other elements are conjugate vectors of the first L elements;

performing a finite field inverse Fourier transform on the first vector to obtain a second vector of length n, w ═ w (w ═ w)₀,w₁,…w_n-1) The value of the element in the second vector is 0 or 1;

taking the first L elements of the second vector to form a binary vector with the length of e, and taking the binary vector as a first row to perform cyclic shift to obtain an L multiplied by L binary cyclic sub-matrix;

and constructing a time domain matrix array based on the binary cycle submatrices corresponding to all the submatrices.

According to some embodiments of the invention, the check matrix construction unit is configured to:

cutting the time domain matrix array according to the requirements of code length and code rate;

and replacing partial submatrices in the cut time domain matrix array with all-zero submatrices.

The QC-LDPC code construction equipment based on finite field Fourier transform comprises the following components: a memory, a processor and a computer program stored on the memory and executable on the processor, the computer program, when executed by the processor, implementing the steps of the method for constructing a QC-LDPC code based on finite field fourier transform as described above.

According to the computer readable storage medium of the embodiment of the present invention, the computer readable storage medium stores thereon an implementation program of information transfer, which when executed by a processor implements the steps of the QC-LDPC code construction method based on finite field fourier transform as described above.

By adopting the embodiment of the invention, on one hand, the whole construction process is systematic and has lower construction complexity. On the other hand, by flexibly setting row-column replacement, arbitration and mask operation modes, QC-LDPC codes with different parameters can be obtained, and the QC-LDPC codes have higher construction flexibility.

The foregoing description is only an overview of the technical solutions of the present invention, and the embodiments of the present invention are described below in order to make the technical means of the present invention more clearly understood and to make the above and other objects, features, and advantages of the present invention more clearly understandable.

Drawings

Various other advantages and benefits will become apparent to those of ordinary skill in the art upon reading the following detailed description of the embodiments. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the invention. In the drawings:

FIG. 1 is a flow chart of a method for constructing a QC-LDPC code based on finite field Fourier transform according to an embodiment of the present invention;

FIG. 2 is a schematic diagram of frequency domain permutation matrix generation according to an embodiment of the present invention;

FIG. 3 is a schematic diagram of the generation of a time domain matrix array in an embodiment of the present invention;

FIG. 4 is a schematic diagram of generating a QC-LDPC code check matrix from a time domain matrix array according to an embodiment of the present invention;

FIG. 5 is a block diagram of a construction system of a QC-LDPC code based on finite field Fourier transform according to an embodiment of the present invention;

FIG. 6 is a block diagram of a device structure for constructing QC-LDPC codes based on finite field Fourier transform according to an embodiment of the present invention.

Detailed Description

Exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the invention are shown in the drawings, it should be understood that the invention can be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.

As shown in fig. 1, an embodiment of a first aspect of the present invention provides a method for constructing a QC-LDPC code based on finite field fourier transform, including:

performing finite field Fourier transform on a binary vector meeting a specific constraint condition to obtain a frequency domain diagonal matrix, wherein the value of an element in the binary vector is 0 or 1, and the specific constraint condition comprises: the length n of the binary vector satisfies: n +1 is a prime number, and the difference values between all elements in the element subscript vector with all elements taking the value of 1 are different under the modulo n operation;

sequentially carrying out matrix blocking and element transformation on the frequency domain diagonal matrix to obtain a frequency domain permutation matrix;

sequentially carrying out finite field inverse Fourier transform and cyclic sub-matrix processing on the frequency domain permutation matrix to obtain a time domain matrix array;

and sequentially cutting and masking the time domain matrix array to obtain a check matrix corresponding to the QC-LDPC code.

By adopting the embodiment of the invention, on one hand, the whole construction process is systematic and has lower construction complexity. On the other hand, by flexibly setting row-column replacement, arbitration and mask operation modes, QC-LDPC codes with different parameters can be obtained, and the QC-LDPC codes have higher construction flexibility.

On the basis of the above-described embodiment, various modified embodiments are further proposed, and it is to be noted herein that, in order to make the description brief, only the differences from the above-described embodiment are described in the various modified embodiments.

According to some embodiments of the invention, the sequentially performing matrix blocking and element transformation on the frequency domain diagonal matrix comprises:

dividing an n × n frequency domain diagonal matrix into an e × e matrix array, wherein the size of each sub-matrix in the matrix array is L × L, and n, e and L satisfy: e × L ═ n;

determining elements of each sub-matrix in the matrix array based on the frequency domain diagonal matrix by adopting replication and multiplication/addition operation on a finite field, wherein the sub-matrices are all diagonal matrices or all-zero matrices, and the sub-matrices on the diagonal of the matrix array are the same.

According to some embodiments of the present invention, the sequentially performing inverse finite field fourier transform and cyclic sub-matrix processing on the frequency domain permutation matrix to obtain a time domain matrix array includes:

for each of the sub-matrices, determining a corresponding first vector of length n, u ═ n (u ═ n)₀,u₁,…u_n-1) The first L elements in the first vector are diagonal elements of the sub-matrix, and the other elements are conjugate vectors of the first L elements;

performing a finite field inverse Fourier transform on the first vector to obtain a second vector of length n, w ═ w (w ═ w)₀,w₁,…w_n-1) The value of the element in the second vector is 0 or 1;

taking the first L elements of the second vector to form a binary vector with the length of e, and taking the binary vector as a first row to perform cyclic shift to obtain an L multiplied by L binary cyclic sub-matrix;

and constructing a time domain matrix array based on the binary cycle submatrices corresponding to all the submatrices.

According to some embodiments of the invention, said sequentially clipping and masking the time domain matrix array comprises:

cutting the time domain matrix array according to the requirements of code length and code rate;

and replacing partial submatrices in the cut time domain matrix array with all-zero submatrices.

The methods provided herein are not inherently related to any particular computer, virtual machine system, or other apparatus. Various general purpose systems may also be used with the teachings herein. The required structure for constructing such a system will be apparent from the description above. Moreover, the present invention is not directed to any particular programming language. It is appreciated that a variety of programming languages may be used to implement the teachings of the present invention as described herein, and any descriptions of specific languages are provided above to disclose the best mode of the invention.

A method for constructing a QC-LDPC code based on finite field fourier transform according to an embodiment of the present invention is described in detail in a specific embodiment with reference to fig. 1 to 4. It is to be understood that the following description is illustrative only and is not intended to be in any way limiting. All similar structures and similar variations thereof adopted by the invention are intended to fall within the scope of the invention.

Fig. 1 is a schematic diagram of a finite field fourier transform-based QC-LDPC code construction method according to an embodiment of the present invention, and the core idea is: firstly, carrying out finite field Fourier transform on the binary vector meeting specific constraint conditions to obtain a frequency domain diagonal matrix. And then carrying out matrix blocking and element transformation on the frequency domain diagonal matrix to obtain a frequency domain permutation matrix. And carrying out finite field inverse Fourier transform and cyclic sub-matrix generation on the frequency spectrum permutation matrix to obtain a time domain matrix array. And finally, performing cutting and masking operation on the time domain matrix array to obtain a check matrix corresponding to the QC-LDPC code.

Specifically, as shown in fig. 1, the method for constructing a QC-LDPC code based on finite field fourier transform according to the embodiment of the present invention includes:

step 1: provided is a frequency domain diagonal matrix generation method.

Let the input binary vector be v ═ (v)₀,v₁,…v_n-1) Wherein the element is 0 or 1, and let all the subscript vectors of the element with value of 1 be a ═ a (a)₀,a₁,…a_r-1) The binary vector needs to satisfy the following specific constraints:

(1) the binary vector length n satisfies: n +1 is a prime number;

(2) the difference between all elements in the subscript vector is different under modulo n operation.

And (3) performing finite field Fourier transform on the binary vector based on a finite field GF (q) to obtain a frequency domain vector with the length of GF (q) being n, wherein the frequency domain vector is taken as a diagonal element, and the other positions are zero elements on GF (q), so that a frequency domain diagonal matrix with the size of n multiplied by n can be obtained.

Example 1: a binary vector of length 42 and 1 element subscript vector (61015232526) satisfies the above constraints. Based on the binary vector, after finite field fourier transform, a frequency domain vector with a length of 42 can be obtained as follows: (28253225251815, 11240195934, 13427227203140, 13521391581, 113330163723, 127171010310), wherein the values represent the power of the primitive 5 in the finite field GF (43), the frequency domain vector is taken as the diagonal element, and the other positions are zero elements on GF (43), so that the frequency domain diagonal matrix with the size of 42 × 42 can be obtained.

Step 2: provided is a frequency domain permutation matrix generation method.

Fig. 2 is a schematic diagram of frequency domain permutation matrix generation. Firstly, partitioning a frequency domain diagonal matrix, namely dividing the frequency domain diagonal matrix of n × n into a matrix array of e × e, wherein the size of each sub-matrix in the matrix array is L × L, and n, e and L are required to meet the relationship that e × L is equal to n. Each sub-matrix in the matrix array is a diagonal matrix or an all-zero matrix, wherein elements in the matrix are obtained by element transformation in a frequency domain diagonal matrix, the transformation mode comprises copying and multiplication or addition operation in a finite domain, and the sub-matrices on the matrix array diagonal are required to be the same. And obtaining a matrix array meeting the requirements after element transformation, namely a frequency domain permutation matrix.

Example 2: the diagonal matrix of 42 × 42 in the frequency domain over GF (43) in example 1 is partitioned, where e is 6 and L is 7, to finally obtain a 6 × 6 matrix array, where each sub-matrix in the matrix array has a size of 7 × 7. Performing element transformation on the frequency domain diagonal matrix to obtain a frequency domain permutation matrix, wherein elements in 11 submatrices of a first row and a first column of the frequency domain permutation matrix are as follows:

A1＝[0 4 8 12 16 20 24]

A2＝[0 4 8 12 16 20 24]

A3＝[0 2 4 6 8 10 12]

A4＝[0 1 2 3 4 5 6]

A5＝[0 3 6 9 12 15 18]

A6＝[0 0 0 0 0 0 0]

A7＝[0 1 2 3 4 5 6]

A8＝[0 4 8 12 16 20 24]

A9＝[0 2 4 6 8 10 12]

A10＝[0 3 6 9 12 15 18]

A11＝[0 5 10 15 20 25 30]

and step 3: a time domain matrix array generating method.

For each sub-matrix in the frequency domain permutation matrix, a vector u-q (u) of length n over gf (q) is generated based on the sub-matrix diagonal elements₀,u₁,…u_n-1) The first L elements in the vector are diagonal elements of the submatrix, and the remaining elements are conjugate vectors of the first L elements, and the vector is subjected to finite field inverse fourier transform over gf (q) to obtain a vector w (w) with a length n₀,w₁,…w_n-1) And taking the first L elements of the vector to form a binary vector with the length of e, taking the vector as a first row, and performing cyclic shift to finally obtain an L multiplied by L binary cyclic sub-matrix. And performing the finite element inverse Fourier transform and the cyclic sub-matrix generation operation on all the sub-matrixes in the frequency domain permutation matrix to finally obtain the time domain matrix array which is formed by the L multiplied by L sub-matrixes and has the size of e multiplied by e. FIG. 3 is a schematic diagram of time domain matrix array generation.

Example 3: for diagonal element a1 of the first sub-matrix over GF (43) in example 2, [04812162024], after supplementing the conjugate vector, performing finite field inverse fourier transform, cyclically shifting the first 7 elements that generate the binary vector, and finally generating a 7 × 7 cyclic sub-matrix:

and 4, step 4: a QC-LDPC code check matrix generation method.

And according to the actual code length and code rate requirements, cutting the time domain matrix array, namely selecting a part of submatrices in the time domain matrix array. In order to improve the performance of the code through row and column readjustment, masking operation is carried out on the extracted partial time domain matrix array, namely, partial submatrices are replaced by all-zero submatrices, the finally obtained matrix array is the check matrix of the QC-LDPC code, and the construction process is finished. FIG. 4 is a schematic diagram of a QC-LDPC code check matrix generated by a time domain matrix array.

In the above process: on the one hand, the whole construction process is systematic with low construction complexity. On the other hand, by flexibly setting row-column replacement, arbitration and mask operation modes, QC-LDPC codes with different parameters can be obtained, so that the method has greater construction flexibility.

It should be noted that the above-mentioned embodiments are only preferred embodiments of the present invention, and are not intended to limit the present invention, and those skilled in the art can make various modifications and changes. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

An embodiment of the second aspect of the present invention provides a QC-LDPC code construction system 1 based on finite field fourier transform, as shown in fig. 5, including:

a frequency domain diagonal matrix constructing unit 10, configured to perform finite field fourier transform on a binary vector that satisfies a specific constraint condition to obtain a frequency domain diagonal matrix, where values of elements in the binary vector are 0 or 1, and the specific constraint condition includes: the length n of the binary vector satisfies: n +1 is a prime number, and the difference values between all elements in the element subscript vector with all elements taking the value of 1 are different under the modulo n operation;

a frequency domain permutation matrix constructing unit 20, configured to perform matrix blocking and element transformation on the frequency domain diagonal matrix in sequence to obtain a frequency domain permutation matrix;

a time domain matrix array constructing unit 30, configured to perform finite field inverse fourier transform and cyclic sub-matrix processing on the frequency domain permutation matrix in sequence to obtain a time domain matrix array;

and the check matrix construction unit 40 is used for sequentially cutting and masking the time domain matrix array to obtain a check matrix corresponding to the QC-LDPC code.

By adopting the embodiment of the invention, on one hand, the whole construction process is systematic and has lower construction complexity. On the other hand, by flexibly setting row-column replacement, arbitration and mask operation modes, QC-LDPC codes with different parameters can be obtained, and the QC-LDPC codes have higher construction flexibility.

On the basis of the above-described embodiment, various modified embodiments are further proposed, and it is to be noted herein that, in order to make the description brief, only the differences from the above-described embodiment are described in the various modified embodiments.

According to some embodiments of the invention, the frequency domain permutation matrix construction unit 20 is configured to:

dividing an n × n frequency domain diagonal matrix into an e × e matrix array, wherein the size of each sub-matrix in the matrix array is L × L, and n, e and L satisfy: e × L ═ n;

determining elements of each sub-matrix in the matrix array based on the frequency domain diagonal matrix by adopting replication and multiplication/addition operation on a finite field, wherein the sub-matrices are all diagonal matrices or all-zero matrices, and the sub-matrices on the diagonal of the matrix array are the same.

According to some embodiments of the invention, the time domain matrix array construction unit 30 is configured to:

for each of the sub-matrices, determining a corresponding first vector of length n, u ═ n (u ═ n)₀,u₁,…u_n-1) The first L elements in the first vector are diagonal elements of the sub-matrix, and the other elements are conjugate vectors of the first L elements;

performing a finite field inverse Fourier transform on the first vector to obtain a second vector of length n, w ═ w (w ═ w)₀,w₁,…w_n-1) The value of the element in the second vector is 0 or 1;

taking the first L elements of the second vector to form a binary vector with the length of e, and taking the binary vector as a first row to perform cyclic shift to obtain an L multiplied by L binary cyclic sub-matrix;

and constructing a time domain matrix array based on the binary cycle submatrices corresponding to all the submatrices.

According to some embodiments of the invention, the check matrix construction unit 40 is configured to:

cutting the time domain matrix array according to the requirements of code length and code rate;

and replacing partial submatrices in the cut time domain matrix array with all-zero submatrices.

Those skilled in the art will appreciate that the various modules or steps of the invention described above can be implemented using a general purpose computing device, that they can be centralized on a single computing device or distributed across a network of computing devices, and that they can alternatively be implemented using program code executable by a computing device, such that the steps illustrated and described herein can be performed by a computing device stored in a memory device and, in some cases, performed in an order different than that used herein, or separately fabricated into various integrated circuit modules, or multiple modules or steps thereof, and implemented as a single integrated circuit module. Thus, the present invention is not limited to any specific combination of hardware and software.

An embodiment of the third aspect of the present invention provides an edge node device, as shown in fig. 6, including: a memory 1010, a processor 1020 and a computer program stored on the memory 1010 and executable on the processor 1020, wherein the computer program when executed by the processor 1020 implements the steps of the method for constructing a QC-LDPC code based on finite field fourier transform as described in the first aspect of the embodiments.

By adopting the embodiment of the invention, on one hand, the whole construction process is systematic and has lower construction complexity. On the other hand, by flexibly setting row-column replacement, arbitration and mask operation modes, QC-LDPC codes with different parameters can be obtained, and the QC-LDPC codes have higher construction flexibility.

Through the above description of the embodiments, those skilled in the art will clearly understand that the method of the above embodiments can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware, but in many cases, the former is a better implementation manner. Based on this understanding, the technical solutions of the present invention may be embodied in the form of software products, which essentially or partially contribute to the prior art.

An embodiment of a fourth aspect of the present invention provides a computer-readable storage medium, where an implementation program for information transmission is stored, and when the program is executed by a processor, the program implements the steps of the method for constructing a QC-LDPC code based on finite field fourier transform as described in the embodiment of the first aspect.

By adopting the embodiment of the invention, on one hand, the whole construction process is systematic and has lower construction complexity. On the other hand, by flexibly setting row-column replacement, arbitration and mask operation modes, QC-LDPC codes with different parameters can be obtained, and the QC-LDPC codes have higher construction flexibility.

It should be noted that the computer-readable storage medium in this embodiment includes, but is not limited to: ROM, RAM, magnetic or optical disks, and the like. The program can be a mobile phone, a computer, a server, an air conditioner, or a network device.

In the present invention, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.

Any reference signs placed between parentheses shall not be construed as limiting the claim. The word "a" or "an" preceding an element does not exclude the presence of a plurality of such elements. The usage of the words first, second and third, etcetera do not indicate any ordering. These words may be interpreted as names.

Similarly, it should be appreciated that in the foregoing description of exemplary embodiments of the invention, various features of the invention are sometimes grouped together in a single embodiment, figure, or description thereof for the purpose of streamlining the invention and aiding in the understanding of one or more of the various inventive aspects. However, the method of the invention should not be construed to reflect the intent: that the invention as claimed requires more features than are expressly recited in each claim. Rather, as the following claims reflect, inventive aspects lie in less than all features of a single foregoing inventive embodiment. Thus, the claims following the detailed description are hereby expressly incorporated into this detailed description, with each claim standing on its own as a separate embodiment of this invention. In some instances, well-known methods, structures and techniques have not been shown in detail in order not to obscure an understanding of this description.