A method and system for constructing a 3x3 kernel matrix polar code based on pga

Abstract

The application belongs to the technical field of channel coding, and discloses a 3*3 kernel matrix polar code design method and system based on PGA, which generalizes the segment Gaussian approximation (PGA) design method based on 2*2 kernel matrix polar code to 3*3 kernel matrix polar code design. A recursive formula of the log-likelihood ratio mean value of G3 kernel matrix polar code is derived, and a PGA design algorithm of G3 polar code is given. Simulation results show that the FER performance of the 3*3 kernel matrix polar code constructed by the PGA method is better than that of the 3*3 kernel matrix polar code constructed by the exact Gaussian approximation (EGA) and the approximate Gaussian approximation (AGA) methods. The application provides certain reference and reference value for the research in the related field of subsequent larger kernel matrix polar code design. When the application is generalized to G3 kernel matrix polar code design, the FER performance cannot be well exhibited when the code length is short, but the FER performance can be kept when the code length is long.

Description

Technical Field

[0001] This invention belongs to the field of channel coding technology, and particularly relates to a method and system for constructing a 3×3 core matrix polar code based on PGA. Background Technology

[0002] Polar codes are the first channel coding schemes proposed by Professor Arikan in 2009 based on the polarization phenomenon. They are the first to be proven to achieve binary symmetric channel capacity and have low encoding and decoding complexity when the code length approaches infinity.

[0003] Arikan's original polar code is based on a kernel matrix. Yes, its Ts. Kronecker The corresponding code length is Linear block codes. The polarization phenomenon can be generalized to linear block codes of dimension 1. kernel matrix This is called the large kernel matrix. Based on The kernel matrix, for any The frame error rate under SC decoding is ,in , This is called the polarization factor. Through years of research, scholars have now developed numerous polarization kernel matrices with larger polarization factors. Generally, the larger the polarization factor, the faster the polarization speed, thus achieving better decoding performance with shorter code lengths.

[0004] Most current methods for polar code design are based on... The kernel matrix is ​​used for decoding polar codes, and the main methods include the Bach parameter method, density evolution method, Tal-Vardy upper and lower approximation methods, Gaussian Approximation (GA) method, and Monte Carlo (MC) method. These methods produce polar codes with similar decoding performance, with the GA method exhibiting the lowest computational complexity.

[0005] Gaussian Approximation (GA) was first used by Chung in 2001 to construct LDPC codes in AWGN channels. Later, in 2012, Trifonov first applied GA to construct polar codes. Initially, GA was expressed in integral form, known as the Exact Gaussian Approximation (EGA), which had very high computational complexity, increasing exponentially. Chung subsequently provided an approximate algorithm for GA (Approximate GA, AGA), but this method... There is a significant error at certain points, and decoding performance degrades with longer code lengths. In 2004, Ha, Kim, and others proposed a method to approximate AGA using a three-segment function, called HKGA. This method improves upon AGA in terms of... The problem of inaccurate numerical calculations in the vicinity was addressed. In 2022, Oliveira proposed the Piecewise Gaussian Approximation (PGA) method, which, referencing the piecewise format of the HKGA method, further improved decoding performance. Overall, PGA not only eliminates complex integral calculations but also... In kernel matrix polar code design, it has better decoding performance than EGA, AGA and HKGA, regardless of whether the code length is short or long.

[0006] Based on the above analysis, the problems and shortcomings of the existing technology are as follows: the existing polar code design methods have high computational complexity and poor decoding performance. Summary of the Invention

[0007] To address the problems existing in the prior art, this invention provides a method and system for constructing a 3×3 core matrix polar code based on PGA, realizing the design of the corresponding polar code under the AWGN channel.

[0008] This invention is implemented as follows: a method for constructing a 3×3 core matrix polar code based on PGA includes:

[0009] S1, for Polar codes Expression analysis and calculation yielded the recursive formula for the mean log-likelihood ratio (LLR) of a 3×3 core matrix polar code, namely... An expression used to recursively calculate the mean of the bit channel LLR of a polar code;

[0010] S2, for Optimize the function;

[0011] S3 is calculated continuously using the recursive formula in S1 to complete the process. PGA design for polar codes.

[0012] Furthermore, S1 specifically includes:

[0013] The log-likelihood ratio form of the kernel matrix polar code The expression is as follows:

[0014]

[0015] in,

[0016]

[0017] Assuming the input is a zero-codeword, according to The expression yields the following recursive formula for the mean:

[0018]

[0019] in, .

[0020] Furthermore, in S2 The formula for the function is:

[0021] .

[0022] Furthermore, in S3, The PGA design algorithm for polar codes includes:

[0023] S301: Given code length bitrate Design signal-to-noise ratio The unit is decibels (dB). Create a two-dimensional array matrix with n+1 rows and N columns to store the average value generated by each recursive operation.

[0024] S302: Obtain the variance using the formula shown below:

[0025] ;

[0026] S303: Initialize the mean of the channel log-likelihood ratio The mean value of all bit channel LLR values ​​is calculated using a recursive formula. ;

[0027] S304: By sorting, select the value with the smallest value. indivual Corresponding index Write it to the file as a freeze bit.

[0028] Another objective of this invention is to provide a polar code design system based on a PGA-based 3×3 core matrix polar code construction method. This 3×3 core matrix polar code design system includes:

[0029] The recursive calculation module, for Polar codes Expression analysis and calculation yields a recursive formula for the mean LLR of a 3×3 core matrix polar code, which is used to recursively calculate the mean LLR of the bit channel of the polar code.

[0030] The function optimization module is used to optimize functions. Optimize the function;

[0031] The PGA design module uses recursive formulas to continuously calculate and complete... PGA design for polar codes.

[0032] Another object of the present invention is to provide a computer device, the computer device including a memory and a processor, the memory storing a computer program, and when the computer program is executed by the processor, causing the processor to perform the steps of the PGA-based 3×3 core matrix polar code construction method.

[0033] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the PGA-based 3×3 core matrix polar code construction method.

[0034] Another objective of this invention is to provide an information data processing terminal for implementing the aforementioned PGA-based 3×3 core matrix polar code construction system.

[0035] Based on the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solution to be protected by this invention are as follows:

[0036] First, this invention is based on the likelihood ratio form. The expression gives the form of the log-likelihood ratio. Expression deduction All bit channels of the kernel matrix polar code The recursive formula for the mean is used to obtain the set of information bits, thus completing the design of the polar code. The latest PGA calculation method is employed, which has relatively low computational complexity and more accurate numerical calculations. It was first applied to... Based on simulation results, the PGA method for core matrix polar code design exhibits both lower computational complexity and better performance compared to EGA and AGA.

[0037] Second, this invention can be extended to... When designing core matrix polar codes, the 3×3 core matrix polar code designed using the PGA method outperforms the polar codes constructed using the Exact Gaussian Approximation (EGA) and Approximate Gaussian Approximation (AGA) methods in terms of frame error rate (FER). While it doesn't show a significant advantage in FER performance at shorter code lengths, it maintains good FER performance at longer code lengths.

[0038] Third, the technical solution of this invention fills a technological gap in the industry both domestically and internationally: most current methods for polar code design are based on... Based on years of research, numerous polarization kernel matrices with larger polarization factors have been identified, known as large kernel matrices. Generally, the larger the polarization factor, the faster the polarization speed, thus achieving better decoding performance with a shorter code length. This invention applies PGA technology to big-core matrix polar codes to design polar codes with better decoding performance in AWGN channels.

[0039] This invention addresses a long-standing but unresolved technical challenge: polar codes with large kernel matrices exhibit higher polarization rates than those with original 2×2 kernel matrices, resulting in better decoding and error correction performance for the same block length. This invention extends the PGA design method based on 2×2 kernel matrix polar codes to 3×3 kernel matrix polar codes. A recursive formula for the mean log-likelihood ratio of 3×3 kernel matrix polar codes is derived, and a PGA design algorithm for 3×3 kernel matrix polar codes is presented. Simulation results show that the frame error rate of the 3×3 kernel matrix polar codes constructed using the PGA method is superior to that constructed using Exact Gaussian Approximation (EGA) and Approximate Gaussian Approximation (AGA).

[0040] Fourth, a 3×3 core matrix polar code design method based on PGA (Polarization Generating Algorithm). The specific technical advancements for each step are as follows:

[0041] S1: Polar code expression analysis and calculation

[0042] In this step, the polar code expression is analyzed and calculated to obtain a recursive formula for the mean LLR of the 3×3 core matrix polar code. This recursive formula is used to recursively calculate the mean LLR of the bit channel of the polar code. The technical advancement of this step lies in obtaining a specific recursive formula through analysis and calculation, which provides a foundation for subsequent PGA design.

[0043] S2: Function Optimization

[0044] In this step, the relevant functions are optimized. Specifically, this may involve optimizing the calculation steps or parameters in the recursive formula to improve computational efficiency or accuracy. The technological advancement in this step lies in further improving the performance of polar code design by optimizing the relevant functions.

[0045] S3: PGA Design

[0046] Using the recursive formula obtained in S1, polar codes are continuously calculated and generated. PGA is a polar code generation algorithm based on recursive calculation. By repeatedly applying the recursive formula, polar codes of different lengths can be generated. The technological advancement in this step lies in using the PGA method for polar code design, which results in polar codes with good performance characteristics.

[0047] This PGA-based 3×3 core matrix polar code construction method achieves efficient polar code design through three steps: polar code expression analysis and computation, function optimization, and PGA design. Through recursive computation and optimization, the generated polar codes exhibit good performance and efficiency. Attached Figure Description

[0048] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments of the present invention will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0049] Figure 1 This is a flowchart of the method for constructing a 3×3 core matrix polar code based on PGA provided in an embodiment of the present invention;

[0050] Figure 2 This is a schematic diagram of the structure of a 3×3 core matrix polar code construction system based on PGA provided in an embodiment of the present invention;

[0051] Figure 3 The N=2 provided in the embodiment of the present invention 8 A comparative diagram of FER of polar codes designed by EGA, AGA, and PGA methods under the IMSC decoding method.

[0052] Figure 4 The N=3 provided in the embodiment of the present invention 5 N=3 6 N=3 7 A schematic diagram comparing the FER of polar codes designed using the EGA, AGA, and PGA methods under the IMSC decoding method. Detailed Implementation

[0053] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0054] To address the problems existing in the prior art, this invention provides a method and system for constructing a 3×3 core matrix polar code based on PGA. The invention will be described in detail below with reference to the accompanying drawings.

[0055] like Figure 1 As shown, the method for constructing a 3×3 core matrix polar code based on PGA provided in this embodiment of the invention includes:

[0056] S1, for Polar codes Expression analysis and calculation yield the recursive formula for the mean value of the 3×3 core matrix polar code LLR.

[0057] S2, for Optimize the function;

[0058] S3 is calculated continuously using the recursive formula in S1 to complete the process. PGA design for polar codes.

[0059] like Figure 2 As shown, the 3×3 core matrix polar code construction system based on PGA provided in this embodiment of the invention includes:

[0060] The recursive calculation module, for Polar codes Expression analysis and calculation yields a recursive formula for the mean LLR of a 3×3 core matrix polar code, which is used to recursively calculate the mean LLR of the bit channel of the polar code.

[0061] The function optimization module is used to optimize functions. Optimize the function;

[0062] The PGA design module uses recursive formulas to continuously calculate and complete... PGA design for polar codes.

[0063] 1. Polar code design

[0064] The encoding method of polar codes is fixed, and the code length is given. Bitrate Design signal-to-noise ratio and information bit set ( yes The complement of the given information bits determines the corresponding polar code. Code length, code rate, and designed signal-to-noise ratio are usually given before design, so designing a polar code is equivalent to determining the set of information bits. In other words, when the parameter is polar codes ( (Generated from source code) Individual Channel Select the most reliable one Individual channel, with its corresponding index By constructing an information bit set A and using these bit channels to transmit information bits, the design of the polar code is completed. The reliability of a polar channel is generally determined by the symmetric channel capacity. Parity parameters Error probability under maximum likelihood decoding Three indicators are used to measure it. A larger value indicates a more reliable bit channel. and The smaller the value, the more reliable the channel.

[0065] When Arikan discusses channel polarization, he is referring to binary discrete memoryless channels (B-DMC). However, the Bhattacharyya parameters, which need to be calculated when constructing polar codes, are applicable to binary erroneous channels (BEC). BEC is a subset of B-DMC. When the channel is not BEC, such as a binary symmetric channel (BSC) or a binary additive white Gaussian noise channel (B-AWGNC), the applicability of the Bhattacharyya parameters is exceeded, and the individual bits of the channel... However, it is impossible to obtain the exact value. To more accurately estimate the reliability of each bit in the channel polarization, Mori et al. proposed the Density Evolution (DE) construction method, which is applicable to all types of B-DMC. But in most research scenarios, the transmission channel model for channel coding is AWGNC, under which the reliability of each bit in the polarization process can be determined. The distribution of values ​​is approximated by a Gaussian distribution, which is called the Gaussian approximation.

[0066] 2. Gaussian approximation (GA)

[0067] The intermediate values ​​generated by LDPC codes in the BP decoding algorithm can be approximated as symmetric and consistent Gaussian random variables, and the process performed by polar codes in the SC decoding algorithm is essentially the same. Therefore, the intermediate values ​​generated in each iteration of the polarization process can also be approximated as Gaussian random variables. The values ​​are all approximately Gaussian random variables that satisfy symmetry and uniformity. Under B-AWGNC, BPSK modulation is used. If the received signal obtained from the channel is... ,but , where the encoded codeword , It is noise, with a mean of 0 and a variance of . Gaussian distribution .so It is also a Gaussian random variable. Assuming the input is an all-zero codeword, then... Follows Gaussian distribution It is easy to obtain the log-likelihood ratio as:

[0068]

[0069] so It is also a random variable that follows a Gaussian distribution. Based on the properties of expectation and variance, Since the Gaussian distribution is completely determined by its mean and variance, only the mean and variance need to be considered in the calculation of the probability density function. This allows us to obtain... The probability density function is:

[0070]

[0071] It is a random variable Any one of its implementations, from which we can know Since the symmetric consistency condition is satisfied, the mean of the log-likelihood ratio is half the variance. Therefore, the calculation of the probability density function can be simplified to the calculation of the one-dimensional mean, greatly reducing the computational burden.

[0072] Trifonov based on The recursive formula gives Bit channels of kernel matrix polar codes The recursive formula for the mean is as follows:

[0073]

[0074]

[0075] The initial value is:

[0076]

[0077] , These represent bit channels. of Value and The mean of the values.

[0078]

[0079] This uses an integral function, called the Exact Gaussian Approximation (EGA), to give the error probability for each bit channel:

[0080]

[0081] in,

[0082] .

[0083] 3. Polar codes Recursive calculation of the mean

[0084] Based on The piecewise Gaussian approximation (PGA) design method for kernel matrix polar codes is extended to kernel matrices where... The design of polar codes, in which .and The design of the kernel matrix polar code is the same. The key to designing a core matrix polar code also lies in determining the set of information bits A, which is given below. The design process of PGA for kernel matrix polar codes.

[0085] Based on likelihood ratio The expression is easy to give Log-likelihood ratio form The expression is as follows:

[0086]

[0087] in,

[0088] .

[0089] The priority of is higher than +, which can be noted. They are all random variables, and They are independently and identically distributed. Taking the average of both sides of the above equation after transformation yields:

[0090]

[0091] make , ,make , , Then expand the above equation using the definition of expectation:

[0092]

[0093] make It is a function that is monotonically decreasing on [0, +∞). .Will Substituting the function into the above equation, we get...

[0094]

[0095] Assuming the input is a zero-codeword, according to Following the same method, we can obtain the following recursive formula:

[0096]

[0097]

[0098]

[0099] in, That's how we got it. Kernel matrix polar code The recursive formula for the mean.

[0100] 4. Function optimization

[0101] Because EGA uses complex integration operations, its computational complexity becomes extremely high as the code length increases. Furthermore, EGA also suffers from a numerical problem: when x is very large... It can arbitrarily approach zero, resulting in numerical inaccuracies. Therefore, the AGA method is presented, in which... The function is shown in the following formula:

[0102]

[0103] Furthermore, due to the AGA method in At this point, the function value is greater than 0, causing numerical errors and degrading the performance of the constructed polar code when the code length is long. In this embodiment of the invention, the improved method PGA is used, expressed as follows. This is a three-segment expression obtained by exhaustive search to find the minimum FER, which eliminates the complex integral calculations compared to EGA, and improves upon the... Place, The problem is that this approximation improves accuracy, but it is still composed of transcendental functions.

[0104]

[0105] 5. PGA design algorithm for polar codes

[0106] The codeword length is calculated continuously using a recursive formula. ,exist Select from the individual channel The largest mean The index corresponding to each digit channel is used as the information bit set. This completes the design of the polar code. The algorithm mainly consists of the following steps:

[0107] Step 1: Given the code length bitrate Design signal-to-noise ratio The unit is decibels (dB). Create a two-dimensional array matrix with n+1 rows and N columns to store the average value generated by each recursive operation.

[0108] Step 2: Obtain the variance using the formula shown below:

[0109] .

[0110] Step 3: Initialize the mean of the channel log-likelihood ratio The mean value of all bit channel LLR values ​​is calculated using a recursive formula. .

[0111] Step 4: Sort the values ​​and select the smallest ones. indivual Corresponding index Write it to the file as a freeze bit.

[0112] An application embodiment of the present invention provides a computer device, which includes a memory and a processor. The memory stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of a PGA-based 3×3 core matrix polar code construction method.

[0113] An application embodiment of the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of a PGA-based 3×3 core matrix polar code construction method.

[0114] An application embodiment of the present invention provides an information data processing terminal, which is used to implement a 3×3 core matrix polar code construction system based on PGA.

[0115] Based on the file containing freeze bit information, all freeze bits are set to 0, and the PGA method is designed accordingly. The polar code is decoded using IMSC to obtain FER performance, which is then compared with other methods. The specific algorithm is shown below:

[0116] 1. Input: Code length bitrate Design signal-to-noise ratio;

[0117] 2. Output: Average ratio of the logarithmic likelihood ratio for each bit channel. ;

[0118] 3. Initialize the mean of the channel log-likelihood ratio:

[0119]

[0120] 4.

[0121]

[0122]

[0123]

[0124]

[0125] / / in

[0126]

[0127]

[0128] 5. / / save

[0129]

[0130]

[0131] 6. Select the largest one indivual Corresponding index Constitutes a set of information bits .

[0132] Figure 3 It is a code length of 2 8 The results at 256 show that the polar codes designed by the PGA method have better FER performance than those designed by the EGA and AGA methods. Figure 4 The design has a signal-to-noise ratio of 2.0dB and code lengths of [missing information]. , , The code rate is 0.5, and the decoding stops when the number of erroneous frames reaches 200. A comparison of the FER (Fault Emission Rate) of polar codes designed using the EGA, AGA, and PGA methods under the IMSC decoding algorithm is presented. Simulation results show that the polar codes designed using the PGA method outperform those designed using the EGA and AGA methods, with a more significant improvement at longer code lengths.

[0133] This invention provides a method and system for deriving an improved set of polar code information bits for a given input code length, code rate, and design signal-to-noise ratio. The polar code construction method of this embodiment can be applied to terminal devices, specifically those with storage and data processing capabilities. The method provided in this invention selects the set of information bits and frozen bits before polar code encoding. Polar code encoding is then performed at the transmitting end, transmitted via binary input AWGN, and decoded at the receiving end using the IMSC (Improved Sequential Cancellation) algorithm. Compared to the EGA and AGA algorithms for polar code construction, the PGA polar code construction method provided in this invention has a better frame error rate. That is, after constructing the polar code using the method provided in this invention, the receiving end receives more complete information.

[0134] The embodiments of the present invention have achieved some positive results during the research and development or use process, and have indeed great advantages compared with the prior art. The following content describes them in conjunction with the data, charts and other information of the experimental process.

[0135] The following is combined Figure 3 , Figure 4The polar code construction method provided by this invention has a better frame error rate (FER). The signal-to-noise ratio is designed with BPSK, B-AWGNC, IMSC, G2 kernel matrix, R=1 / 2, and 2.0dB. The simulation loop uses 200 frames of error count as the stopping criterion. The results are as follows... Figure 3 As shown, the FER performance of polar codes designed using the PGA method is superior to that of polar codes designed using the EGA and AGA methods. Furthermore, in the embodiments presented in this paper, we compared the EGA, AGA, and PGA methods at a block length of N=3. 5 =243、N=3 6 =729 and N=3 7 Frame error rate performance at 2187. Similarly, we simulated the signal-to-noise ratio (SNR) for BPSK modulation, B-AWGNC channel, IMSC decoding, G3 kernel matrix, R=1 / 2, and 2.0dB design. Compared to the EGA and AGA methods, we observed a significant improvement in FER for the PGA method. Furthermore, the improvement is even more pronounced with longer code lengths.

[0136] The following are two specific application examples and their implementation schemes:

[0137] Application Example 1: Target Recognition Based on Multi-View Features

[0138] 1. Data Acquisition: Collect a dataset of multi-view images containing the target object.

[0139] 2. Preprocessing: Preprocessing the image data, such as image enhancement and size unification.

[0140] 3. Model building: Convolutional Neural Network (CNN) is used as the basic model, and the network structure is designed according to actual needs.

[0141] 4. Multi-view feature extraction: Introduce a multi-view feature extraction module into the network. For example, input images from multiple views into different branches of the network and extract feature representations for each view through convolution operations.

[0142] 5. Feature fusion: Features extracted from different perspectives can be fused using methods such as convolutional operations and fully connected layers.

[0143] 6. Target recognition: Input the fused features into the classifier to perform target recognition and classification.

[0144] 7. Model Training and Optimization: Train the model using the labeled dataset and optimize it, such as defining the loss function and adjusting the learning rate.

[0145] 8. Model Evaluation: Use the test set to evaluate the model's performance, such as accuracy and recall.

[0146] Application Example 2: PGA-based Communication Channel Coding

[0147] 1. Polar code parameter selection: Select appropriate polar code length and dimension based on the characteristics and requirements of the communication channel.

[0148] 2. Polar code generation matrix construction: Based on the PGA algorithm, construct the polar code generation matrix with the corresponding length and dimensions.

[0149] 3. Allocation of information bits and check bits: Determine the allocation scheme of information bits and check bits according to the requirements of the communication system.

[0150] 4. Encoder Design: Using a polar code generation matrix and bit allocation scheme, design an encoder module to encode the input information bits into a polar code sequence.

[0151] 5. Channel modulation: Modulating the polar code sequence into a symbol sequence, for example, by using modulation techniques such as QAM, PSK, etc.

[0152] 6. Channel transmission: Transmitting the modulated symbol sequence through a channel, which may include channel coding, modulation, modulation and demodulation.

[0153] 7. Channel demodulation: The receiver demodulates the transmitted symbol sequence to recover the received polar code sequence.

[0154] 8. Decoder Design: Using the polar code generation matrix and bit allocation scheme, design a decoder module to decode the received polar code sequence and recover the original information bit sequence.

[0155] 9. Information Decoding: Further processing of the decoded information bit sequence, such as decryption and error correction.

[0156] 10. Performance Evaluation: Performance evaluation is conducted through simulated or actual communication systems, including the measurement of metrics such as bit error rate and bit error rate.

[0157] It should be noted that embodiments of the present invention can be implemented in hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuitry such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field-programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of the above-described hardware circuitry and software, such as firmware.

[0158] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for constructing a 3×3 core matrix polar code based on PGA, characterized in that, include: S1, by analyzing and calculating the l-expression of the G3 polar code, a recursive formula for the mean LLR of the 3×3 core matrix polar code is obtained, which is used to recursively calculate the mean LLR of the bit channel of the polar code. S2, optimize the φ function; S3, using the recursive formula in S1 to continuously calculate, completes the PGA design of the G3 polar code; S1 specifically includes: The L-expression of the G3 log-likelihood ratio is as follows: ； ； ； in, ； Assuming the input is an all-zero codeword, according to the L-expression, we can obtain the following recursive formula: ； ； ； Where i = 1, 2, ..., N, N = 3m, (m = 0, 1, 2...); The formula for the φ function in S2 is: ； In S3, the PGA design algorithm for G3 polar codes includes: S301: Given a code length N = 3n and a code rate R = K / N, design a signal-to-noise ratio (DSNR) in decibels. Create a two-dimensional array matrix with n+1 rows and N columns to store the mean value generated by each recursive operation. S302: Obtain the variance using the formula shown below: ； S303: Based on the mean of the initial channel log-likelihood ratio Calculate the mean LLR value of all bit channels using a recursive formula. ; S304: By sorting, select the NK values ​​with the smallest values. Write the corresponding index i to the file as the freeze bit; The polar code is encoded at the sending end and then transmitted via binary input AWGN.

2. A PGA-based 3×3 core matrix polar code construction system, which applies a PGA-based 3×3 core matrix polar code construction method, comprising: The recursive calculation module is used to recursively calculate the LLR mean of polar codes to obtain the recursive formula for the LLR mean of 3×3 core matrix polar codes. The function optimization module is used to optimize the φ function; The PGA design module uses recursive formulas to continuously calculate and complete the PGA design of the G3 polar code.

3. A computer device, comprising a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of the method for constructing a 3×3 core matrix polar code based on PGA as described in claim 1.

4. A computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the PGA-based 3×3 core matrix polar code construction method as described in claim 1.

5. An information data processing terminal, the information data processing terminal being used to implement the PGA-based 3×3 core matrix polar code construction system as described in claim 2.

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