Decoding method and decoder for product codes with row-column parity consistency
By coupling the row and column check structure of product codes through a cross-attention mechanism based on the Transformer architecture, efficient row and column check consistency decoding of product codes is achieved, solving the problems of high computational complexity and high resource consumption in existing technologies, and improving decoding performance and scalability.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SHANDONG UNIV
- Filing Date
- 2026-04-17
- Publication Date
- 2026-07-14
AI Technical Summary
Existing product code decoding methods have high computational complexity and high resource consumption, and fail to make full use of row and column check structures, making it difficult to achieve efficient row and column check consistency decoding.
A decoding model based on the Transformer architecture is constructed. The row and column verification structures are coupled through a cross-attention mechanism, and a verification consistency message passing mechanism between the row and column fields is built. The product code's row and column verification structure is used for decoding.
It significantly improves decoding performance, reduces computational complexity and storage overhead, is suitable for long codewords and complex encoding structures, and has good scalability.
Smart Images
Figure CN122394575A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the fields of communication and machine learning technology, and specifically to a decoding method and decoder for product codes with row and column check consistency. Background Technology
[0002] Product codes are a class of linear codes with a special algebraic structure. Any codeword can be represented in matrix form and simultaneously satisfies the check constraints of both row and column components. This inherent row-column check structure allows for constraint expression in both row and column directions, laying the foundation for structured implementation of encoding and decoding. In communication systems, data transmission typically involves three stages: encoding at the transmitting end, channel transmission, and decoding at the receiving end. The transmitting end encodes the original information into codewords that satisfy the constraints and modulates them before transmission. Noise and signal attenuation in the channel introduce bit errors. The receiving end then needs to recover the original codewords from the disturbed signal using a decoding algorithm. The performance and complexity of the decoding method directly affect the reliability, real-time performance, and hardware implementation cost of the communication system.
[0003] Existing product code decoding methods mostly employ row-column iterative decoding based on algebraic structures, and their component code decoding often utilizes algorithms such as Belief Propagation (BP). However, such methods have significant shortcomings: First, they have high computational complexity, requiring multiple iterations in the row and column directions in long code and high-complexity scenarios, resulting in significant computational overhead from calling the BP algorithm; second, they consume a lot of resources, with multiple iterations and the storage of a large amount of intermediate information leading to high memory usage and increased hardware implementation costs, making it difficult to meet the requirements of high throughput and low latency; third, the structure utilization is still insufficient, lacking a unified and efficient model for the deep coupling relationship between row and column information and the consistency propagation mechanism between different check domains.
[0004] In recent years, Transformer-based decoders have attracted attention due to their ability to model long-distance dependencies. Methods such as ECCT have improved the ability of neural decoders to model codeword structures through masked self-attention mechanisms. However, most existing Transformer decoders are designed for general linear codes, treating the input codeword and checksum as a one-dimensional sequence. They fail to specifically model the row and column checksum structure unique to product codes, neither explicitly modeling the checksum relationship between row and column fields nor effectively establishing a checksum consistency message passing mechanism between them, making it difficult to fully leverage the structural advantages of product codes. Furthermore, the computational and storage requirements of the Transformer's global attention mechanism increase quadratically with the input length. Directly applying it to long product codes can easily lead to an excessive number of model parameters, inference latency, and memory consumption, limiting its practicality and scalability.
[0005] Therefore, existing technologies suffer from high computational complexity, high resource consumption, and insufficient structural utilization, making it difficult to efficiently achieve row and column check consistency decoding of product codes. Summary of the Invention
[0006] To address the aforementioned issues, this invention proposes a decoding method and decoder for product codes that features row and column check consistency. This method improves decoding efficiency while reducing computational complexity and storage overhead, making it suitable for decoding scenarios involving long codewords and complex encoding structures.
[0007] According to some embodiments, the present invention adopts the following technical solution: Decoding methods for product codes with row and column check consistency include: Obtain the channel output to be decoded, preprocess the channel output, and construct a composite matrix; The decoding model, constructed using a row-column check structure based on product codes, maps the composite matrix to the corresponding embedding matrix. The embedding matrix is then iteratively updated using a cross-attention mechanism to achieve message passing for check consistency between the row and column domains, thereby obtaining the initial decoding result. The initial decoding results are post-processed to obtain the final decoding results.
[0008] According to some embodiments, the present invention adopts the following technical solution: Decoders for product codes with row and column check consistency include: The preprocessing module is configured to: acquire the channel output to be decoded, preprocess the channel output, and construct a composite matrix; The decoding module is configured to: map the composite matrix to the corresponding embedding matrix through a decoding model constructed based on the row and column check structure of the product code, and iteratively update the embedding matrix through a cross attention mechanism to realize the verification consistency message transmission between the row and column fields, thereby obtaining the preliminary decoding result; The post-processing module is configured to perform post-processing on the preliminary decoding results to obtain the final decoding results.
[0009] According to some embodiments, the present invention adopts the following technical solution: A computer program product includes a computer program that, when executed by a processor, implements the decoding method for product codes with row and column check consistency.
[0010] According to some embodiments, the present invention adopts the following technical solution: A non-transitory computer-readable storage medium is provided for storing computer instructions, which, when executed by a processor, implement the decoding method for product codes with row and column check consistency.
[0011] According to some embodiments, the present invention adopts the following technical solution: An electronic device includes a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to cause the electronic device to perform the decoding method for product codes with row and column check consistency.
[0012] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention is based on the Transformer architecture. By utilizing the inherent row and column check structure of product codes, a unified checksum is introduced during the decoding process to couple the row and column check constraints, thereby constructing a message passing mechanism with row and column check consistency. This optimizes the decoding process of Transformer-based product codes. Through the above design, this invention can improve decoding performance while reducing computational complexity and the number of parameters, thus providing a feasible solution for efficient decoding in scenarios with long codewords and complex encoding structures. Attached Figure Description
[0013] 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.
[0014] Figure 1 This is a structural diagram of the decoding model in Embodiment 1 of the present invention; Figure 2 This is a schematic diagram of the decoding layer structure in Embodiment 1 of the present invention; Figure 3 This is a schematic diagram of the cross-attention module structure in Embodiment 1 of the present invention; Figure 4 This is a schematic diagram of the output layer structure in Embodiment 1 of the present invention; Figure 5 This is a performance comparison chart of long code product codes in Embodiment 1 of the present invention. Detailed Implementation
[0015] The present invention will be further described below with reference to the accompanying drawings and embodiments.
[0016] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration 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.
[0017] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.
[0018] Example 1 One embodiment of the present invention provides a decoding method for product codes with row and column check consistency, which improves decoding efficiency while reducing computational complexity and storage overhead, and is suitable for decoding scenarios with long codewords and complex encoding structures. Specific steps include: Step S1: Obtain the channel output to be decoded, preprocess the channel output, and construct a composite matrix; Furthermore, the composite matrix is obtained by splicing signal amplitude, row checksum, column checksum, and unified checksum according to a preset dimension.
[0019] Furthermore, the specific construction process of the composite matrix is as follows: The signal amplitude is the absolute value of the channel output; Based on the parity check matrices of the row and column component codes of the product code, calculate the row parity and column parity of the channel output respectively; A unified checksum is constructed by using row checksums and column checksums.
[0020] Specifically, for product codes ,in for Linear code, for The linear code, and the corresponding parity-check matrices are respectively and .
[0021] Channel output matrix (i.e., the channel output to be decoded) is converted into a binary mapping. ,in, This indicates that the value is binarized. This represents the sign-resetting function.
[0022] Constructed composite matrix Defined by the following formula:
[0023]
[0024]
[0025]
[0026]
[0027] in, The absolute value of the channel output matrix represents the signal amplitude. , , These represent row checksums, column checksums, and uniform checksums, respectively.
[0028] The following structural identity can be further derived:
[0029]
[0030] This indicates that the unified checksum A checksum that can be considered a checksum (i.e.) and The checksum) unifies cross-dimensional dependencies into a single state variable, i.e. The row and column verification information are coupled together, forming a bridge for passing verification consistency messages.
[0031] Step S2: Using the decoding model constructed based on the row and column check structure of the product code, the composite matrix is mapped to the corresponding embedding matrix, and the embedding matrix is iteratively updated through the cross attention mechanism to realize the verification consistency message transmission between the row and column fields, thereby obtaining the preliminary decoding result; Furthermore, the decoding model is a Transformer network structure, used to jointly model the amplitude information, row parity information, column parity information, and unified parity information in the composite matrix.
[0032] Furthermore, the decoding model includes an embedding layer, a decoding layer, and an output layer; The embedding layer is used to map the composite matrix to the corresponding embedding matrix; The decoding layer is used to iteratively update the embedding matrix through a cross-attention mechanism; The output layer is used to perform feature aggregation and mapping on the recombined embedding matrix along the row and column domains respectively, so as to obtain the preliminary decoding result.
[0033] Furthermore, the verification consistency message transmission between the row field and the column field includes: In the column field, the amplitude information and row checksum information are updated based on the column checksum and the unified checksum. In the row domain, the amplitude information and column checksum information are updated based on the row checksum and the unified checksum. Perform reverse message propagation in the column domain to update the column check sub-information and the unified check sub-information; Perform reverse message propagation within the row domain to update the row checksum and uniform checksum.
[0034] Specifically, based on the row and column check structure of product codes, a decoding model with Transformer as its foundation is constructed for decoding composite matrices with check constraints.
[0035] The decoding model is based on a Transformer network structure, such as... Figure 2 As shown, it includes an embedding layer, a decoding layer, and an output layer. This decoding model is used to jointly model the amplitude information, row checksum information, column checksum information, and unified checksum information in the composite matrix.
[0036] Unlike existing decoding methods that treat product codes as one-dimensional sequences, this embodiment processes the four types of information in the product code as different information domains, while maintaining its two-dimensional structural relationship during decoding. Specifically, the decoding model sets... There are several decoding layers, which are stacked sequentially. The output of the previous decoding layer serves as the input of the next decoding layer, so as to update information layer by layer.
[0037] The three layers will be explained separately below: 1. Embedding layer: Maps the composite matrix to the corresponding embedding matrix.
[0038] Embedding layer for composite matrix The elements in the matrix are embedded and mapped to a higher-dimensional embedding space to obtain the corresponding embedding matrix. Embedding matrix According to the composite matrix The block structure is divided into four embedded sub-matrices, namely , , and These correspond to the amplitude, row, column, and unified verification sub-information, respectively.
[0039] In one specific implementation, each element of the composite matrix is mapped to a dimension of The embedding vectors are such that the last dimension of the corresponding embedding matrix is the embedding dimension. .
[0040] II. Decoding Layer: The embedding matrix is iteratively updated through a cross-attention mechanism to achieve consistent message passing between row and column fields.
[0041] like Figure 2 As shown, each decoding layer includes four cross-attention modules, which are used to perform directed message passing between different information domains so that amplitude information, row check information, column check information, and unified check information can be interactively updated according to the row and column check structure of the product code.
[0042] like Figure 3 As shown, the input to the cross-attention module includes the target matrix. Context matrix and the mask matrix derived from the parity check matrix. , , where the target matrix The context matrix represents the content to be updated. The mask matrix represents the content that provides constraint and structural information for the target matrix. This is used to restrict attention to be computed only between positions that satisfy the product code check structure constraints.
[0043] Specifically, the target matrix After linear transformation, it is mapped to a query matrix. Context matrix After independent linear transformations, it is mapped to a bond matrix. Sum matrix The updated target matrix is obtained through masked cross-attention calculation and a feedforward neural network. The output of the cross-attention mechanism can be expressed as:
[0044] in, This represents the attention feature dimension, i.e., the embedding dimension.
[0045] In one specific implementation, the masking function for constructing the mask matrix is defined as:
[0046] in, It is a binary matrix used to characterize the check connection relationship of the product code.
[0047] Therefore, when cross-attention is performed in the column domain, the mask matrix can be derived from... Or its transpose; when cross-attention is performed in the row domain, the mask matrix can be constructed from... Or its transpose; with the help of the above mask constraints, cross attention performs information exchange only between positions that satisfy the row and column check relationship of the product code.
[0048] In one specific implementation, each cross-attention module in the decoding layer sequentially executes a message passing process, denoted as process A, B, C, and D. These four processes together constitute a complete bidirectional, check-consistent message passing loop, specifically as follows: 1. Process A: In the column field, update the amplitude information and row check information based on the column checksum and the unified checksum.
[0049] Amplitude information embedding and row check embedding As the target input, column validator embedding and unified checksum embedding As contextual input, specifically, these are concatenated into two inputs for the cross-attention module: ,
[0050] Furthermore, based on the parity-check matrix of the column component codes, a column field mask is constructed. The target matrix is updated using the aforementioned cross-attention module, ensuring that the magnitude information and row checksum information receive structural information from the column checksum and unified checksum under column domain constraints. The updated result is... and .
[0051] 2. Process B: In the row field, update the amplitude information and column checksum information based on the row checksum and the unified checksum.
[0052] Embed the amplitude information updated in the previous step Embedded column checksums Embed the row checksum as the target input. and unified checksum embedding As contextual input, specifically, the two inputs to the cross-attention module are constructed as follows: ,
[0053] In one specific implementation, to align the cross-attention operation with the row domain structure, for and Transpose the data along the row and column dimensions, and construct a row field mask based on the parity check matrix of the row component codes. Through the processing of the cross-attention module, the amplitude information and column checksum information receive structural information from the row checksum and unified checksum under row domain constraints, and are then updated to obtain... and .
[0054] 3. Procedure C: Perform reverse message propagation in the column field to update the column checksum and uniform checksum.
[0055] Performing cross-attention update in the opposite information flow direction to process A allows the updated amplitude and row checksum information to be further propagated back to the column checksum and unified checksum information domains. Through this reverse message propagation process, the column checksum and unified checksum can absorb the update results from the amplitude and row checksum information domains, thereby obtaining... and .
[0056] 4. Procedure D: Perform reverse message propagation in the row field to update the row check sub-information and the unified check sub-information.
[0057] Performing cross-attention updates in the opposite information flow direction to process B allows the updated amplitude and column checksum information to be further propagated back to the row checksum and unified checksum information domains. Through this reverse message propagation process, the row checksum and unified checksum can absorb the update results from the amplitude and column checksum information domains, thereby obtaining... and .
[0058] After the AD process, the decoding layer outputs the updated four-class embedding matrices. , , and .
[0059] In one specific implementation, the cross-attention modules in the process AD share the same set of parameters to reduce the number of model parameters while maintaining message transformation consistency; after multiple decoding layers are stacked in sequence, the ability to propagate verification consistency information between row and column fields can be further enhanced.
[0060] In one specific implementation, the training objective of the decoding model is to learn the mapping relationship between the received signal and the target noise estimation result. Each training sample in the training dataset includes: a received signal sample obtained by modulation and channel transmission of the transmitted codeword; a composite matrix constructed based on the received signal sample; and a target noise label corresponding to the received signal sample.
[0061] During training, the composite matrix is input into the decoding model to obtain a noise estimation output, and a loss function value is calculated based on the difference between the noise estimation output and the target noise label to update the parameters of the decoding model.
[0062] In one specific implementation, the target noise label is a binary label representing the noise state at each location, and the loss function is a binary cross-entropy loss function used to measure the difference between the noise estimation output and the target noise label.
[0063] III. Output Layer: The updated embedding matrix is subjected to feature aggregation and mapping to obtain preliminary decoding results.
[0064] In one specific implementation, after the last decoding layer, the output layer updates the four types of embedding matrices. , , and The composite embedding matrix is recombined according to the block structure corresponding to the composite matrix. Then, the composite embedding matrix is first normalized and then feature mapping is performed through three sequentially connected fully connected layers to obtain the preliminary decoding result.
[0065] Specifically, such as Figure 4 As shown, the output layer consists of a normalization layer and three sequentially connected fully connected layers. The normalization layer adjusts the feature distribution of the combined embedding matrix to improve the stability of subsequent mapping processes. The three fully connected layers perform step-by-step mapping and dimensionality transformation on the normalized embedding features, ultimately outputting noise estimation results corresponding to the positions of the codewords to be decoded.
[0066] In one specific implementation, the output layer performs feature aggregation and mapping on the combined embedding matrix along both the row and column domains. In the row domain direction, embedded features within the same row are aggregated to integrate information from column check constraints; in the column domain direction, embedded features within the same column are aggregated to integrate information from row check constraints. Through bidirectional feature aggregation in both the row and column domains, compressed representation and structural enhancement of the embedded features are achieved while maintaining the two-dimensional structural relationship of the product code.
[0067] In one specific implementation, Figure 4 The numbers on the right represent the dimensionality of the output features at each layer, including the embedded feature dimension and the feature dimension after mapping through fully connected layers. These numbers reflect the size changes of the feature tensors at each stage of the output layer, illustrating how the combined embedding matrix, after normalization and multi-layer fully connected mapping, is gradually transformed into an output form corresponding to the target noise estimation result.
[0068] Through the above-described normalization, row and column feature aggregation, and multi-layer fully connected mapping, the output layer can retain key information related to the row and column check structure of the product code while reducing feature redundancy and model parameter count, and output a preliminary decoding result, which is an estimation result of the multiplicative noise. .
[0069] Step S3: Post-process the preliminary decoding result to obtain the final decoding result.
[0070] In the post-processing stage, the noise estimation result obtained in step S2 is combined with the channel output matrix to calculate the final decoding result, which can be expressed as follows: .
[0071] The product code decoding method based on the Transformer architecture proposed in this embodiment explicitly introduces the inherent row-column check structure of the product code into the decoding model and constructs a message passing mechanism with check consistency between the row and column fields. This solves several problems existing in the current decoding methods and has the following advantages: 1. Significantly improves the utilization of product code structure information. Existing neural decoding methods for product codes typically treat product codes as general linear codes and fail to specifically model the row and column parity structure unique to product codes. Therefore, it is difficult to fully utilize the structural advantages of product codes in the row and column directions.
[0072] This embodiment constructs a composite matrix consisting of signal amplitude, row parity, column parity, and unified parity, integrating the row and column constraints of the product code, as well as the consistency relationship between them, into the decoding process. The unified parity is used to explicitly couple the row and column parity, allowing cross-dimensional dependencies to enter the decoding model in a structured form.
[0073] Therefore, this embodiment can make fuller use of the algebraic structure information of the product code than existing decoding methods that flatten the product code, thereby improving the model's ability to express the constraint relationship of the product code.
[0074] 2. Construct a message passing mechanism for verification consistency between row and column fields to improve decoding performance. The core of this embodiment is to treat amplitude information, row check sub-information, column check sub-information and unified check sub-information as four different information domains, and to perform targeted message passing between different information domains through a cross-attention mechanism.
[0075] Specifically, in each decoding layer, a complete bidirectional, check-consistent message passing loop is formed through four processes: column-domain forward message passing, row-domain forward message passing, column-domain reverse message passing, and row-domain reverse message passing. With this mechanism, constraint information in the row and column directions can be coupled and propagated through a unified checksum, enabling the decoding model to simultaneously satisfy the structural constraints of both the row and column domains during the update process.
[0076] Table 1 compares the decoding performance of the ProductMPT method in this embodiment with that of RCID (Row-Column Iterative Decoding) and other similar neural network methods (using the CrossMPT decoder). The data represent the negative natural logarithm of the bit error rate (BER) of each model at signal-to-noise ratios of 3, 4, and 5 dB. Experimental results show that the proposed ProductMPT decoder achieves better BER performance than existing neural decoding baselines on various tested product codes, especially in the medium-to-high signal-to-noise ratio region, where it typically achieves a bit error rate reduction of about an order of magnitude compared to existing CrossMPT decoders.
[0077] Table 1. Decoding Performance Comparison Table
[0078] 3. Effectively reduces model parameter count, computational complexity, inference latency, and memory usage. Existing Transformer-based decoders typically rely on performing global attention calculations on the flattened sequence, and the size of their attention matrix usually grows quadratically with the input length. When applied to product codes, especially long product codes, this can easily lead to an excessive number of model parameters, too many floating-point operations, long inference latency, and large intermediate activation storage overhead.
[0079] This embodiment utilizes a row- and column-domain cross-attention mechanism oriented towards the product code structure to achieve localized message interaction, making the computation process correspond to the two-dimensional structure of the product code. As a result, the model complexity is transformed from a form dependent on the square of the overall code length under traditional global attention methods to a decompositional complexity form dependent on the dimensions of the row and column component codes, thus significantly reducing computational and storage overhead.
[0080] Furthermore, in this embodiment, the same set of cross-attention module parameters are shared for the four message passing processes within each decoding layer, which reduces the size of trainable parameters while ensuring the consistency of message transformation.
[0081] Table 2 Comparison of Parameter Quantity, Computational Complexity, and Resource Consumption
[0082] In one specific implementation, the complexity of the proposed ProductMPT decoder is compared with that of the existing CrossMPT decoder. As shown in Table 2, on various tested product codes, the number of parameters in ProductMPT is approximately 20%–30% of that in CrossMPT, while its floating-point operations and inference latency are also significantly reduced. For some tested code types, inference latency can be reduced by approximately 70%–75%. Furthermore, in terms of memory usage, ProductMPT consumes approximately 15–21 MiB of memory per codeword, significantly lower than existing ECCT and CrossMPT decoders.
[0083] 4. Suitable for long code and long product code scenarios, with good scalability. For long product codes, existing Transformer decoders that rely on global attention mechanisms are often impractical due to the excessively large size of the attention matrix. In contrast, this embodiment explicitly utilizes the row and column check structure of the product code to decompose the decoding process into a structured message passing process between row and column fields, thereby avoiding direct global modeling of the entire flattened sequence.
[0084] Figure 5 The results show a comparison of the bit error rate between the decoder proposed in this embodiment and the classic row-column iterative decoding method on two sets of long code length product codes. Figure 5 In the middle, the horizontal axis is The unit is decibel (dB), which represents the ratio of energy per bit to noise power spectral density; the vertical axis is the bit error rate (BER), which represents the proportion of bit errors in the decoded output.
[0085] Depend on Figure 5 It can be seen that this embodiment is not only applicable to product code scenarios with shorter code lengths, but can also be well extended to product code scenarios with longer code lengths and more complex component codes, and has good engineering feasibility and application value.
[0086] Example 2 One embodiment of the present invention provides a decoder for product codes and having row and column check consistency, comprising: The preprocessing module is configured to: acquire the channel output to be decoded, preprocess the channel output, and construct a composite matrix; The decoding module is configured to: map the composite matrix to the corresponding embedding matrix through a decoding model constructed based on the row and column check structure of the product code, and iteratively update the embedding matrix through a cross attention mechanism to realize the verification consistency message transmission between the row and column fields, thereby obtaining the preliminary decoding result; The post-processing module is configured to perform post-processing on the preliminary decoding results to obtain the final decoding results.
[0087] Example 3 One embodiment of the present invention provides a computer program product, including a computer program that, when executed by a processor, implements the decoding method for product codes with row and column check consistency.
[0088] Example 4 In one embodiment of the present invention, a non-transitory computer-readable storage medium is provided for storing computer instructions. When the computer instructions are executed by a processor, they implement the decoding method for product codes with row and column check consistency.
[0089] Example 5 One embodiment of the present invention provides an electronic device, including: a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to cause the electronic device to execute the decoding method for product codes with row and column check consistency.
[0090] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.
[0091] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.
[0092] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.
Claims
1. A decoding method for product codes with row and column parity consistency, characterized in that, include: Obtain the channel output to be decoded, preprocess the channel output, and construct a composite matrix; The decoding model, constructed using a row-column check structure based on product codes, maps the composite matrix to the corresponding embedding matrix. The embedding matrix is then iteratively updated using a cross-attention mechanism to achieve message passing for check consistency between the row and column domains, thereby obtaining the initial decoding result. The initial decoding results are post-processed to obtain the final decoding results.
2. The decoding method for product codes with row and column check consistency as described in claim 1, characterized in that, The composite matrix is obtained by splicing signal amplitude, row checksum, column checksum, and unified checksum according to a preset dimension.
3. The decoding method for product codes with row and column check consistency as described in claim 1, characterized in that, The specific construction process of the composite matrix is as follows: The signal amplitude is the absolute value of the channel output; Based on the parity check matrices of the row and column component codes of the product code, calculate the row parity and column parity of the channel output respectively; A unified checksum is constructed by using row checksums and column checksums.
4. The decoding method for product codes with row and column check consistency as described in claim 3, characterized in that, The decoding model is a Transformer network structure used to jointly model the amplitude information, row parity information, column parity information, and unified parity information in the composite matrix.
5. The decoding method for product codes with row and column check consistency as described in claim 1, characterized in that, The decoding model includes an embedding layer, a decoding layer, and an output layer; The embedding layer is used to map the composite matrix to the corresponding embedding matrix; The decoding layer is used to iteratively update the embedding matrix through a cross-attention mechanism; The output layer is used to perform feature aggregation and mapping on the recombined embedding matrix along the row and column domains respectively, so as to obtain the preliminary decoding result.
6. The decoding method for product codes with row and column check consistency as described in claim 1, characterized in that, The transmission of the verification consistency message between the row field and the column field includes: In the column field, the amplitude information and row checksum information are updated based on the column checksum and the unified checksum. In the row domain, the amplitude information and column checksum information are updated based on the row checksum and the unified checksum. Perform reverse message propagation in the column domain to update the column check sub-information and the unified check sub-information; Perform reverse message propagation within the row domain to update the row checksum and uniform checksum.
7. A decoder for product codes and having row and column parity consistency, characterized in that, include: The preprocessing module is configured to: acquire the channel output to be decoded, preprocess the channel output, and construct a composite matrix; The decoding module is configured to: map the composite matrix to the corresponding embedding matrix through a decoding model constructed based on the row and column check structure of the product code, and iteratively update the embedding matrix through a cross attention mechanism to realize the verification consistency message transmission between the row and column fields, thereby obtaining the preliminary decoding result; The post-processing module is configured to perform post-processing on the preliminary decoding results to obtain the final decoding results.
8. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the decoding method for product codes with row and column check consistency as described in any one of claims 1-6.
9. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium is used to store computer instructions, which, when executed by a processor, implement the decoding method for product codes and having row and column check consistency as described in any one of claims 1-6.
10. An electronic device, characterized in that, include: The electronic device includes a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to cause the electronic device to perform a decoding method for product codes with row and column check consistency as described in any one of claims 1-6.