A method for designing LDPC codes for super-Nyquist systems

Abstract

This invention discloses a customized LDPC code design method for super Nyquist systems, comprising: S1, performing polynomial fitting based on the mutual information of the detector input and output of the super Nyquist system; S2, establishing an external information transfer graph analysis of the super Nyquist system based on the polynomial fitting; S3, obtaining infinitely long decoding thresholds for different codes based on the external information transfer graph analysis; S4, masking the original modulus graph basis matrix of the 5G standard LDPC code to minimize the decoding threshold; S5, obtaining the original modulus graph basis matrix with the minimum threshold by searching and expanding it according to the 5G standard to obtain customized LDPC code parity-check matrices with different code lengths and code rates. This invention achieves a performance gain of approximately 0.6 dB or more in traditional Nyquist systems compared to the 5G standard LDPC code at the same spectral efficiency. Furthermore, this invention is applicable to different code lengths and rates, and retains the rate compatibility and raptor-like structure of the original 5G standard LDPC code, achieving backward compatibility and improving system performance.

Description

Technical Field

[0001] This invention belongs to the technical field of digital communication, specifically relating to a design method for LDPC codes used in super Nyquist systems. Background Technology

[0002] Faster-than-Nyquist (FTN) systems, as a signal transmission method that breaks through the traditional Nyquist sampling theorem, aim to provide higher spectral efficiency (SE) than traditional Nyquist systems by transmitting information symbols at a higher rate than the Nyquist rate. This technology was first proposed by Shannon in 1948 and formally introduced by Mazo in 1975. In FTN systems, because the transmission rate of information symbols exceeds the Nyquist rate, the system introduces additional degrees of freedom, making the design and optimization of the coded modulation system more flexible. FTN signals have a Shannon capacity close to that of unconstrained pulse shaping quantities and have been shown to have better performance in non-sinc pulse-shaped Nyquist systems.

[0003] However, the introduction of FTN signals is accompanied by inter-symbol interference (ISI), a characteristic that prevents traditional channel coding designed for Nyquist systems from achieving ideal performance under FTN transmission. Therefore, designing customized channel coding schemes for FTN systems is crucial for improving system performance. Low-density parity-check codes (LDPC codes), as a primary coding scheme in modern communication systems, have been widely applied in modern communication standards such as 5G, DVB-S2, and WiMAX due to their excellent decoding performance. In FTN systems, LDPC codes have also become a research hotspot due to their excellent decoding performance and flexible design features. Existing research on the application of LDPC codes in FTN systems mainly focuses on constructing quasi-cyclic LDPC codes with larger cycle lengths using asymptotic edge growth algorithms, uniform shortening schemes to reduce ISI effects, and directly applying 5G LDPC codes to FTN systems and performing performance simulations. However, these LDPC code construction methods lack sufficient analytical support, especially in decoding threshold analysis, where there is a lack of sufficient theoretical basis for optimization design. The decoding threshold, a crucial indicator for evaluating coding performance, can be obtained through external information transfer graph (EXIT graph) analysis and is an important tool for optimizing LDPC code design. While existing research has explored the numerical upper bound of the information rate after introducing LDPC codes into FTN systems, the complexity of FTN detectors has prevented the accurate determination of the formula or approximate formula for the input-output mutual information function (MI). Therefore, to date, the optimization design of LDPC codes in FTN systems lacks complete EXIT graph analysis, leading to inaccurate calculation of the decoding threshold and making the optimization design of LDPC codes in FTN systems a significant challenge. Summary of the Invention

[0004] The main objective of this invention is to overcome the shortcomings and deficiencies of existing technologies and provide a customized LDPC code design method for super Nyquist systems based on the Ungerboeck observation model. Through EXIT graph analysis, the decoding threshold in FTN systems is accurately predicted, and the design of LDPC codes for FTN systems is optimized based on this analysis. This invention can meet different code rate and code length requirements, designing customized LDPC codes. This not only significantly improves the decoding performance in FTN systems but also retains the rate compatibility and raptor-like structure of 5G standard LDPC codes, ensuring that the system possesses strong flexibility and backward compatibility while improving performance.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] This invention provides a method for designing custom LDPC codes for super Nyquist systems, comprising the following steps:

[0007] (1) Based on the mutual information input to the FTN detector and output mutual information and the current signal-to-noise ratio Polynomial fitting is performed to obtain the relationship between input and output. ;

[0008] (2) Based on the established detector input-output relationship and combined with the external information transfer analysis of LDPC code, the iterative receiver external information transfer analysis based on the Ungerboeck observation model is obtained;

[0009] (3) Based on the external information transfer graph analysis, calculate the minimum signal-to-noise ratio for different codes to converge, given the number of iterations of the external detector and the number of iterations of the internal decoder. This minimum signal-to-noise ratio corresponds to the condition that the posterior mutual information satisfies The minimum value of , where For a very small offset value, Corresponding decoding threshold;

[0010] (4) For sizes of The original pattern of the 5G standard LDPC code is masked to reduce the decoding threshold. Minimum;

[0011] (5) Based on the actual bitrate and bit length requirements, the obtained size is... The original graph of the verification matrix is ​​expanded by the factor of The hash yields a code length of The information bit length is Customized LDPC codes.

[0012] As a preferred technical solution, in step (1), the input-output mutual information of the FTN detector is generated offline; the offline multinomial fitting method includes, but is not limited to, least squares-based and regularized fitting techniques.

[0013] As a preferred technical solution, the detector model includes, but is not limited to, a soft-in, soft-out detector model based on the sum-product algorithm.

[0014] As a preferred technical solution, in step (2), the external information transfer analysis of the LDPC code includes, but is not limited to, the LDPC code constructed through the original model diagram. This analysis is applicable to all LDPC codes constructed in both regular and irregular ways.

[0015] As a preferred technical solution, in step (3), the conditions for satisfying the posterior mutual information include, but are not limited to, conditions based on the target threshold and conditions based on the target error rate.

[0016] As a preferred technical solution, in step (4), the masking operation on the original model image includes, but is not limited to, random masking or masking operation under other search algorithms.

[0017] As a preferred technical solution, in step (4), the 5G standard original model diagram is not subjected to information bit punching processing, so as to obtain the original model diagram of the verification matrix of the FTN system customized LDPC code.

[0018] As a preferred technical solution, the hashing process used in step (5) includes, but is not limited to, hashing methods based on 5G standard matrices.

[0019] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0020] 1. This invention provides a method for fitting the input-output mutual information of an FTN detector based on polynomial fitting, which can effectively fit a soft-input, soft-output FTN detector and provide theoretical support for further decoding performance analysis.

[0021] 2. This invention uses a random masking method to mask the original 5G base map and optimize the design of the original model map by combining the results of threshold analysis. This method can significantly improve the decoding threshold and system performance in FTN systems.

[0022] 3. This invention proposes a customized LDPC code for FTN systems based on the original model diagram, which can meet the requirements of different code lengths and code rates. At the same time, this design retains the rate compatibility and structural characteristics of the original 5G standard LDPC code. Attached Figure Description

[0023] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0024] Figure 1 This is a schematic diagram of the LDPC code design method for the super Nyquist system in Embodiment 1 of the present invention;

[0025] Figure 2 This is the parity check matrix original model diagram structure of the customized LDPC code under the FTN system in Embodiment 2 of the present invention;

[0026] Figure 3This is a schematic diagram of the decoding threshold and simulation performance of 5G standard LDPC code and customized LDPC code under the FTN system in Embodiment 2 of the present invention;

[0027] Figure 4 This is a comparison chart of the simulation performance of customized LDPC codes for FTN systems and 5G LDPC codes for traditional Nyquist systems under the same spectral efficiency and different acceleration factors in Embodiment 3 of the present invention.

[0028] Figure 5 This is a comparison chart of the simulation performance of the customized LDPC code of the FTN system and the 5G LDPC code of the traditional Nyquist system under the same spectral efficiency and different code lengths in Embodiment 4 of the present invention. Detailed Implementation

[0029] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of the present application, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present application without creative effort are within the scope of protection of the present application.

[0030] In this application, the reference to "embodiment" means that a specific feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a mutually exclusive, independent, or alternative embodiment. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described in this application can be combined with other embodiments.

[0031] Example 1

[0032] This embodiment 1 provides a method for designing LDPC codes for super Nyquist systems, such as... Figure 1 As shown, it includes the following steps:

[0033] (1) Based on the mutual information input to the FTN detector and output mutual information and the current signal-to-noise ratio Polynomial fitting is performed to obtain the relationship between input and output. ;

[0034] Furthermore, in step (1), the polynomial fitting method used can be generated offline, including but not limited to least squares-based and regularized fitting techniques.

[0035] (2) Based on the established detector input-output relationship and combined with the external information transfer analysis of LDPC code, the iterative receiver external information transfer analysis based on the Ungerboeck observation model is obtained;

[0036] Furthermore, in step (2), the external information transfer analysis method used is applicable to all LDPC codes, whether regular or irregular in construction.

[0037] (3) Based on the external information transfer graph analysis, calculate the minimum signal-to-noise ratio for different codes to converge, given the number of iterations of the external detector and the number of iterations of the internal decoder. This signal-to-noise ratio corresponds to the condition that the posterior mutual information satisfies The minimum value of , where For a very small offset value, Corresponding decoding threshold;

[0038] (4) For sizes of The original pattern of the 5G standard LDPC code is masked to reduce the decoding threshold. Minimum In particular, the 5G standard prototype diagram used does not perform information bit punching, thus obtaining the original prototype diagram of the parity check matrix of the FTN system customized LDPC code;

[0039] Furthermore, in step (4), the method used for each The order determines whether algebraic decoding needs to be performed, and the basis for this determination includes, but is not limited to, a threshold for the number of cases where the syntactic expression is satisfied or not satisfied.

[0040] (5) Based on the actual bitrate and bit length requirements, the obtained size is... The expansion factor of the original graph of the verification matrix is: The hash is obtained for The information bit length is Customized LDPC codes.

[0041] Furthermore, in step (5), the hashing process used may include, but is not limited to, the matrix hashing method of the 5G standard.

[0042] This invention provides a customized LDPC code design for a Super Nyquist system based on the Ungerboeck model. Through EXIT graph analysis, it accurately predicts the decoding threshold in the FTN system and optimizes the LDPC code design for the FTN system based on this analysis. This invention can meet different code rate and code length requirements, designing customized LDPC codes that not only significantly improve decoding performance in the FTN system but also retain the rate compatibility and raptor-like structure of 5G standard LDPC codes, ensuring that the system possesses strong flexibility and backward compatibility while improving performance.

[0043] Example 2

[0044] Example 2 provides a performance case study of a custom LDPC code design for a Super Nyquist system based on the Ungerboeck model. It considers an FTN system using LDPC encoding and sets the compression factor of the FTN system. The maximum number of external iterations is The maximum number of internal iterations is This system uses three different code constructions. : The LDPC code constructed from the original 5G standard; : Non-punchable LDPC code based on 5G architecture; The FTN system designed in this invention uses customized LDPC codes, with the same information bit length. 7680 and the same bitrate It employs BPSK modulation. Figure 2 The construction of the original model diagram of the parity-check matrix for a customized LDPC code under the FTN system is given, where the red circles indicate the masked positions in the original model diagram. Figure 3 This paper demonstrates the bit error rate (BER) performance of LDPC codes with different constructions in an FTN system, highlighting the effectiveness of customized LDPC codes in FTN systems. It exhibited a lower decoding threshold and better decoding performance, followed by (Based on 5G, constructing LDPC codes without holes), and (LDPC codes constructed based on 5G standards) performed the worst. Specifically, compared to standard 5G LDPC codes, the LDPC code design for the super Nyquist system proposed in this invention had the worst performance in terms of BER. A performance gain of more than 0.4 dB can be obtained at this time.

[0045] Example 3

[0046] This embodiment 3 provides a performance example of a customized LDPC code design for a super Nyquist system based on the Ungerboeck model. Considering an LDPC-coded FTN system using BPSK modulation, the compression factor is... For FTN transmission systems, the LDPC code lengths proposed in this invention are respectively... and And the bitrate is For the Nyquist system, to achieve the same spectral efficiency as the FTN scheme, standard 5G LDPC codes are used, with code lengths consistent with the FTN system. and The bitrate is . Figure 4 The BER performance of the 5G standard LDPC code under Nyquist and the customized LDPC code design for the FTN system proposed in this invention are presented under the same spectral efficiency. It can be seen that compared with the 5G standard LDPC code under the Nyquist system, the customized LDPC code under the FTN system can achieve a performance gain of about 0.6 dB.

[0047] Example 4

[0048] Example 4 provides a performance example of a customized LDPC code design for a super Nyquist system based on the Ungerboeck model. Consider an LDPC-coded FTN system using BPSK modulation, where the FTN compression factors are set to... and For FTN transmission systems, the LDPC code length proposed in this invention is [length missing]. ,in The bitrate at that time , The bitrate at that time To achieve different spectral efficiencies. For Nyquist signal transmission, standard 5G LDPC codes are used, with code lengths consistent with FTN systems. The bitrates are respectively and To achieve the same spectral efficiency as the corresponding FTN scheme. Figure 5 The BER performance of the 5G standard LDPC code under Nyquist conditions and the customized LDPC code design for the FTN system proposed in this invention are presented at the same spectral efficiency. For spectral efficiencies of 0.75 and 0.80 bits per dimension, the code proposed in this invention can achieve coding gains of over 0.6 dB and 0.4 dB, respectively. The results show that the proposed customized LDPC code achieves good coding gains for different compression factors. Both have universal applicability.

[0049] It should be noted that, for the sake of simplicity, the aforementioned method embodiments are all described as a series of actions. However, those skilled in the art should understand that the present invention is not limited to the described order of actions, because according to the present invention, some steps can be performed in other orders or simultaneously.

[0050] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and RAMbus dynamic RAM (RDRAM), etc.

[0051] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0052] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A method for designing customized LDPC codes for super Nyquist systems, characterized in that, Includes the following steps: (1) Based on the mutual information input to the FTN detector and output mutual information and the current signal-to-noise ratio Polynomial fitting is performed to obtain the relationship between input and output. ; (2) Based on the established detector input-output relationship and combined with the external information transfer analysis of LDPC code, the iterative receiver external information transfer analysis based on the Ungerboeck observation model is obtained; (3) Based on the external information transfer graph analysis, calculate the minimum signal-to-noise ratio for different codes to converge, given the number of iterations of the external detector and the number of iterations of the internal decoder. This minimum signal-to-noise ratio corresponds to the condition that the posterior mutual information satisfies The minimum value of , where For a very small offset value, Corresponding decoding threshold; (4) For sizes of The original pattern of the 5G standard LDPC code is masked to reduce the decoding threshold. Minimum; (5) Based on the actual bitrate and bit length requirements, the obtained size is... The original graph of the verification matrix is ​​expanded by the factor of The hash yields a code length of The information bit length is Customized LDPC codes.

2. The method for designing customized LDPC codes for super Nyquist systems according to claim 1, characterized in that, In step (1), the input-output mutual information of the FTN detector is generated offline; the offline multinomial fitting method includes, but is not limited to, least squares-based and regularized fitting techniques.

3. The method for designing customized LDPC codes for super Nyquist systems according to claim 1, characterized in that, The detector model includes, but is not limited to, a soft-in, soft-out detector model based on a sum-product algorithm.

4. The method for designing a customized LDPC code for a super Nyquist system according to claim 1, characterized in that, In step (2), the external information transfer analysis of the LDPC code includes, but is not limited to, LDPC codes constructed through the original model diagram. This analysis is applicable to all LDPC codes constructed in a regular and irregular manner.

5. The method for designing customized LDPC codes for super Nyquist systems according to claim 1, characterized in that, In step (3), the conditions for satisfying the posterior mutual information include, but are not limited to, conditions based on the target threshold and conditions based on the target error rate.

6. The method for designing customized LDPC codes for super Nyquist systems according to claim 1, characterized in that, In step (4), the masking operation on the original model image includes, but is not limited to, random masking or masking operation under other search algorithms.

7. The method for designing customized LDPC codes for super Nyquist systems according to claim 1, characterized in that, In step (4), the 5G standard original model diagram is not subjected to information bit punching, thereby obtaining the original model diagram of the check matrix of the FTN system customized LDPC code.

8. The method for designing customized LDPC codes for super Nyquist systems according to claim 1, characterized in that, In step (5), the hashing process used includes, but is not limited to, hashing methods based on the 5G standard matrix.

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