An LDPC decoding method and related apparatus

Abstract

This invention belongs to the field of signal processing and communication systems, and discloses an LDPC decoding method and related apparatus. It acquires the log-likelihood ratio data to be decoded and inputs it into a pre-trained neural network LDPC decoding model. This model constructs multiple iterative layers based on an LDPC graph structure, with each layer containing a check node and a variable node layer. A normalization layer is introduced into the inter-layer message passing path for standardization processing. Simultaneously, the model is trained using a mixed signal-to-noise ratio dataset. This method significantly improves decoding performance and convergence speed while maintaining low implementation complexity, and enhances generalization and adaptability in real-world communication scenarios. This solves the problems of traditional algorithms struggling to balance performance and complexity, as well as the slow convergence and insufficient signal-to-noise ratio generalization of neural network decoding models.

Description

Technical Field

[0001] This invention belongs to the field of signal processing and communication system technology, and particularly relates to an LDPC decoding method and related apparatus. Background Technology

[0002] In recent years, with the continuous enhancement of computing power and the rapid development of artificial intelligence-related technologies, the integration of deep learning and communication technologies has received widespread attention and has become a research hotspot in the fields of signal processing and communication systems. Channel coding and channel decoding, as key core modules of communication systems, play an irreplaceable role in improving the reliability of data transmission in noisy channels. Developing a more efficient and widely applicable deep learning-based LDPC decoding framework is a necessary exploration for the future optimization and upgrading of communication systems. Low-density parity check (LDPC) codes, as a type of linear block code, possess outstanding advantages such as excellent performance, approximation of the Shannon limit, high throughput, low decoding complexity, and flexible structural design due to their unique sparse parity check matrix structure. They have been widely used in many fields such as deep space communication, fiber optic communication, 5G mobile communication, and satellite transmission. The combination of neural networks and traditional LDPC decoding algorithms further opens up broader prospects for research in this field.

[0003] Currently, the mainstream LDPC decoding methods in the industry mainly include the Sum-Product (SP) algorithm and its derivatives, the Min-Sum (MS) algorithm and the Normalized Min-Sum (NMS) algorithm. While the SP algorithm boasts good decoding performance, it involves numerous complex calculations, consuming significant time and negatively impacting hardware implementation. The MS algorithm simplifies the SP algorithm's computational flow, significantly reducing computational complexity and hardware implementation difficulty, but at the cost of some decoding performance. The NMS algorithm introduces a correction factor based on the MS algorithm, improving decoding performance to some extent without increasing complexity, but it still cannot overcome the inherent defects of traditional neural network decoding algorithms. Traditional neural network decoding algorithms tend to exhibit slow convergence speeds in deep network architectures, and the signal-to-noise ratio (SNR) in real-world physical layer communication systems is not a fixed value but fluctuates within a certain range. Existing training methods struggle to improve the network model's generalization ability to SNR, resulting in models that cannot well adapt to the needs of real-world communication scenarios.

[0004] It is evident that existing LDPC decoding algorithms suffer from the problem of balancing performance and implementation complexity, slow convergence speed of traditional neural network decoding models, and insufficient signal-to-noise ratio generalization ability, thus failing to meet the requirements of real-world communication systems for decoding reliability and scenario adaptability. Summary of the Invention

[0005] This invention provides an LDPC decoding method and related apparatus. Using this method can improve the convergence speed and signal-to-noise ratio generalization ability of the neural network LDPC decoding model, thus meeting the requirements of real-world communication systems for decoding reliability and scenario adaptability.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: An LDPC decoding method, comprising: Obtain the log-likelihood ratio data to be decoded; The log-likelihood ratio data is input into a pre-trained neural network LDPC decoding model. The basic model of the neural network LDPC decoding model is constructed based on a graph structure of a low-density parity-check code, including multiple iterative layers, each of which includes a check node layer and a variable node layer. A normalization layer is introduced along the message passing path between the multiple iterative layers. This normalization layer is used to standardize the log-likelihood ratio data passed through the iterations to mitigate the distribution shift of the log-likelihood ratio data during transmission. The neural network LDPC decoding model is trained based on a mixed signal-to-noise ratio dataset. The decoding result is output through the neural network LDPC decoding model.

[0007] Furthermore, the introduction of a normalization layer on the message passing path between multiple iterative layers includes: The normalization layer is set on the message passing path between the verification node layer and the variable node layer.

[0008] Furthermore, the normalization layer standardizes the log-likelihood ratio of the iterative pass, including: The log-likelihood ratio input to the normalization layer is normalized to ensure that the processed log-likelihood ratio distribution satisfies the preset mean and variance conditions.

[0009] Furthermore, the basic model of the neural network LDPC decoding model is trained using a mixed signal-to-noise ratio dataset, including: Select multiple signal-to-noise ratio points within a preset signal-to-noise ratio range; Generate decoding training data corresponding to each signal-to-noise ratio point; The decoding training data is mixed to construct a multi-signal-to-noise ratio hybrid dataset; The parameters of the basic model of the neural network LDPC decoding model are optimized using a mixed dataset with multiple signal-to-noise ratios to obtain a trained neural network LDPC decoding model.

[0010] Furthermore, in the process of optimizing the parameters of the basic model of the neural network LDPC decoding model using a multi-signal-to-noise ratio mixed dataset, the loss function used for parameter optimization is a weighted mixture of the cross-entropy loss function and the mean squared error loss function.

[0011] Furthermore, during the iterative decoding process, the neural network LDPC decoding model applies the verification weight parameters and variable weight parameters obtained during training to perform weighted processing on the verification node update messages and variable node update messages, respectively.

[0012] Furthermore, the verification node layer and the variable node layer include verification node message passing and variable node message passing processes; wherein; The verification node message passing involves message updates from the verification node to the variable node, as shown in the following formula:

[0013] Variable node message passing involves message updates from the variable node to the check node, as shown in the following formula:

[0014] In the formula, and It is the first The weight parameters of the hidden layer; For decoding iteration rounds; For verifying the node index; Index for variable nodes; To remove variable nodes Other than the verification node A set of connected nodes; To remove the verification node Other than variable nodes A set of connected nodes; For log-likelihood ratio messages; For the first Messages from the layer verification node to the variable node; For the first Messages from layer variable nodes to verification nodes; It is a symbolic function; For variable nodes The initial log-likelihood ratio of the channel; For the first -Messages from the level 1 variable node to the verification node; For adjacent check node index; For the adjacent variable node index.

[0015] An LDPC decoding system, comprising: The data acquisition module is used to acquire the log-likelihood ratio data to be decoded; A decoding module is used to input log-likelihood ratio data into a pre-trained neural network LDPC decoding model. The basic model of the neural network LDPC decoding model is constructed based on a graph structure of a low-density parity-check code, including multiple iterative layers, each of which includes a check node layer and a variable node layer. A normalization layer is introduced along the message passing path between the multiple iterative layers. This normalization layer is used to standardize the log-likelihood ratio data passed through the iterations to mitigate the distribution shift of the log-likelihood ratio data during transmission. The neural network LDPC decoding model is trained based on a mixed signal-to-noise ratio dataset. The result output module is used to output the decoding result through the neural network LDPC decoding model.

[0016] An LDPC decoding device, comprising: Memory, used to store computer programs; A processor is used to implement the above-described LDPC decoding method when executing the computer program.

[0017] A computer-readable storage medium storing a computer program, which, when executed by a processor, is used to implement the above-described LDPC decoding method.

[0018] Compared with the prior art, the present invention has the following beneficial effects: This invention provides an LDPC decoding method. It obtains the log-likelihood ratio (LPR) data to be decoded and inputs it into a pre-trained neural network LDPC decoding model. This model constructs multiple iterative layers based on an LDPC graph structure, with each layer containing a check node and a variable node layer. A normalization layer is introduced along the message passing path between layers for standardization. Simultaneously, the model is trained using a mixed dataset with multiple signal-to-noise ratios (SNRs). This method effectively mitigates the distribution shift of the LPR data during iteration through the normalization layer, improving training stability. Furthermore, multi-SNR training enhances the model's adaptability to fluctuations in different SNRs. This allows the method to significantly improve decoding performance and convergence speed while maintaining low implementation complexity, and enhances its generalization and adaptability in real-world communication scenarios. This solves the problems of traditional algorithms struggling to balance performance and complexity, as well as the slow convergence and insufficient SNR generalization of neural network decoding models. Attached Figure Description

[0019] Figure 1 This is a decoder framework diagram provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the iterative structure of the NMS decoding model provided in this embodiment of the invention; Figure 3This is a schematic diagram of the structure of the neural network LDPC decoding model provided in an embodiment of the present invention; Figure 4 This is a comparison chart of model training curves under different learning rates provided in the embodiments of the present invention; Figure 5 This is a comparison chart of bit error rate performance curves under different loss functions provided in the embodiments of the present invention; Figure 6 This is a comparison chart of bit error rate performance curves under different network layers provided in the embodiments of the present invention; Figure 7 This is a comparison chart of bit error rate performance curves under different activation function strategies provided in the embodiments of the present invention; Figure 8 This is a comparison chart of the bit error rate performance of the NNMS algorithm provided in this embodiment of the invention and the traditional algorithm; Figure 9 This is a performance comparison chart between the INNMS model based on multi-signal-to-noise ratio hybrid training and a single model provided in the embodiments of the present invention; Figure 10 This is a comparison chart of the model convergence speed before and after the introduction of the normalization layer provided in the embodiments of the present invention; Figure 11 This is a comparison diagram of the distribution of LLR values ​​in the intermediate layers of the network before and after the introduction of the normalization layer, provided in an embodiment of the present invention. Figure 12 This is a flowchart of the core steps of an LDPC decoding method provided in an embodiment of the present invention; Figure 13 This is a schematic diagram of the structure of an LDPC decoding system provided in an embodiment of the present invention. Detailed Implementation

[0020] To further understand the content of this invention, the invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments are merely illustrative and not limiting of the invention.

[0021] For example, this embodiment provides an LDPC decoding method that can effectively solve the problems of slow convergence speed and insufficient signal-to-noise ratio generalization ability of the existing neural network LDPC decoding model. This method solves the distribution offset problem by introducing a normalization layer between neural network layers, and improves the generalization ability by adopting a multi-signal-to-noise ratio hybrid training strategy, thereby achieving a significant improvement in model convergence speed and decoding robustness.

[0022] like Figure 12 As shown, this embodiment provides an LDPC decoding method, including: Obtain the log-likelihood ratio data to be decoded; The log-likelihood ratio data is input into a pre-trained neural network LDPC decoding model. The basic model of the neural network LDPC decoding model is constructed based on a graph structure of a low-density parity-check code, including multiple iterative layers, each of which includes a check node layer and a variable node layer. A normalization layer is introduced along the message passing path between the multiple iterative layers. This normalization layer is used to standardize the log-likelihood ratio data passed through the iterations to mitigate the distribution shift of the log-likelihood ratio data during transmission. The neural network LDPC decoding model is trained based on a mixed signal-to-noise ratio dataset. The decoding result is output through the neural network LDPC decoding model.

[0023] Specifically, the LDPC decoding method provided in this embodiment will now be described with reference to the accompanying drawings: like Figure 1 As shown, this LDPC decoding method is applied to a decoder. The decoder framework follows a typical communication link: information bits are encoded, modulated using Binary Phase Shift Keying (BPSK), and then additive white Gaussian noise is superimposed in the channel to simulate the real environment; the channel LLR value calculated at the receiver is then input into the neural network decoder; the process includes the following steps: The specific steps for training a neural network LDPC decoding model are as follows: Step S100: Based on the graph structure of the low-density parity-check code, a neural network model is constructed. The neural network model includes multiple iterative layers, and each iterative layer includes a check node layer and a variable node layer.

[0024] In this embodiment, the Tanner graph structure of the LDPC code is directly mapped to the topology of a neural network. Traditional LDPC decoding algorithms (such as the Normalized Minimum Sum (NMS) algorithm) achieve decoding through iterative message passing between variable nodes and check nodes. This embodiment adopts a "model-driven" approach, unfolding each iteration process into a hidden layer of the neural network. Specifically, check nodes in the Tanner graph are mapped to check node layers in the neural network, variable nodes are mapped to variable node layers, and the connections between nodes are mapped to weighted connections in the network. This construction method does not treat the decoding process as a black box, but preserves the iterative structure and message passing logic of the LDPC algorithm, giving the neural network a clear physical meaning. The weight parameters in the network (such as the scaling factor when the check node is updated) are set as trainable parameters and optimized through deep learning algorithms, thereby improving decoding performance while maintaining the interpretability of the algorithm.

[0025] Step S200: A normalization layer is introduced on the message passing path between the multi-layer iterative layers. The normalization layer is configured to normalize the log-likelihood ratio of the iterative transmission to alleviate the distribution shift of the log-likelihood ratio during the transmission process.

[0026] In deep neural network decoding models, as the number of network layers increases, the log-likelihood ratio (LLR) is prone to "internal covariate shift" during inter-layer propagation. This means the statistical distribution (mean and variance) of the LLR fluctuates drastically, causing deep neurons to enter the saturation region of the activation function, leading to the vanishing gradient problem and significantly slowing down the model's convergence speed. This embodiment introduces a normalization layer (e.g., batch normalization layer, BN) along the message passing path between iterative layers. Its core function is to adjust the LLR data passed iteratively. This normalization layer standardizes the input LLR, bringing its distribution back to near a standard normal distribution with a mean of 0 and a variance of 1, thus stabilizing the data distribution range. It should be understood that this normalization layer is not simply a stacking of network layers, but rather embedded in the critical message passing path, specifically adjusting the LLR distribution characteristics in communication decoding scenarios, effectively solving the numerical instability problem caused by deep iteration.

[0027] The specific NMS decoding model structure is as follows: Figure 2 As shown, the main difference between the NMS algorithm and the MS algorithm lies in the message update process of the verification node. This process normalizes the message amplitude by introducing a correction factor α. Theoretically, the optimal value of the correction factor α should change dynamically with the number of iterations, but in practical applications, to simplify implementation complexity, it is usually set to a fixed constant; the iteration is repeated until the convergence condition is met.

[0028] Step S300: Optimize the parameters of the neural network model based on the multi-signal-to-noise ratio hybrid dataset to obtain the trained neural network LDPC decoding model.

[0029] The trained neural network LDPC decoding model is used to process the log-likelihood ratio data to be decoded and output the decoding result.

[0030] Explained, traditional neural network decoding models are typically trained for a single signal-to-noise ratio (SNR) condition, resulting in insufficient generalization ability when facing dynamically changing channel environments. This embodiment employs a multi-SNR hybrid training strategy, constructing a dataset containing different SNR conditions. During training, the model can learn a wider range of channel features, rather than overfitting to a specific channel state. Through this hybrid training, a unified model capable of adapting to a certain SNR range is ultimately obtained, avoiding the problem of frequently switching models or retraining due to SNR changes in practical applications, significantly improving the model's robustness and engineering applicability.

[0031] As another preferred embodiment, in this embodiment, a normalization layer is introduced on the message passing path between the multi-layer iteration layers, including: setting the normalization layer on the message passing path between the verification node layer and the variable node layer.

[0032] In the iterative process of LDPC decoding, message transmission is bidirectional, including both external information transmitted from variable nodes to check nodes and check information transmitted from check nodes to variable nodes. In this embodiment, the normalization layer is mainly set on the path from the output of the check node layer to the input of the variable node layer.

[0033] like Figure 3 As shown, in the l-th iteration, the log-likelihood ratio message output by the verification node layer is processed by the normalization layer before being passed to the next variable node layer. This setup allows for direct intervention on critical values ​​during the iterative update process, preventing the accumulation of errors. It should be understood that although the figure shows the normalization layer after the verification node layer, in other embodiments, the normalization layer can also be placed on the transmission path from the variable node layer to the verification node layer, or simultaneously on both transmission paths, to further enhance numerical stability.

[0034] Furthermore, the normalization layer standardizes the log-likelihood ratio passed in the iteration, including: normalizing the log-likelihood ratio input to the normalization layer so that the processed log-likelihood ratio distribution satisfies the preset mean and variance conditions.

[0035] The specific trained neural network LDPC decoding model (NMS decoding model) is as follows: Figure 3 As shown, the neural network LDPC decoding model includes multiple iterative layers, each of which includes a verification node layer and a variable node layer; a normalization layer is introduced on the message passing path between the multiple iterative layers; the verification node layer and the variable node layer include verification node message passing and variable node message passing processes; wherein; The verification node message passing involves message updates from the verification node to the variable node, as shown in the following formula:

[0036] Variable node message passing involves message updates from the variable node to the check node, as shown in the following formula:

[0037] In the formula, and It is the first The weight parameters of the hidden layer; For decoding iteration rounds; For verifying the node index; Index for variable nodes; To remove variable nodes Other than the verification node A set of connected nodes; To remove the verification node Other than variable nodes A set of connected nodes; For log-likelihood ratio messages; For the first Messages from the layer verification node to the variable node; For the first Messages from layer variable nodes to verification nodes; It is a symbolic function; For variable nodes The initial log-likelihood ratio of the channel; For the first -Messages from the level 1 variable node to the verification node; For adjacent check node index; For the adjacent variable node index.

[0038] In deep neural network decoding models, the numerical distribution of the log-likelihood ratio (LLR) changes significantly with the increase of the number of iteration layers. For example... Figure 11 As shown, without a normalization layer, the LLR values ​​of the intermediate layers in deep networks exhibit an extremely wide distribution range, with the distribution center significantly deviating from the origin. This phenomenon is known as "internal covariate shift." This shift causes the inputs of neurons in subsequent layers to fall into the saturation region of the activation function, leading to the vanishing gradient problem and making the model difficult to converge. This embodiment uses a normalization layer to standardize the input LLR calculation, specifically employing batch normalization, layer normalization, or group normalization. Taking batch normalization as an example, the calculation process includes: first, calculating the mean and variance of the current batch of LLR data; then, using the mean and variance to scale and shift the LLR, forcibly pulling its distribution back to near a standard normal distribution with a mean of 0 and a variance of 1. This processing method ensures that the input of each neuron remains in the non-saturation region, guaranteeing the effective propagation of gradients during backpropagation, thereby significantly accelerating the model's convergence speed. It is important to emphasize that the normalization process in this embodiment is the log-likelihood ratio in the context of communication decoding. Its physical meaning represents the confidence level of bit information. This is fundamentally different from the normalization process for image feature maps in the general deep learning field. The latter usually deals with abstract feature representations, while this embodiment directly applies to channel soft information with clear physical meaning, which can more accurately correct numerical deviations in the decoding process.

[0039] In another preferred embodiment of the present invention, the neural network model is optimized based on a multi-signal-to-noise ratio (SNR) hybrid dataset, including: selecting multiple SNR points within a preset SNR range; generating decoding training data corresponding to each SNR point; and mixing the decoding training data to construct the multi-signal-to-noise ratio hybrid dataset.

[0040] In real-world communication scenarios, the channel environment is often dynamically changing, and the signal-to-noise ratio (SNR) is not a fixed value. Traditional neural network decoding models are typically trained for a single SNR, meaning they are optimized using only data under a specific SNR condition. While this approach can achieve superior performance at a specific SNR, it leads to overfitting the model to that particular channel state. When the actual SNR changes, the model's decoding performance significantly degrades, resulting in insufficient generalization ability. To address this issue, this embodiment employs a multi-SNR hybrid training strategy. When constructing the training dataset, multiple SNR points are first selected within a preset SNR range. For example, ... Figure 9 As shown, six signal-to-noise ratio (SNR) points (0dB, 1dB, 2dB, 3dB, 4dB, and 5dB) can be selected within the range of 0dB to 5dB, with 1dB intervals. It should be understood that the above range and intervals are only examples and can be adjusted according to channel conditions and performance requirements in actual applications. For each selected SNR point, corresponding decoding training data is generated. The specific process includes: generating a random information bit sequence, performing LDPC encoding to obtain codewords, modulating the codewords (e.g., BPSK modulation), superimposing Gaussian white noise under the corresponding SNR condition, and finally calculating the log-likelihood ratio (LLR) at the receiver as the input data for the neural network, using the original information bits as labels. The decoding training data generated from each SNR point are mixed to construct a unified training set containing information from multiple channel states. The neural network model is trained based on this mixed dataset, allowing the model to be exposed to channel features under different SNR conditions during training, thereby learning more robust feature representations rather than being limited to a single channel state.

[0041] like Figure 8As shown, the INNMS model maintains a stable bit error rate (BER) across the entire 0-5 dB range. Although its performance is slightly lower than that of the NNMS model optimized for a specific SNR, it is still significantly better than the traditional SP, MS, and NMS algorithms overall. For example, at BER = 10^-5, INNMS can still achieve a gain of approximately 0.45 dB. More importantly, the INNMS model uses the same set of network parameters at different SNR test points, eliminating the need to train and maintain multiple models separately for each SNR. Compared to traditional solutions that require maintaining and switching between multiple sets of model parameters for different SNRs, the single unified model constructed in this embodiment greatly reduces storage overhead (by more than 80%) and computational complexity, avoids latency caused by model switching, and has extremely high engineering practical value.

[0042] As a further improvement, in this embodiment, the loss function used in the parameter optimization process is a weighted mixture of the cross-entropy loss function and the mean squared error (MSE) loss function. In the training of a neural network decoding model, the choice of loss function directly affects the model's convergence speed and decoding accuracy. While the traditional mean squared error (MSE) loss function can reflect the numerical distance between the predicted and true values, it often has a slow convergence speed when dealing with classification or decision problems, and is not sensitive enough to bit error rate optimization in high signal-to-noise ratio regions. While the cross-entropy (CE) loss function has a faster convergence speed, it is prone to fluctuations in the later stages of training, affecting the model's stability. This embodiment uses a weighted mixture of the two as the optimization objective, combining the stability of MSE in numerical fitting with the sensitivity of CE in classification and decision-making. Figure 5 As shown, compared to single MSE or CE loss functions, the model using a hybrid loss function performs better on the bit error rate (BER) performance curve, especially in the high signal-to-noise ratio (SNR) region, effectively reducing the BER. This design balances the stability of the training process with the accuracy of the final decoding decision, ensuring the model's robustness under complex channel conditions. Furthermore, the neural network model uses the Sigmoid activation function during the training phase and the Sign activation function during the inference phase.

[0043] This differentiation strategy aims to balance the gradient propagation requirements during deep learning training with the hard-decision requirements in real-world decoding scenarios. During training, the neural network needs to update weight parameters via backpropagation, requiring the activation function to have good differentiability to ensure effective gradient propagation. The Sigmoid function, a smooth sigmoid function with a non-zero derivative everywhere, effectively avoids the vanishing gradient problem, facilitating deep training and parameter optimization. However, in the inference phase, i.e., in practical decoding applications, the decoder output should be a definite bit decision (0 or 1), not a probability value. The Sign function, as a step function, directly maps the input to a binary output, conforming to the hard-decision characteristic of LDPC decoding.

[0044] As shown in Figure 7, the model employing the "Sigmoid for training, Sign for inference" strategy (Sigmoid-Sign) achieved optimal bit error rate performance under all signal-to-noise ratio (SNR) conditions. Particularly in the high SNR region, its performance significantly outperformed the scheme using the Sigmoid function throughout. This demonstrates that the differentiated activation function strategy can maximize decoding performance during the inference phase while ensuring training effectiveness.

[0045] Furthermore, regarding the setting of training hyperparameters, this embodiment determined the optimal learning rate through experimental verification. For example... Figure 4 As shown, when the learning rate is set to 0.0001, the model converges slowly, requiring more than 100 iterations to reach a stable state. While initial convergence is faster with a learning rate of 0.001, significant oscillations occur in the later stages of training, affecting the model's final performance. However, when the learning rate is set to 0.0005, the model converges quickly within approximately 50 iterations, and the training curve is smooth and stable. Therefore, preferably, this embodiment uses a learning rate of 0.0005, combined with the Adam optimizer for parameter updates, to achieve optimal training efficiency and model performance. It should be understood that the specific values ​​of the learning rate mentioned above are merely examples, and in practical applications, they can be appropriately adjusted based on factors such as network depth and data size.

[0046] In this implementation, the complexity of the aforementioned neural network LDPC decoding model was also analyzed in detail: To analyze the complexity of the algorithm, let the code length be... The number of verification nodes is The average column weight and row weight are respectively and The number of edges satisfies = The number of iterations is .

[0047] When updating check nodes, during the comparison operation, for each check node, finding the minimum and second minimum values ​​requires reduction. This involves several comparisons. The total number of comparisons in the entire matrix is... There are [number] verification nodes, with a total cost of [amount]. = In multiplication operations, learnable weights are introduced. Each edge corresponds to one multiplication, and the cost of each iteration is... In logical operations, the overhead of the XOR operation on the sign bit is... .

[0048] When updating variable nodes, in addition operations, each variable node needs to accumulate its connected nodes. The information for each edge, with a total cost of [missing information]. = Addition; in multiplication, weights are introduced. The initial channel information is scaled. Each edge corresponds to one multiplication, and the cost of each iteration is... .

[0049] During decision and verification, the cumulative cost of posterior LLR is: = Additions; hard decision cost is Second comparison; verification check The cost is .

[0050] Unlike the traditional NMS algorithm, the increased complexity of NNMS mainly lies in the storage of weights: NMS only stores one normalization factor, while NNMS stores a larger number of weight parameters. .

[0051] NNMS, building upon NMS, expands the single normalization factor into a weight matrix obtained through deep learning training. Although it adds some multiplication operations, due to its inheritance of the sparsity of the LDPC parity-check matrix, the total computational cost remains within the range of... It is far lower than that of a conventional fully connected neural network.

[0052] This embodiment uses Mean Squared Error (MSE), Cross-Entropy Loss (CE), and a weighted mixture of the two loss functions for training. Experimental results are as follows: Figure 5As shown, the model converges slowly when using MSE, and its bit error rate performance is poor in high signal-to-noise ratio regions; the model converges faster when using CE, but there are slight fluctuations in some signal-to-noise ratio ranges; in comparison, the hybrid loss function of CE and MSE can balance training stability and decision accuracy, and performs best in overall bit error rate performance. Therefore, this embodiment selects the hybrid loss function as the training objective.

[0053] A neural network decoder was built using the TensorFlow-based computing framework. The neural network was trained using the mini-batch gradient descent method, with each mini-batch consisting of 100 data blocks. The learning rate was 0.0005, and the Adam optimizer was used. The loss function was a hybrid loss combining cross-entropy and mean squared error.

[0054] The simulation process was performed using Python software, with training accelerated using an NVIDIA GeForce RTX 4060 Laptop GPU.

[0055] The obtained dataset is input into the neural network, and after 100 rounds of training, the LDPC decoding network can be obtained.

[0056] according to Figure 6 The performance curves show that when the number of hidden layers is within 10, increasing the number of layers can effectively improve decoding performance; however, when the number of layers reaches 15, the performance gradually converges to the upper limit, and it is difficult to obtain further improvement by simply increasing the depth. Since increasing the network depth only brings limited performance improvement and more computational cost, the number of hidden layers is set to 10 in the following experiments.

[0057] Figure 7 Experimental results show that the Sigmoid-Sign scheme, which uses the Sigmoid activation function during training and the Sign activation function during testing, achieves the best bit error rate performance under various signal-to-noise ratio (SNR) conditions. In the 0–2 dB region, the differences between the schemes are small; however, in the 3–5 dB region, the performance gap increases significantly. Compared to Sigmoid-Sigmoid, Sigmoid-Sign maintains a significant advantage at higher SNRs. This indicates that using the Sigmoid function during training is beneficial for model stability optimization, while using the Sign function for hard decision-making during testing is more consistent with the binary decision-making characteristics of LDPC decoding. In contrast, although Tanh-Sign is superior to Sigmoid-Sigmoid, its overall performance is slightly inferior because Tanh is more prone to entering the saturation region in large input ranges. The Sigmoid function is... The Sign function is The Tanh function is .

[0058] Within the SNR range of 0 to 5 dB, sampling points were set at 1 dB intervals. The neural network was trained using channel data corresponding to each SNR, and the model performance was evaluated using an independent test set generated under the same SNR conditions.

[0059] The SP algorithm, MS algorithm, NMS algorithm, and the proposed NNMS algorithm were used to decode an LDPC code with a code length of 576 and a code rate of 3 / 4. The bit error rate test results are as follows: Figure 8 As shown.

[0060] The results show that the decoding performance of the NNMS algorithm is not significantly different from that of the SP, MS, and NMS algorithms in the 0-3dB range, but is significantly better than the other algorithms in the 3-5dB range. Compared with the NMS algorithm, the performance of the NNMS algorithm can be improved by up to 0.5dB.

[0061] Explained, the training and testing of neural networks are both performed under the same fixed SNR condition, meaning that a separate model needs to be trained for each SNR point. While this approach can achieve optimal performance at a specific SNR, in real-world communication systems, the channel SNR typically changes dynamically over time, and frequent model switching will incur additional storage and computational overhead.

[0062] To improve the model's adaptability under different signal-to-noise ratio (SNR) conditions, this section adopts a multi-SNR hybrid training strategy. Specifically, sampling is performed in 1dB intervals within the range of 0dB to 5dB. The encoded and decoded data generated under each SNR condition are mixed to construct a unified training set, and the improved model (Improved Neural Normalized Min-sum, NNMS, INNMS) is trained based on this dataset.

[0063] like Figure 9 As shown, INNMS maintains a stable bit error rate across the entire 0–5 dB range. While its performance is slightly lower than NNMS optimized for a single SNR, it is still significantly better than traditional SP, MS, and NMS algorithms overall. For example, at BER=10... -5 A gain of approximately 0.45 dB can be obtained at this point. At SNR=4.5 dB, the bit error rate of INNMS is approximately 10. -6 This reduces the speed by an order of magnitude compared to the traditional SP and MS algorithms.

[0064] Further analysis shows that INNMS uses the same model for evaluation across different SNR test points, eliminating the need to train a separate network for each SNR. In contrast, the traditional NNMS model exhibits a significant performance drop when deviating from the training SNR, while INNMS's performance curve is smoother and less sensitive to SNR changes, demonstrating stronger cross-SNR adaptability.

[0065] Although INNMS suffers a performance loss of approximately 0.15 dB compared to NNMS optimized for a specific signal-to-noise ratio, it can achieve unified decoding within a certain SNR range. Furthermore, since only one set of network parameters needs to be maintained across the entire range, storage overhead is reduced by more than 80% compared to multi-model switching schemes. It also avoids the complex process of repeatedly training multiple models, making it more practical from an engineering implementation perspective.

[0066] Explained, in this embodiment, compared to the traditional neural network model based on the NMS decoding algorithm, a BN layer is added to the network to accelerate convergence.

[0067] like Figure 10 As shown, the convergence speed of the optimized neural network model has been significantly improved. Under the same training conditions, the number of training rounds required for the model to converge has been reduced from 102 to 50, a reduction of about 50%, and the convergence curve is also smoother.

[0068] To investigate the reasons for the above results, a statistical analysis was performed on the distribution of the log-likelihood ratio (LLR) values ​​of neuron transmission in deep unfolded networks.

[0069] In a deep unfolded decoding network built on a Tanner graph, each hidden layer corresponds to one decoding iteration. As the network depth increases, the LLR information frequently transmitted between variable nodes and check nodes is prone to "internal covariate shift," meaning that the mean and variance of the LLR fluctuate drastically during inter-layer transmission, causing deep neurons to enter the saturation region of the activation function, leading to gradient vanishing and slowing convergence. Therefore, this embodiment extracts the LLR statistical features of intermediate layers before and after the introduction of the Batch Normalization (BN) layer during model training. The distribution histogram is shown below. Figure 11 As shown, in unnormalized deep decoding networks, the dynamic range of LLR values ​​fluctuates drastically, with the distribution center deviating significantly from the origin, causing neurons to enter the saturation region. After introducing a Batch Normalization (BN) layer, the distribution of LLR values ​​is remapped to a standard region with a mean close to 0 and a standard deviation close to 1. This stability of the distribution ensures that gradients can be effectively propagated during backpropagation, resulting in a significant improvement in model convergence speed and a smoother convergence curve on a macroscopic level.

[0070] Ablation experiments were also conducted on the decoding method proposed in this embodiment. The specific experimental analysis is shown in Table 1. Table 1 summarizes the ablation analysis.

[0071] In summary, the decoding method provided in this embodiment achieves targeted optimizations in performance, training efficiency, and generalization ability by combining learnable neural weights, BN layers, and multi-SNR training strategies. Furthermore, the modules are complementary, collectively forming a higher-performance and more practical LDPC decoding framework.

[0072] This embodiment addresses the slow convergence speed and insufficient signal-to-noise ratio (SNR) generalization ability of traditional neural network LDPC decoding methods in deep structures. It proposes a model-driven neural normalized minimum sum (NNMS) decoding algorithm based on improved batch normalization (BN). This method maps the NMS decoding process to a neural network structure through deep unfolding and introduces learnable weights to optimize the information transmission of edges in the Tanner graph. Simultaneously, a BN layer is introduced into the network to alleviate the internal covariate offset problem during LLR propagation between layers, thereby improving training stability and accelerating convergence. Furthermore, a multi-SNR hybrid training strategy enhances the model's generalization ability under different channel conditions.

[0073] Simulation results show that, under AWGN channel conditions, the proposed NNMS algorithm achieves a performance gain of approximately 0.5 dB compared to the traditional NMS algorithm in terms of bit error rate (BER). Regarding convergence performance, the introduction of the BN layer reduces the number of training epochs required for the model to reach a stable state by approximately 50%, significantly improving training efficiency. Within the SNR range of 0–5 dB, the improved model based on multi-SNR training (INNMS) maintains stable decoding performance across the entire range, achieving a BER of 10 dB. -5 It still achieves a performance gain of about 0.45dB, while avoiding the additional storage and computational overhead of training models separately for different SNRs, reducing model storage overhead by more than 80%.

[0074] In summary, the LDPC decoding method provided in this embodiment has achieved significant improvements in decoding performance, convergence speed, and SNR generalization capability, verifying the application value of batch normalization in the model-driven LDPC decoding framework. This method is suitable for communication scenarios with high requirements for reliability and adaptability to complex channels, such as deep space communication, satellite communication, and fiber optic communication, and has good engineering application prospects.

[0075] like Figure 13 As shown, exemplarily, this embodiment also provides an LDPC decoding system, including: The data acquisition module is used to acquire the log-likelihood ratio data to be decoded; A decoding module is used to input log-likelihood ratio data into a pre-trained neural network LDPC decoding model. The basic model of the neural network LDPC decoding model is constructed based on a graph structure of a low-density parity-check code, including multiple iterative layers, each of which includes a check node layer and a variable node layer. A normalization layer is introduced along the message passing path between the multiple iterative layers. This normalization layer is used to standardize the log-likelihood ratio data passed through the iterations to mitigate the distribution shift of the log-likelihood ratio data during transmission. The neural network LDPC decoding model is trained based on a mixed signal-to-noise ratio dataset. The result output module is used to output the decoding result through the neural network LDPC decoding model.

[0076] The present invention also provides an LDPC decoding device, comprising: a memory for storing a computer program; and a processor for executing the computer program to implement the steps of the LDPC decoding method.

[0077] The present invention also provides a computer program product, including a computer program / instructions that, when executed by a processor, implement the steps of the LDPC decoding method.

[0078] When the processor executes the computer program, it implements the above-described LDPC decoding steps, for example: acquiring the log-likelihood ratio data to be decoded; inputting the log-likelihood ratio data into a pre-trained neural network LDPC decoding model; wherein the basic model of the neural network LDPC decoding model is constructed based on the graph structure of a low-density parity-check code, including multiple iterative layers, each iterative layer including a check node layer and a variable node layer; introducing a normalization layer on the message passing path between the multiple iterative layers; wherein the normalization layer is used to standardize the log-likelihood ratio data passed in the iterations to alleviate the distribution shift of the log-likelihood ratio data during the transmission process; the neural network LDPC decoding model is trained based on a multi-signal-to-noise ratio mixed dataset; and outputting the decoding result through the neural network LDPC decoding model.

[0079] For example, the computer program may be divided into one or more modules / units, which are stored in the memory and executed by the processor to complete the present invention. The one or more modules / units may be a series of computer program instruction segments capable of performing a preset function, the instruction segments describing the execution process of the computer program in the LDPC decoding device. For example, the computer program can be divided into a data acquisition module, a decoding module, and a result output module; the specific functions are as follows: the data acquisition module is used to acquire the log-likelihood ratio data to be decoded; the decoding module is used to input the log-likelihood ratio data into a pre-trained neural network LDPC decoding model; wherein, the basic model of the neural network LDPC decoding model is constructed based on the graph structure of a low-density parity-check code, including multiple iterative layers, each iterative layer including a check node layer and a variable node layer; a normalization layer is introduced on the message passing path between the multiple iterative layers; wherein, the normalization layer is used to standardize the log-likelihood ratio data passed in the iteration to alleviate the distribution shift of the log-likelihood ratio data during the transmission process; the neural network LDPC decoding model is trained based on a multi-signal-to-noise ratio mixed dataset; the result output module is used to output the decoding result through the neural network LDPC decoding model.

[0080] The LDPC decoding device can be a computing device such as a desktop computer, laptop, handheld computer, or cloud server. The LDPC decoding device may include, but is not limited to, a processor and memory. Those skilled in the art will understand that the above are examples of LDPC decoding devices and do not constitute a limitation on the LDPC decoding device. It may include more components than described above, or combine certain components, or different components. For example, the LDPC decoding device may also include input / output devices, network access devices, buses, etc.

[0081] The processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor, or any conventional processor. The processor is the control center of the LDPC decoding, connecting various parts of the LDPC decoding device via various interfaces and lines.

[0082] The memory can be used to store the computer program and / or modules. The processor implements various functions of the LDPC decoding device by running or executing the computer program and / or modules stored in the memory and by calling the data stored in the memory.

[0083] The memory may primarily include a program storage area and a data storage area. The program storage area may store the operating system and at least one application program required for a function (such as sound playback, image playback, etc.). The data storage area may store data created based on the use of the mobile phone (such as audio data, phonebook, etc.). Furthermore, the memory may include high-speed random access memory and non-volatile memory, such as hard disks, RAM, plug-in hard disks, smart media cards (SMC), secure digital cards (SD cards), flash cards, at least one disk storage device, flash memory device, or other volatile solid-state storage devices.

[0084] The present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the LDPC decoding method described above.

[0085] If the modules / units integrated in the LDPC decoding system are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium.

[0086] Based on this understanding, the present invention can implement all or part of the processes in the above-described LDPC decoding method by instructing related hardware through a computer program. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the above-described LDPC decoding method. The computer program includes computer program code, which can be in the form of source code, object code, executable file, or a preset intermediate form, etc.

[0087] The computer-readable storage medium may include: any entity or device capable of carrying the computer program code, recording media, USB flash drive, portable hard drive, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signal, telecommunication signal, and software distribution medium, etc.

[0088] It should be noted that the content contained in the computer-readable storage medium may be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, the computer-readable storage medium does not include electrical carrier signals and telecommunication signals.

[0089] In summary, compared with existing decoding methods, this invention provides an LDPC decoding method with the following advantages: This method first maps the NMS decoding algorithm to a deep neural network structure based on the CCSDS standard LDPC code, utilizing deep expansion theory. The iterative decoding process between check nodes and variable nodes is expanded into a neural network model, and deep learning is used to optimize edge weights to improve decoding performance. To address the convergence issue of deep neural networks, a Batch Normalization (BN) layer is added to accelerate model convergence. This method optimizes edge weights in the Tanner graph using deep learning. Secondly, a BN layer is introduced between neural network layers to alleviate the internal covariate shift problem in the log-likelihood ratio distribution during propagation through normalization, thereby accelerating model convergence. Finally, a multi-signal-to-noise ratio (SNR) hybrid training strategy is employed to improve the model's generalization performance. Simulation results show that compared with the traditional NMS algorithm, the proposed NMS algorithm achieves a maximum gain of 0.5 dB in bit error rate performance. After introducing the BN layer, the internal parameter distribution of the network becomes more stable, the model convergence speed is improved by approximately 2 times, and it exhibits good robustness under different SNR channels. The above embodiments are merely one of the implementation methods for achieving the technical solution of the present invention. The scope of protection claimed by the present invention is not limited to this embodiment, but also includes any variations, substitutions and other implementation methods that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention.

[0090] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the present invention.

Claims

1. An LDPC decoding method, characterized in that, include: Obtain the log-likelihood ratio data to be decoded; The log-likelihood ratio data is input into a pre-trained neural network LDPC decoding model. The basic model of the neural network LDPC decoding model is constructed based on a graph structure of a low-density parity-check code, including multiple iterative layers, each of which includes a check node layer and a variable node layer. A normalization layer is introduced along the message passing path between the multiple iterative layers. This normalization layer is used to standardize the log-likelihood ratio data passed through the iterations to mitigate the distribution shift of the log-likelihood ratio data during transmission. The neural network LDPC decoding model is trained based on a mixed signal-to-noise ratio dataset. The decoding result is output through the neural network LDPC decoding model.

2. The LDPC decoding method according to claim 1, characterized in that, The introduction of a normalization layer on the message passing path between multiple iterative layers includes: The normalization layer is set on the message passing path between the verification node layer and the variable node layer.

3. The LDPC decoding method according to claim 1, characterized in that, The normalization layer standardizes the log-likelihood ratio of the iterative pass, including: The log-likelihood ratio input to the normalization layer is normalized to ensure that the processed log-likelihood ratio distribution satisfies the preset mean and variance conditions.

4. The LDPC decoding method according to claim 1, characterized in that, The basic model of the neural network LDPC decoding model is trained using a mixed dataset with multiple signal-to-noise ratios, including: Select multiple signal-to-noise ratio points within a preset signal-to-noise ratio range; Generate decoding training data corresponding to each signal-to-noise ratio point; The decoding training data is mixed to construct a multi-signal-to-noise ratio hybrid dataset; The parameters of the basic model of the neural network LDPC decoding model are optimized using a mixed dataset with multiple signal-to-noise ratios to obtain a trained neural network LDPC decoding model.

5. The LDPC decoding method according to claim 4, characterized in that, In the process of optimizing the parameters of the basic model of the neural network LDPC decoding model using a multi-signal-to-noise ratio mixed dataset, the loss function used for parameter optimization is a weighted mixture of the cross-entropy loss function and the mean squared error loss function.

6. The LDPC decoding method according to claim 1, characterized in that, During the iterative decoding process, the neural network LDPC decoding model applies the verification weight parameters and variable weight parameters obtained during training to perform weighted processing on the verification node update messages and variable node update messages, respectively.

7. The LDPC decoding method according to claim 1, characterized in that, The verification node layer and the variable node layer include verification node message passing and variable node message passing processes; in; The verification node message passing involves message updates from the verification node to the variable node, as shown in the following formula: Variable node message passing involves message updates from the variable node to the check node, as shown in the following formula: In the formula, and It is the first The weight parameters of the hidden layer; For decoding iteration rounds; For verifying the node index; Index for variable nodes; To remove variable nodes Other than the verification node A set of connected nodes; To remove the verification node Other than variable nodes A set of connected nodes; For log-likelihood ratio messages; For the first Messages from the layer verification node to the variable node; For the first Messages from layer variable nodes to verification nodes; It is a symbolic function; For variable nodes The initial log-likelihood ratio of the channel; For the first -Messages from the level 1 variable node to the verification node; For adjacent check node index; For the adjacent variable node index.

8. An LDPC decoding system, characterized in that, include: The data acquisition module is used to acquire the log-likelihood ratio data to be decoded; A decoding module is used to input log-likelihood ratio data into a pre-trained neural network LDPC decoding model. The basic model of the neural network LDPC decoding model is constructed based on a graph structure of a low-density parity-check code, including multiple iterative layers, each of which includes a check node layer and a variable node layer. A normalization layer is introduced along the message passing path between the multiple iterative layers. This normalization layer is used to standardize the log-likelihood ratio data passed through the iterations to mitigate the distribution shift of the log-likelihood ratio data during transmission. The neural network LDPC decoding model is trained based on a mixed signal-to-noise ratio dataset. The result output module is used to output the decoding result through the neural network LDPC decoding model.

9. An LDPC decoding device, characterized in that, include: Memory, used to store computer programs; A processor for implementing the LDPC decoding method of any one of claims 1-7 when executing the computer program.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it is used to implement the LDPC decoding method according to any one of claims 1-7.

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