Finite geometric code decoding method and system based on generalized check matrix

Abstract

The invention discloses a finite geometric code decoding method and system based on a generalized check matrix, and relates to the communication technology, and the method comprises the following steps: constructing a corresponding generalized check matrix according to an algebraic structure of a multi-step large number logic decodable finite geometric code; sending a finite geometric code sequence, transmitting the sequence after coding and BPSK modulation, and receiving a posterior probability log-likelihood ratio sequence by a receiving end; and carrying out iterative decoding on the finite geometric code received by the receiving end based on the constructed generalized check matrix. According to the invention, a new generalized check matrix is constructed according to the algebraic structure of the finite geometric code, and multi-step large-number logic iterative decoding is carried out on the finite geometric code based on the matrix, so that the iterative decoding performance of the multi-step large-number logic decodable finite geometric code is improved.

Description

Technical Field

[0001] This application relates to the field of communication technology, and in particular to a finite geometric code decoding method and system based on a generalized parity-check matrix. Background Technology

[0002] In recent years, driven by the rapid development of digital and intelligent technologies, optical communication and storage systems have placed higher demands on the performance of forward error correction schemes. With the gradual maturation and application of Turbo codes, LDPC codes, and Polar codes, iteratively decodable codes have received increasing attention. A common problem is that when the code length is short, iteratively decodable codes often have a relatively small minimum distance, meaning their decoding performance may not significantly improve with increasing signal-to-noise ratio (SNR), and may even deteriorate. From the perspective of performance curves, this manifests as a sudden change in the slope of the error rate curve in the high SNR region, i.e., the appearance of an error flattening. Increasing the minimum distance of the code is an important method to improve the performance of error flattening.

[0003] Compared to the iteratively decodable codes mentioned above, finite geometric codes based on finite geometric constructions possess excellent minimum distance properties. Although their parity-check matrix may contain numerous short cycles of length 4, leading to poor performance in iterative decoding, from the code's perspective, the large minimum distance inherently gives finite geometric codes an advantage over other iteratively decodable codes. Furthermore, due to the construction method of finite geometric codes, these codes possess rich algebraic structures, providing more usable resources for iterative decoding. Therefore, improving the iterative decoding performance of finite geometric codes is a very meaningful research topic.

[0004] Finite geometric codes are constructed from the associative structures of finite geometry (Euclidean or projective geometry). They are a class of large number logic decodable codes, exhibiting cyclic or quasi-cyclic characteristics and possessing a good algebraic structure. Large number logic decoding algorithms, as a type of hard-decision decoding algorithm, have the advantages of simple implementation, fast decoding speed, and no need for large storage space, and are widely used in engineering practice. However, this algorithm only provides moderate error correction capability and has low coding gain.

[0005] For one-step large number logic decodable finite geometric codes, besides using large number logic decoding algorithms, they also exhibit good decoding performance under traditional iterative decoding algorithms, such as LDPC codes constructed based on points and lines in finite geometry. For multi-step large number logic decodable finite geometric codes, hard-decision large number logic decoding algorithms can also be used. However, in soft-decision iterative decoding, the performance of traditional iterative decoding algorithms is limited due to the influence of the 4-ring in the factor graph. Research on decoding algorithms for such codes mainly focuses on how to reduce or avoid the influence of short rings and improve iterative decoding performance. Constructing a generalized parity-check matrix (GPCD) for decoding is an effective method to avoid the influence of short rings. Such matrices are designed by introducing extended bits and extended parity rows into the original GPCD, and are often constructed using computer search methods. However, for finite geometric codes constructed based on finite geometry, their algebraic structure characteristics are not utilized for GPCD construction. Summary of the Invention

[0006] This application provides a finite geometric code decoding method and system based on a generalized parity-check matrix, which is used to improve the iterative decoding performance of multi-step large number logic translatable finite geometric codes.

[0007] This application provides a finite geometric code decoding method based on a generalized parity-check matrix, comprising the following steps: Construct the corresponding generalized parity-check matrix based on the algebraic structure of multi-step large number logic-decipherable finite geometric codes. ; Sending finite geometric code sequences The sequence is transmitted after encoding and BPSK modulation. The receiving end receives the posterior probability log-likelihood ratio sequence. ; Based on the constructed generalized parity-check matrix Iterative decoding is performed on the finite geometric code received at the receiving end.

[0008] This application also provides a finite geometric code decoding system based on a generalized parity-check matrix, including a processor and a memory. The memory stores a computer program, which, when executed by the processor, implements the steps of the finite geometric code decoding method based on a generalized parity-check matrix as described above.

[0009] The method in this application constructs a new generalized parity check matrix based on the algebraic structure of finite geometric codes, and performs multi-step large number logic iterative decoding on finite geometric codes based on this matrix, thereby improving the iterative decoding performance of multi-step large number logic translatable finite geometric codes.

[0010] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, specific embodiments of this application are given below. Attached Figure Description

[0011] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of this application. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings: Figure 1 This is a basic flowchart illustrating the finite geometric code decoding method based on the generalized parity-check matrix in this application embodiment; Figure 2 This is a block diagram of a digital communication system model used in the method of the embodiments of this application; Figure 3 This is a schematic diagram of the generalized parity check matrix constructed in the method of the embodiments of this application; Figure 4 This is a submatrix in the generalized parity-check matrix of the (7, 4) finite geometric code under the method of the embodiments of this application. B Structural diagram; Figure 5 This is a comparison of the decoding performance of the method in the embodiments of this application with that of other algorithms for (63, 48) finite geometric codes; Figure 6 This is a comparison of the decoding performance of the method in the embodiments of this application with that of other algorithms for (511, 448) finite geometric codes. Detailed Implementation

[0012] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented 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 disclosure to those skilled in the art.

[0013] This application provides a finite geometric code decoding method based on a generalized parity-check matrix, such as... Figure 1 As shown, it includes the following steps: In step S101, the corresponding generalized parity-check matrix is ​​constructed based on the algebraic structure of the multi-step large number logic-decorative finite geometric code. In some instances of this invention (decoding of finite geometric codes constructed based on points and two-dimensional planes in Euclidean geometry, such as the decoding of (7, 4), (63, 48), and (511, 448) codes), the constructed generalized parity-check matrix... include , , , There are a total of 4 submatrices; The generalized parity check matrix The verification nodes are divided into two parts: the upper verification node represents a two-dimensional plane in Euclidean geometry, and the lower verification node represents a straight line in Euclidean geometry. The generalized parity check matrix The variable nodes are divided into two parts: the variable nodes on the left represent points in Euclidean geometry, and the variable nodes on the right represent lines in Euclidean geometry.

[0014] The generalized parity check matrix The four submatrices connect points, lines, and two-dimensional planes in Euclidean geometry, where: The generalized parity check matrix The submatrix at the top left It is an all-zero matrix; upper right submatrix A matrix consisting of lines and two-dimensional planes is obtained by expanding each two-dimensional plane in Euclidean geometry using different forms of lines. A two-dimensional plane has... J +1 different ways to expand a straight line, corresponding to the submatrix In J +1 row, each row has a row weight of J ,in J The number of two-dimensional planes orthogonal to the same straight line. J The code length of finite geometric codes N satisfy Quantitative relationships; the submatrix in the lower left corner. This is a matrix composed of points and lines in Euclidean geometry; the submatrix in the lower right corner. As an identity matrix, the entire matrix It does not contain ring 4.

[0015] In step S102, a finite geometric code sequence is sent to the receiving end. The sequence is encoded and modulated using BPSK and then transmitted in an AWGN channel. The receiver receives the posterior probability log-likelihood ratio sequence. , , N The code length is a finite geometric code.

[0016] In step S103, based on the constructed generalized parity-check matrix Iterative decoding is performed on the finite geometric code received at the receiving end. In one application example of this application, in the decoding of finite geometric codes constructed based on points and two-dimensional planes in Euclidean geometry, such as the decoding of (7, 4), (63, 48), and (511, 448) codes, step S103 includes (assuming the current iteration number is...). k The maximum number of iterations is K. max ): Define the Euclidean geometry of a plane that does not contain the origin or pass through the origin. The CCP A straight line, using It means, Represents a straight line Given a set of indices of interior points, calculate the log-likelihood ratio of all lines: make Indicates the presence of a straight line The t A set of indices of lines in a two-dimensional plane (excluding lines) (in addition) Calculate the submatrix The sum of log-likelihood ratios for two-dimensional planes orthogonal to the same line (excluding the orthogonal line): .

[0017] In some embodiments, based on the constructed generalized parity-check matrix Iterative decoding of the finite geometric code received at the receiver also includes: For every point in finite geometry , : In the submatrix Based on the connection between a point and the line passing through that point, calculate the log-likelihood ratio of the line (excluding the point itself): in, Indicates the containing point The y Index of a straight line, ; Will The log-likelihood ratio of each straight line is calculated by summing the log-likelihood ratios of the two-dimensional plane orthogonal to the lines, thus obtaining all points passing through the lines. The sum of external information transmitted from the two-dimensional plane.

[0018] In some embodiments, based on the constructed generalized parity-check matrix Iterative decoding of the finite geometric code received at the receiver also includes: averaging the sum of the external information and comparing it with the initial channel message at that point. Add: Multiply the sum by the correction factor. to complete point News update: .

[0019] In some embodiments, the method further includes: repeating the decoding process iteratively until decoding is successful or the maximum number of iterations is reached, and outputting the final decoding result.

[0020] Figure 2 This is a block diagram of the digital communication system model used in the embodiments of this application. Without loss of generality, taking a two-step large-number logic-decorative finite geometric code constructed based on points and two-dimensional planes in Euclidean geometry as an example (such as (7, 4), (63, 48), (511, 448) finite geometric codes), the decoding method of finite geometric codes based on a generalized parity-check matrix is ​​introduced: Step A1: Construct the corresponding generalized parity-check matrix based on the algebraic structure of the multi-step large number logic-decipherable finite geometric code. ,like Figure 3 and Figure 4 As shown, the code length of the finite geometric code is N .

[0021] 1a) Figure 3 Generalized parity check matrix in Depend on , , , It consists of 4 sub-matrices, the one in the upper left corner. A matrix consisting entirely of zeros; the upper right submatrix This is a matrix composed of lines and two-dimensional planes, obtained by expanding each two-dimensional plane in Euclidean geometry using different forms of lines; the submatrix in the lower left corner. This is a matrix composed of points and lines in Euclidean geometry; the submatrix in the lower right corner. It is an identity matrix. Determine the submatrices. After constructing the structure, a submatrix can be built based on the lines represented by each column and the points within those lines. Both and the all-zero matrix and identity matrix Together they form a matrix .

[0022] 2b) Figure 4 The matrix in the matrix is ​​a generalized parity-check matrix constructed based on the algebraic structure of the (7, 4) finite geometric code. Neutron matrix The structural diagram shows that, due to the presence of 7 two-dimensional planes and 21 lines in this finite geometry, with 2 two-dimensional planes orthogonal to the same line, and each two-dimensional plane consisting of 2 lines with 3 possible ways to expand the lines, the submatrix in the diagram... The size is 21 rows × 21 columns, and the row weight is 2.

[0023] Step A2: Send a finite geometric code sequence The sequence is encoded and modulated using BPSK and then transmitted in an AWGN channel. The receiver receives the posterior probability log-likelihood ratio sequence. , .

[0024] Step A3: Iteratively decode the multi-step large number logic translatable finite geometric code based on the constructed generalized parity check matrix.

[0025] In the k In this iteration (the maximum number of iterations is K) max ): A3a) First, calculate the log-likelihood ratio of all lines in the finite geometry according to the following formula: in Represents a straight line in finite geometry, with a total of strip, Represents a straight line The set of indices of interior points .

[0026] A3b) Then calculate the submatrix according to the following formula. The sum of log-likelihood ratios for two-dimensional planes orthogonal to the same line (excluding the orthogonal line): in Indicates the presence of a straight line The t A set of indices of lines in a two-dimensional plane (excluding lines) Besides), there are a total of J A two-dimensional plane like this, J This represents the number of two-dimensional planes orthogonal to the same straight line.

[0027] A3c) For every point in a finite geometry First in the submatrix The log-likelihood ratio of the line is calculated using the following formula (excluding that point): in, Indicates the containing point The y The index of the line, totaling A straight line like this; then according to the following formula The log-likelihood ratio of each straight line is calculated by summing the log-likelihood ratios of the two-dimensional plane orthogonal to the lines, and the average of these values ​​is then compared with the initial channel message at that point. Add: Finally, multiply the result of the above calculation by the correction factor. You can complete the point. The message update is as follows: A3d) Repeat the above iterative decoding process to output the final decoding result.

[0028] The finite geometric code decoding method based on the generalized parity-check matrix applied in this application is shown in Table 1 for simulation parameters. Table 1 Simulation parameters of the decoding method in this application parameter value (Code length, information bit length) (63, 48)、(511, 448) Modulation method BPSK Channel AWGN Maximum number of iterations 30 Correction factor 0.45、0.65 Simulation Results and Analysis Figure 5 The red solid line marked with a cross in the middle represents the bit error rate performance of the two-step large number logic hard decision decoding algorithm for decoding (63, 48) finite geometric codes under BPSK modulation and AWGN channel model.

[0029] Figure 5 The red dotted lines marked with crosses represent the frame error rate performance of the two-step large number logic hard decision decoding algorithm for decoding (63, 48) finite geometric codes under BPSK modulation and AWGN channel model.

[0030] Figure 5 The green solid line marked with a right triangle in the middle represents the bit error rate performance of the sum-product decoding algorithm for decoding (63, 48) finite geometric codes under BPSK modulation and AWGN channel model, with a maximum number of iterations of 30.

[0031] Figure 5 The green dotted line marked with a right triangle in the middle represents the frame error rate performance of the sum-product decoding algorithm for decoding (63, 48) finite geometric codes under BPSK modulation and AWGN channel model, with a maximum number of iterations of 30.

[0032] Figure 5 The light blue solid line marked with a left-hand triangle represents the bit error rate performance of the proposed method for decoding (63, 48) finite geometric codes under BPSK modulation and AWGN channel models. The maximum number of iterations is 30, and the correction factor is [missing value]. .

[0033] Figure 5 The light blue dotted line marked with a left triangle represents the frame error rate performance of the proposed method for decoding (63,48) finite geometric codes under BPSK modulation and AWGN channel models. The maximum number of iterations is 30, and the correction factor is [missing information]. .

[0034] Figure 6 The red solid line marked with a cross in the middle represents the bit error rate performance of the two-step large number logic hard decision decoding algorithm for decoding (511, 448) finite geometric code under BPSK modulation and AWGN channel model.

[0035] Figure 6 The red dotted lines marked with crosses represent the frame error rate performance of the two-step large number logic hard decision decoding algorithm for decoding (511, 448) finite geometric codes under BPSK modulation and AWGN channel model.

[0036] Figure 6 The green solid line marked with a right triangle in the middle represents the bit error rate performance of the sum-product decoding algorithm for decoding the (511, 448) finite geometric code under the BPSK modulation and AWGN channel model, with a maximum number of iterations of 30.

[0037] Figure 6 The green dotted line marked with a right triangle represents the frame error rate performance of the sum-product decoding algorithm for decoding the (511, 448) finite geometric code under the BPSK modulation and AWGN channel model, with a maximum number of iterations of 30.

[0038] Figure 6 The light blue solid line marked with a left-hand triangle represents the bit error rate performance of the proposed method for decoding (511, 448) finite geometric codes under BPSK modulation and AWGN channel models. The maximum number of iterations is 30, and the correction factor is [missing value]. .

[0039] Figure 6 The light blue dotted line marked with a left triangle represents the frame error rate performance of the proposed method for decoding (511, 448) finite geometric codes under BPSK modulation and AWGN channel models. The maximum number of iterations is 30, and the correction factor is [missing value]. .

[0040] from Figure 5 and Figure 6 Simulation results show that the finite geometric code decoding method based on the generalized parity-check matrix proposed in this application can improve the iterative decoding performance of multi-step large number logic translatable finite geometric codes; taking the (63, 48) finite geometric code as an example, with a bit error rate of 10... -5 Or a frame error rate of 10-4 At that time, the decoding performance of the method proposed in this invention has an improvement of about 0.2dB compared with the sum-product decoding algorithm, and is significantly better than the decoding performance of the multi-step large number logic hard decision decoding algorithm; taking the (511, 448) finite geometric code as an example, with a bit error rate of 10 -5 Or a frame error rate of 10 -4 At the same time, the decoding performance of the method proposed in this invention has an increase of about 0.5dB compared with the sum-product decoding algorithm, and is also significantly better than the decoding performance of the multi-step large number logic hard decision decoding algorithm.

[0041] This application also proposes a finite geometric code decoding system based on a generalized parity-check matrix, including a processor and a memory. The memory stores a computer program, which, when executed by the processor, implements the steps of the aforementioned finite geometric code decoding method based on a generalized parity-check matrix.

[0042] It should be noted that, in the embodiments of this application, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0043] The sequence numbers of the embodiments in this application are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0044] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) and includes several instructions to cause a terminal (which may be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods described in the various embodiments of this application.

[0045] The embodiments of this application have been described above with reference to the accompanying drawings. However, this application is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of this application without departing from the spirit and scope of the claims. All of these forms are within the protection scope of this application.

Claims

1. A finite geometric code decoding method based on a generalized parity-check matrix, characterized in that, Includes the following steps: Construct the corresponding generalized parity-check matrix based on the algebraic structure of multi-step large number logic-decipherable finite geometric codes. ; Sending finite geometric code sequences The sequence is transmitted after encoding and BPSK modulation. The receiving end receives the posterior probability log-likelihood ratio sequence. ; Based on the constructed generalized parity-check matrix Iterative decoding is performed on the finite geometric code received at the receiving end.

2. The finite geometric code decoding method based on a generalized parity-check matrix as described in claim 1, characterized in that, The constructed generalized parity-check matrix include , , , There are a total of 4 submatrices; The generalized parity check matrix The verification nodes are divided into two parts: the upper verification node represents a two-dimensional plane in Euclidean geometry, and the lower verification node represents a straight line in Euclidean geometry. The generalized parity check matrix The variable nodes are divided into two parts: the variable nodes on the left represent points in Euclidean geometry, and the variable nodes on the right represent lines in Euclidean geometry.

3. The finite geometric code decoding method based on a generalized parity-check matrix as described in claim 2, characterized in that, The generalized parity check matrix The four submatrices connect points, lines, and two-dimensional planes in Euclidean geometry, where: The generalized parity check matrix upper left submatrix A matrix consisting entirely of zeros; the upper right submatrix This is a matrix composed of lines and two-dimensional planes, obtained by expanding each two-dimensional plane in Euclidean geometry using different forms of linear expansion; the submatrix in the lower left corner. This is a matrix composed of points and lines in Euclidean geometry; the submatrix in the lower right corner. It is a unit array.

4. The finite geometric code decoding method based on a generalized parity-check matrix as described in claim 3, characterized in that, Based on the constructed generalized parity-check matrix Iterative decoding of the finite geometric code received at the receiving end includes: Define the Euclidean geometry of a plane that does not contain the origin or pass through the origin. The CCP A straight line, using It means, Represents a straight line Given a set of indices of interior points, calculate the log-likelihood ratio of all lines: make Indicates including lines excluding lines Outside, straight line The t A set of indices of lines contained in a two-dimensional plane. Calculate the submatrix that excludes the orthogonal line. The sum of log-likelihood information for two-dimensional planes orthogonal to the same straight line: 。 5. The finite geometric code decoding method based on a generalized parity-check matrix as described in claim 4, characterized in that, Based on the constructed generalized parity-check matrix Iterative decoding of the finite geometric code received at the receiver also includes: For every point in finite geometry , : In the submatrix Based on the connection between a point and the straight line passing through that point, calculate the log-likelihood ratio of all straight lines except that point: in, Indicates the containing point The y Index of a straight line, ; Will The log-likelihood ratio of each straight line is calculated by summing the log-likelihood ratios of the two-dimensional plane orthogonal to the lines, thus obtaining all points passing through the lines. The sum of external information transmitted from the two-dimensional plane.

6. The finite geometric code decoding method based on a generalized parity-check matrix as described in claim 5, characterized in that, Based on the constructed generalized parity-check matrix Iterative decoding of the finite geometric code received at the receiver also includes: averaging the sum of the external information and comparing it with the initial channel message at that point. Add: Multiply the sum by the correction factor. to complete point News update: 。 7. The finite geometric code decoding method based on a generalized parity-check matrix as described in claim 6, characterized in that, Also includes: Repeat the decoding process iteratively until decoding is successful or the maximum number of iterations is reached, and then output the final decoding result.

8. A finite geometric code decoding system based on a generalized parity-check matrix, characterized in that, It includes a processor and a memory, wherein the memory stores a computer program that, when executed by the processor, implements the steps of the finite geometric code decoding method based on a generalized parity-check matrix as described in any one of claims 1 to 7.

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