A Neural Decoding Method and System for Cyclic Codes Based on Geometric Perception Topological Mapping

Abstract

This invention relates to the field of channel decoding technology, and provides a cyclic code neural decoding method and system based on geometrically perceptual topological mapping. The method includes: for the cyclic code transmitted by the transmitter, calculating a parity-check matrix, continuously cyclically shifting the row vectors of the parity-check matrix to expand it into a cyclic square matrix, and mapping the bit indices of the cyclic code to physical phase angles in polar coordinates; for the channel output value received by the receiver, extracting the amplitude, calculating the parity index based on the cyclic square matrix, concatenating the amplitude and the parity index, and obtaining initial node features through linear projection mapping; and generating the decoding result based on the physical phase angles and the initial node features using an encoder. This enables the model to capture bit dependencies based on Lie distance, which conforms to coding principles, thereby significantly improving decoding performance.

Description

Technical Field

[0001] This invention belongs to the field of channel decoding technology, and particularly relates to a cyclic code neural decoding method and system based on geometric perception topological mapping. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] In modern communication and storage systems, channel coding technology is the cornerstone of ensuring reliable data transmission. Classic schemes, represented by linear block codes, primarily correct errors caused by noise during transmission by introducing redundant information.

[0004] Error correction capability depends on the choice of decoding algorithm. Although maximum likelihood decoding can achieve the best frame error rate performance, its computational complexity increases exponentially with code length, making it difficult to apply to medium and long codes. Therefore, suboptimal iterative algorithms that seek a balance between performance and complexity, such as the confidence propagation (BP) algorithm, have become the mainstream choice in the industry.

[0005] In recent years, deep learning has been used in the field of channel decoding. Early neural decoders were mainly dedicated to improving the traditional BP algorithm (e.g., Neural BP) by weighted parameterization. They used neural networks to fit the message passing process on the Tanner graph (a bipartite graph used to represent the low-density parity-check code structure). However, this method is limited by the local connection structure of the graph and has difficulty capturing long-distance bit dependencies.

[0006] With the emergence of the Transformer architecture and its significant achievements in natural language processing, its core self-attention mechanism, possessing powerful global context modeling capabilities, has been rapidly introduced into the field of error correction codes. Among them, the ECCT (Error Correction Code Transformer) model successfully models the decoding task as a sequence processing problem by transforming the parity check matrix into a mask, and its performance on various code types surpasses that of the traditional BP algorithm.

[0007] Despite the significant potential of Transformer-based decoders, current mainstream architectures still suffer from a noticeable lack of inductive bias when handling cyclic codes. Cyclic codes are a class of linear codes with a strict algebraic structure, whose codewords reside in polynomial quotient rings. It has rotational (cyclic shift) symmetry, here Let n be a binary finite field, and n be the code length. Indicates that the coefficient belongs to The set of all polynomials, Defined polynomial module The computational environment is the mathematical space defined by cyclic codes. Standard Transformer decoder architectures typically employ linear positional encoding, treating codewords as linear sequences in Euclidean space. This leads to the following technical drawbacks: Topological mismatch and boundary effects: Traditional linear embedding methods separate the first and last bits (index 0 and n). 1) In algebra, the adjacency relation is related to the position 0 and n in geometric space. The distance of 1 is maximized (the straight-line distance is n). 1) This makes it difficult for the model to capture validation constraints that cross the beginning and end boundaries. This "straight line-circle" topological mismatch forces the model to consume a large number of parameters to memorize "0 and n". The simple algebraic fact that "1 is a neighbor"; It violates the cyclic shift invariance of cyclic codes: The essential characteristic of cyclic codes is that any cyclic shift of their codewords still results in a valid codeword. The absolute position encoding mechanism in the existing architecture introduces fixed spatial coordinate noise, causing the model's self-attention mechanism to be unable to allocate attention weights solely based on the relative algebraic distance between bits (i.e., Lee distance). In other words, the existing model is "blind" in terms of geometric topology and cannot utilize the invariance of cyclic shifts to enhance the model's generalization ability. It must consume massive amounts of training data to implicitly learn this algebraic structure that should have been explicitly injected. Summary of the Invention

[0008] To address the technical problems mentioned above, this invention provides a cyclic code neural decoding method and system based on geometrically perceptual topological mapping. It extracts the unit circle geometric prior of the cyclic code and explicitly injects the algebraic structural features of the cyclic code into the decoding mechanism of the neural network, enabling the model to capture bit dependencies based on Lie distance, which conforms to the coding principle, thereby significantly improving decoding performance.

[0009] To achieve the above objectives, the present invention adopts the following technical solution: The first aspect of this invention provides a neural decoding method for cyclic codes based on geometry-aware topological mapping, comprising: For the cyclic code sent by the transmitting end, calculate the parity check matrix, continuously cyclically shift the row vectors of the parity check matrix to expand it into a cyclic square matrix, and map the bit index of the cyclic code to the physical phase angle in polar coordinates. For the channel output value received by the receiver, the amplitude is extracted, and the checksum is calculated based on the cyclic matrix. The amplitude and the checksum are concatenated and then linearly projected to obtain the initial node features. Based on the physical phase angle and initial node features, the encoder generates the decoding result.

[0010] Furthermore, the physical phase angle is: Among them, bit index It is the numbering of each bit position in a cyclic code of length n.

[0011] Furthermore, the step of generating the decoding result includes: Based on the dimension of the initial node features, calculate the frequency scaling factor that decays geometrically. Based on the frequency scaling factor, the physical phase angle is extended into a geometric position tensor using sine and cosine basis functions; The initial node features and geometric position tensor are fused to obtain features carrying geometric priors; Based on features carrying geometric priors, the Transformer encoder extracts feature sequences after passing through multiple layers of nonlinear graph message passing, and then generates decoding results through fully connected layers and activation functions.

[0012] Furthermore, the frequency scaling factor is: ;in, The dimension index representing the feature space. Dimensions of the initial node features.

[0013] Furthermore, the geometric position tensor includes: ; ; Among them, bit index It is the numbering of each bit position in a cyclic code of length n. The physical phase angle, The dimension index representing the feature space. This is the frequency scaling factor.

[0014] Furthermore, the step of generating the decoding result includes: based on the physical phase angle and initial node features, through a Transformer encoder, after passing through multiple layers of nonlinear graph message passing, extracting the feature sequence and generating the decoding result through a fully connected layer and activation function; wherein, in the self-attention mechanism of the Transformer encoder, the physical phase angle is used to map the feature vector to the complex plane with the help of Euler's formula, and then a phase rotation operation is performed.

[0015] A second aspect of the present invention provides a cyclic code neural decoding system based on geometry-aware topological mapping, comprising: The cyclic code processing module is configured to: calculate the parity check matrix for the cyclic code sent by the transmitter, perform continuous cyclic shifts on the row vectors of the parity check matrix to expand it into a cyclic square matrix, and map the bit index of the cyclic code to the physical phase angle in polar coordinates. The channel output processing module is configured to: extract the amplitude of the channel output value received by the receiver, calculate the checksum based on the cyclic matrix, concatenate the amplitude and the checksum, and obtain the initial node features through linear projection mapping. The decoding module is configured to generate decoding results based on the physical phase angle and initial node features through an encoder.

[0016] Furthermore, the physical phase angle is: Among them, bit index It is the numbering of each bit position in a cyclic code of length n.

[0017] A third aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the cyclic code neural decoding method based on geometric perception topological mapping as described above.

[0018] A fourth aspect of the present invention provides a computer device including a computer-readable storage medium, a processor, and a computer program stored on the computer-readable storage medium and executable on the processor, wherein the processor executes the program to implement the steps of the cyclic code neural decoding method based on geometric perception topological mapping as described above.

[0019] Compared with the prior art, the beneficial effects of the present invention are: This invention extracts the unit circle geometric prior of cyclic codes and explicitly injects the algebraic structural features of cyclic codes into the decoding mechanism of neural networks, enabling the model to capture bit dependencies based on Lie distance, which conforms to the coding principle, thereby significantly improving decoding performance. Attached Figure Description

[0020] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0021] Figure 1 This is a schematic diagram of the complex plane unit circle phase mapping according to Embodiment 1 of the present invention; Figure 2 This is a schematic diagram of the cyclic phase absolute position encoding according to Embodiment 1 of the present invention; Figure 3 This is a schematic diagram of rotational position encoding based on complex plane phase according to Embodiment 1 of the present invention; Figure 4This is a comparison chart of the BER performance of the ECCT model using additive CPPE under the BCH(63,36) code type in Embodiment 1 of the present invention and the traditional ECCT. Figure 5 This is a comparison chart of the BER performance of the ECCT model using additive CPPE under the BCH(63,45) code type in Embodiment 1 of the present invention and the traditional ECCT. Figure 6 This is a comparison chart of the BER performance of the ECCT model using additive CPPE under the BCH(63,51) code type in Embodiment 1 of the present invention and the traditional ECCT. Figure 7 This is a comparison chart of the BER performance of the ECCT model using Rotary CPPE under the BCH(63,16) code type in Embodiment 1 of the present invention and the traditional ECCT. Figure 8 This is a comparison chart of the BER performance of the ECCT model using Rotary CPPE under the BCH(63,36) code type in Embodiment 1 of the present invention and the traditional ECCT. Figure 9 This is a comparison chart of the BER performance of the ECCT model using Rotary CPPE under the BCH(63,45) code type in Embodiment 1 of the present invention and the traditional ECCT. Figure 10 This is a schematic diagram of the structure of a computer device according to Embodiment 4 of the present invention. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0023] It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0024] Example 1 This embodiment provides a cyclic code neural decoding method based on geometrically perceptual topological mapping.

[0025] This embodiment provides a cyclic code neural decoding method based on geometric perception topological mapping, which can explicitly inject the algebraic structural features of cyclic codes into the decoding mechanism of neural networks, thus solving the defects of existing models in topological mapping and geometric perception.

[0026] To address the issues of "topological mismatch," "boundary effects," and "inability to maintain cyclic shift invariance" in existing neural decoders when processing cyclic codes, this paper proposes a neural decoding mechanism based on geometrically perceptual topological mapping, building upon traditional ECCT. This mechanism extracts the unit circle geometric prior of the cyclic code and provides two independently implementable injection strategies (embedding layer addition strategy and attention layer rotation strategy). The aim is to enable the model to capture bit dependencies based on the Lee distance, which conforms to coding principles, thereby significantly improving decoding performance.

[0027] This embodiment provides a cyclic code neural decoding method based on geometrically aware topological mapping, which includes the following preprocessing and phase mapping steps, as well as two independent geometric prior injection strategies based on the mapping.

[0028] Step 1: Preprocessing of parity check matrix squareization based on algebraic shift properties.

[0029] For a defined in a finite field On Cyclic code ( The total length of the codeword. (representing the length of the original effective information before encoding), the core of a cyclic code is a codeword sequence of length n, and its traditional parity-check matrix... Lacking a symmetric square matrix topology, the original parity-check matrix is ​​extended into a square matrix by continuously cyclically shifting its row vectors using the cyclic shift invariance of cyclic codes. cyclic square matrix .

[0030] When the sending end sends a cyclic code, after transmission through the channel, the receiving end receives the channel output value. Extracting the amplitude information of the signal And based on the cyclic square matrix of cyclic codes The checksum is calculated. ( Represents the binary mapping of y. , yes (the sign function); then, the amplitude Concatenated with the checksum s, and then linearly projected onto a high-dimensional feature space to obtain the initial node feature representation. Where N is the total length of the input sequence, For feature dimensions.

[0031] Step 2: Topological mapping of the complex plane unit circle to bit index.

[0032] To overcome the "topological mismatch" problem caused by linear absolute position encoding in Euclidean space, we abandon treating codewords as one-dimensional line segments and instead establish an isomorphic mapping between them and the unit circle in the complex plane.

[0033] like Figure 1 As shown, for a codeword sequence of length n (i.e., a cyclic code), the discrete one-dimensional bit index is... Mapped to physical phase angle in polar coordinates Its mapping mathematical model is: ; Among them, bit index It is the bit position number in a codeword sequence of length n, where pos=0 corresponds to the first bit, pos=n, and so on. 1 corresponds to the nth bit.

[0034] Theoretical derivation: Under this phase mapping, the eigenvector (in two-dimensional Cartesian coordinates) of any position pos in the sequence on the unit circle of the complex plane can be defined as ; First, calculate the first node (pos=0) and the last node (pos=n) of the sequence. 1) The Euclidean distance in the geometric feature space, with the phase corresponding to the first node pos=0 is: Its coordinates are: ; Tail node The corresponding phase is Based on the periodicity of trigonometric functions, its coordinates are: ; The square of the Euclidean distance between the two The calculation is as follows: ; Using trigonometric identities The above formula can be simplified to: ; Furthermore, a half-width formula is introduced. , will 2 x Replace with ,get: ; Taking the square root of both sides (since n≥2, the sine value is positive), we obtain the geometric chord lengths of the first and last nodes: ; Secondly, calculate the geometric distance between any two adjacent physical nodes in the sequence (e.g., pos=0 and pos=1), where the coordinates of node 1 are... Its distance from node 0 is: ; The above mathematical derivation proves That is, under this mapping rule, the physical distance between algebraically adjacent first and last nodes in the geometric feature space is equivalent to the physical distance between adjacent nodes within the sequence. This fundamentally eliminates the topological boundary breaks artificially introduced by traditional linear positional encoding, and reconstructs the cyclic code in the polynomial quotient ring in the feature space of the neural network. A closed-loop algebraic topology.

[0035] Step 3: Higher-order injection strategy based on geometric priors.

[0036] Based on the phase angle generated in step two It provides two independent methods for multi-scale feature injection to guide message passing in the Transformer network.

[0037] (1) Method 1 (Embedding Mechanism Optimization): Cyclic Phase Absolute Position Encoding (Additive CPPE), such as Figure 2 As shown.

[0038] First, geometric topology is injected during the model feature embedding stage: in order to... Capturing bit correlations at different feature scales in a dimensional feature space, and introducing a frequency scaling factor that decays geometrically. : ; in, The dimension index representing the feature space, when j is small. When j is relatively large, the model perceives position at high frequency, enabling it to accurately capture minute algebraic differences between adjacent bits; when j is relatively large... The model is relatively small, and it perceives location in a low-frequency manner to capture global dependencies that span a large code length range.

[0039] Subsequently, the one-dimensional phase angle is extended into a high-dimensional geometric position tensor using sine and cosine basis functions. PE For even-numbered dimensions of the feature vector and odd dimensions Its encoding mapping formula is: ; ; in, This represents the even-dimensional mapping result of the position tensor at position pos. This represents the odd-dimensional mapping result of the position tensor at position pos. This encoding method uses sine and cosine functions to nonlinearly extend the phase angle pos, thereby constructing a relative positional relationship in the vector space that reflects the geometric structure of the cyclic code.

[0040] Ultimately, geometry-aware embedding is .

[0041] This strategy utilizes the periodic continuity of trigonometric functions to map the originally one-dimensional discrete bit features into a high-dimensional closed ring topological space. This allows the subsequent neural network to process features without being restricted by the physical boundaries of the beginning and end of the sequence, and to naturally perceive the algebraic property of the cyclic code being connected end to end.

[0042] (2) Method 2 (Attention Mechanism Optimization): Rotary CPPE based on complex plane phase, performs Rotary rotation calculation on the query Q / key K matrix in the self-attention layer, and injects relative position information between nodes.

[0043] This approach no longer directly superimposes positional information onto the initial input features. Instead, it performs geometric optimization on the self-attention calculation process within the Transformer encoder, mathematically guaranteeing the shift invariance of the cyclic code in the model.

[0044] In the self-attention mechanism, let the query vector of the m-th bit be... The key vector of the nth bit is .

[0045] Not to and Instead of superimposing any fixed absolute coordinate values, it utilizes the phase angle generated in step two. and The eigenvectors are mapped to the complex plane using Euler's formula, and a phase rotation operation is performed on them: ; ; in, This represents the query vector after phase rotation. This represents the key vector after phase rotation, where i represents the imaginary unit, satisfying... Used to construct Euler's formula Rotation operators in [the context].

[0046] Theoretical derivation: When evaluating the attentional correlation between node m and node n, the self-attention mechanism... Using inner product operations, after the eigenvectors are converted into complex representations, according to the conjugate multiplication rule of complex inner products (in complex mathematics, to calculate the inner product of two complex vectors, the second vector must be taken as its "conjugate" (*), then they are multiplied, and finally the real part (Re) of the result is taken), the attention score after phase rotation is proportional to: ; Substituting the phase rotation formula above, we get: ; Using Euler's formula: , Represents the rotational radian on the complex plane, when When changing, Smooth movement on the unit circle; Expanding the complex exponential term and taking its real part, the formula mathematically simplifies to the product of the characteristic inner product of pure real numbers and the cosine of the angle difference: ; because The phase difference is related to the algebraic Lee distance of the cyclic code: They exhibit a strict correspondence.

[0047] Through the phase-based rotation operation described above, when calculating the correlation between any two bits, the model can retrieve the original absolute physical coordinates (i.e., ...) and The bits themselves are completely canceled out during the subtraction process, leaving only the relative algebraic distance between the two nodes as the sole positional factor determining the attention weights. This characteristic gives the model a natural mathematical immunity to arbitrary cyclic shifts of codewords when processing signals: regardless of how the codeword shifts as a whole on the ring, the relative distance between bits remains unchanged, and its attention weights also remain unchanged. This not only eliminates the computational interference introduced by absolute coordinates but also allows the model to autonomously follow the cyclic symmetry law of cyclic codes without adding additional training data.

[0048] Step 4: Mask constraint and multi-layer soft decision output.

[0049] Features carrying geometric priors are input into stacked Transformer encoder layers. In each layer, a squared-matrix check matrix is ​​used as the input. A cyclically symmetric attention mask is constructed, which rigidly stipulates that non-zero attention interactions can only occur between variable nodes and check nodes that have algebraic relationships. Finally, after multiple layers of nonlinear graph message passing, the network extracts feature sequences and outputs the posterior probability of each bit position being 0 or 1 through fully connected layers and a sigmoid activation function, thus completing the soft-decision decoding process.

[0050] Figure 4 , Figure 5 and Figure 6 This is a graph comparing the bit error rate (BER) performance of the ECCT model using additive CPPE with the baseline ECCT model at different signal-to-noise ratios.

[0051] Figure 7 , Figure 8 and Figure 9 This is a graph comparing the bit error rate (BER) performance of the ECCT model using Rotary CPPE with the baseline ECCT model at different signal-to-noise ratios.

[0052] Compared with existing neural decoders that use linear positional coding, both methods in this embodiment offer significant technical advantages and achieve considerable performance improvements in metrics such as bit error rate. Achieving topological isomorphism and completely eliminating boundary effects: Through CPPE (Cyclic Phase Positional Encoding, a geometric embedding technique specifically designed for cyclic codes, which maps the discrete positions of code elements to absolute phases on a unit circle, enabling the model to perceive the cyclic symmetry of codewords) absolute phase injection, the induced geometric distance has a strict positive monotonic relationship with the Lie distance of the cyclic code. The continuity of trigonometric functions in mathematics eliminates artificially introduced boundary breaks, enabling the model to naturally handle the check constraints of head-to-tail connections, and perfectly restore the closed topology of codewords in the geometric feature space; To ensure the cyclic shift invariance of the cyclic code and improve the purity of attention: By applying Rotary CPPE to the Q / K matrix of the self-attention mechanism, when the model judges the correlation between two bits, their absolute physical coordinates are completely canceled in the calculation, and only their relative algebraic distance is relied upon. This enables the model to ensure the cyclic shift invariance of the cyclic code. This simple mechanism eliminates the coordinate noise pollution caused by absolute position and greatly reduces the amount of data and training cost required to fit algebraic laws. Significant improvement in bit error rate (BER) performance: Experimental results in an additive white Gaussian noise (AWGN) channel demonstrate that for BCH codes with different code rates (such as BCH(31,16), BCH(63,36), BCH(63,45), and BCH(63,51)), both strategies effectively reduce the BER in the high signal-to-noise ratio region without increasing the number of additional model parameters. Taking the BCH(63,36) code type as an example, in the signal-to-noise ratio... Under these conditions, the bit error rate of the benchmark traditional ECCT model is .

[0053] After adopting method one (absolute phase injection of input layer CPPE), the bit error rate was reduced to This proves that closed topology effectively mitigates boundary effects.

[0054] After adopting method two (relative phase rotation of the attention layer Rotary), the bit error rate was further significantly reduced, decreasing to [missing value]. .

[0055] The experimental data above fully demonstrates that the geometric prior mechanism provided in this embodiment can effectively help the model identify and correct a minority of trap sets, significantly improving the error correction capability of the neural decoder in real communication scenarios.

[0056] Example 2 This embodiment provides a cyclic code neural decoding system based on geometric perception topological mapping, such as... Figure 7 As shown, it includes: The cyclic code processing module is configured to: calculate the parity check matrix for the cyclic code sent by the transmitter, perform continuous cyclic shifts on the row vectors of the parity check matrix to expand it into a cyclic square matrix, and map the bit index of the cyclic code to the physical phase angle in polar coordinates. The channel output processing module is configured to: extract the amplitude of the channel output value received by the receiver, calculate the checksum based on the cyclic matrix, concatenate the amplitude and the checksum, and obtain the initial node features through linear projection mapping. The decoding module is configured to generate decoding results based on the physical phase angle and initial node features through an encoder.

[0057] Furthermore, the physical phase angle is: Among them, bit index It is the numbering of each bit position in a cyclic code of length n.

[0058] Furthermore, the step of generating the decoding result includes: Based on the dimension of the initial node features, calculate the frequency scaling factor that decays geometrically. Based on the frequency scaling factor, the physical phase angle is extended into a geometric position tensor using sine and cosine basis functions; The initial node features and geometric position tensor are fused to obtain features carrying geometric priors; Based on features carrying geometric priors, the Transformer encoder extracts feature sequences after passing through multiple layers of nonlinear graph message passing, and then generates decoding results through fully connected layers and activation functions.

[0059] Furthermore, the frequency scaling factor is: ;in, The dimension index representing the feature space. Dimensions of the initial node features.

[0060] Furthermore, the geometric position tensor includes: ; ; Among them, bit index It is the numbering of each bit position in a cyclic code of length n. The physical phase angle, The dimension index representing the feature space. This is the frequency scaling factor.

[0061] Furthermore, the step of generating the decoding result includes: based on the physical phase angle and initial node features, through a Transformer encoder, after passing through multiple layers of nonlinear graph message passing, extracting the feature sequence and generating the decoding result through a fully connected layer and activation function; wherein, in the self-attention mechanism of the Transformer encoder, the physical phase angle is used to map the feature vector to the complex plane with the help of Euler's formula, and then a phase rotation operation is performed.

[0062] It should be noted that each module in this embodiment corresponds one-to-one with each step in Embodiment 1, and their specific implementation processes are the same, so they will not be repeated here.

[0063] Example 3 This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps in the cyclic code neural decoding method based on geometric perception topological mapping as described in Embodiment 1 above.

[0064] Example 4 This embodiment provides a computer device, such as... Figure 10As shown, the system includes a computer-readable storage medium 1003, a processor 1001, a communication interface 1002, and a computer program stored on the computer-readable storage medium 1003 and executable on the processor 1001. The processor 1001, communication interface 1002, and computer-readable storage medium 1003 can be connected via a bus or other means. The communication interface 1002 is used to receive and send data. When the processor 1001 executes the program, it implements the steps in the cyclic code neural decoding method based on geometric perception topological mapping described in Embodiment 1 above.

[0065] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A neural decoding method for cyclic codes based on geometrically perceptual topological mapping, characterized in that, include: For the cyclic code sent by the transmitting end, calculate the parity check matrix, continuously cyclically shift the row vectors of the parity check matrix to expand it into a cyclic square matrix, and map the bit index of the cyclic code to the physical phase angle in polar coordinates. For the channel output value received by the receiver, the amplitude is extracted, and the checksum is calculated based on the cyclic matrix. The amplitude and the checksum are concatenated and then linearly projected to obtain the initial node features. Based on the physical phase angle and initial node features, the encoder generates the decoding result.

2. The cyclic code neural decoding method based on geometric perception topological mapping as described in claim 1, characterized in that, The physical phase angle is: Among them, bit index It is the numbering of each bit position in a cyclic code of length n.

3. The cyclic code neural decoding method based on geometric perception topological mapping as described in claim 1, characterized in that, The steps for generating the decoding result include: Based on the dimension of the initial node features, calculate the frequency scaling factor that decays geometrically. Based on the frequency scaling factor, the physical phase angle is extended into a geometric position tensor using sine and cosine basis functions; The initial node features and geometric position tensor are fused to obtain features carrying geometric priors; Based on features carrying geometric priors, the Transformer encoder extracts feature sequences after passing through multiple layers of nonlinear graph message passing, and then generates decoding results through fully connected layers and activation functions.

4. The cyclic code neural decoding method based on geometric perception topological mapping as described in claim 3, characterized in that, The frequency scaling factor is: ;in, The dimension index represents the feature space. Dimensions of the initial node features.

5. The cyclic code neural decoding method based on geometric perception topological mapping as described in claim 3, characterized in that, The geometric position tensor includes: ； ； Among them, bit index It is the numbering of each bit position in a cyclic code of length n. The physical phase angle, The dimension index represents the feature space. This is the frequency scaling factor.

6. The cyclic code neural decoding method based on geometric perception topological mapping as described in claim 1, characterized in that, The steps for generating the decoding result include: based on the physical phase angle and initial node features, through a Transformer encoder, after passing through multiple layers of nonlinear graph message passing, extracting the feature sequence and generating the decoding result through a fully connected layer and activation function; wherein, in the self-attention mechanism of the Transformer encoder, the physical phase angle is used to map the feature vector to the complex plane with the help of Euler's formula, and then a phase rotation operation is performed.

7. A cyclic code neural decoding system based on geometrically perceptual topological mapping, characterized in that, include: The cyclic code processing module is configured to: calculate the parity check matrix for the cyclic code sent by the transmitter, perform continuous cyclic shifts on the row vectors of the parity check matrix to expand it into a cyclic square matrix, and map the bit index of the cyclic code to the physical phase angle in polar coordinates. The channel output processing module is configured to: extract the amplitude of the channel output value received by the receiver, calculate the checksum based on the cyclic matrix, concatenate the amplitude and the checksum, and obtain the initial node features through linear projection mapping. The decoding module is configured to generate decoding results based on the physical phase angle and initial node features through an encoder.

8. A cyclic code neural decoding system based on geometric perception topological mapping as described in claim 7, characterized in that, The physical phase angle is: Among them, bit index It is the numbering of each bit position in a cyclic code of length n.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the steps in the cyclic code neural decoding method based on geometrically perceptual topological mapping as described in any one of claims 1-6.

10. A computer device comprising a computer-readable storage medium, a processor, and a computer program stored on the computer-readable storage medium and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the cyclic code neural decoding method based on geometric perception topological mapping as described in any one of claims 1-6.

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