Model-driven neural network based decoding algorithm for offset min-sum ldpc codes

Abstract

The application discloses a model-driven neural network-based offset min-sum LDPC code decoding algorithm and relates to an offset min-sum LDPC code decoding algorithm. The application is designed to solve the problems of the traditional LDPC decoding algorithm in convergence speed, calculation complexity, flexibility and the like. The application comprises the following steps: 1, a model-driven offset min-sum algorithm network model is constructed, wherein the network model comprises an input layer, a check node layer, a variable node layer and an output layer; 2, the input layer is used to calculate the received channel LLR by using a received signal y to perform initialization; 3, the check node layer is used to calculate the CN-to-VN LLR value; 4, the variable node layer is used to calculate the VN-to-CN LLR value; and 5, the output layer is used to calculate a final decoding output. The application belongs to the technical field of decoding.

Description

Technical Field

[0001] This invention relates to a minimum offset LDPC code decoding algorithm, belonging to the field of decoding technology. Background Technology

[0002] In modern communication systems, channel coding is a crucial technique for ensuring reliable data transmission. Channel coding adds redundant information to the transmitted data, allowing the receiver to correct errors caused by noise, interference, and signal attenuation. Common channel coding schemes include convolutional codes, turbine codes, and low-density parity-check codes (LDPC codes). LDPC codes are an efficient channel coding method, exhibiting performance close to the Shannon limit. The encoding and decoding processes of LDPC codes are described using graph theory, specifically using sparse graphs (bit graphs and check graphs). Their key characteristics include: 1) Sparsity: The rows and columns of the LDPC matrix contain only a small number of non-zero elements, reducing the computational complexity of encoding and decoding. 2) Scalability: LDPC codes can adjust their length and code rate according to requirements, adapting to different application scenarios.

[0003] Traditional LDPC decoding algorithms mainly include the belief propagation (BP) algorithm and the min-sum algorithm. The belief propagation algorithm is an iterative method that updates the confidence of each bit incrementally by passing messages between the bitmap and the check graph. This method offers excellent performance, but may converge slowly in high signal-to-noise ratio environments. The min-sum algorithm is a simplified version of the belief propagation algorithm, reducing computational complexity by selecting the minimum value, but this comes at the cost of performance.

[0004] In recent years, deep learning technology has made significant progress in many fields, especially in image processing and natural language processing. Researchers have gradually begun to explore the application of deep learning in communication systems, including channel estimation, channel coding, and decoding. Model-driven deep learning combines traditional model design with deep learning, using deep neural networks (DNNs) to approximate complex channel models or decoding processes. The key to this method is: 1) Incorporation of physical knowledge: By combining domain knowledge and data-driven methods, the performance and reliability of the model are improved. 2) Network architecture design: Designing a neural network architecture that can capture channel characteristics, typically including convolutional layers, recurrent layers, etc., to adapt to channel changes and interference characteristics. Researchers have begun to use deep learning methods for LDPC code decoding, mainly including: 1) Neural network decoders: Neural network decoders built based on deep learning can effectively learn channel characteristics and improve decoding performance through training. 2) Model optimization: By optimizing the network structure and training process, the decoding efficiency and accuracy of the neural network for LDPC codes are improved. 3) Data-driven learning: Using simulation-generated datasets to train the network, thereby enhancing its robustness in real channel environments.

[0005] Existing traditional LDPC decoding algorithms typically require multiple iterations to converge, especially in low signal-to-noise ratio (SNR) environments. Slow convergence can lead to decoding delays, impacting the performance of real-time systems. Furthermore, computational overhead increases significantly during high-complexity iterations, particularly as code lengths increase. Belief propagation algorithms involve substantial message passing and computation, resulting in high latency. Finally, while traditional algorithms perform well in many cases, their performance may be limited under certain extreme conditions, preventing them from approaching the Shannon limit.

[0006] In summary, traditional LDPC decoding algorithms have certain shortcomings in terms of convergence speed, computational complexity, and flexibility. However, the application of model-driven neural networks in LDPC code decoding combines the advantages of traditional channel coding with the flexibility of modern deep learning. By combining these two techniques, the decoding performance of LDPC codes can be effectively improved, promoting the development of communication systems in terms of efficiency and reliability. This research direction not only provides new ideas for the application of LDPC codes but also lays the foundation for innovation in next-generation communication technologies. Summary of the Invention

[0007] To address the shortcomings of traditional LDPC decoding algorithms in terms of convergence speed, computational complexity, and flexibility, this invention proposes a model-driven neural network-based offset-minimum LDPC code decoding algorithm.

[0008] The technical solution adopted by the present invention to solve the above problems is as follows: The present invention specifically includes:

[0009] Step 1: Construct a model-driven offset minimum sum algorithm network model, which includes an input layer, a check node layer, a variable node layer, and an output layer;

[0010] Step 2: The input layer initializes the received channel LLR by calculating the received signal y.

[0011] Step 3: Verify the node layer to calculate the LLR value of CN-to-VN;

[0012] Step 4: Calculate the LLR value of VN-to-CN at the variable node layer;

[0013] Step 5: The output layer calculates the final decoded output.

[0014] Furthermore, the calculation formula in step 2 is as follows:

[0015]

[0016] In formula (1), σ 2 This represents the noise variance under additive white Gaussian noise channel conditions.

[0017] Furthermore, the calculation formula in step 3 is as follows:

[0018]

[0019] In formula (2), α represents the correction factor, and V j Vj represents the set of column positions of '1' in the j-th row, and Vj\i represents the set of V that does not contain variable node VNi. j .

[0020] Furthermore, the calculation formula in step 4 is as follows:

[0021]

[0022] In formula (3), Ci represents the set of row positions of '1' in the i-th column (representing the set of CNs connected to VNi), and Ci\j represents Ci that does not contain the check node CNj.

[0023] Furthermore, the calculation formula in step 5 is as follows:

[0024]

[0025] In formula (4), l is the number of iterations, and lmax is the maximum number of iterations. In the output neuron, the training and testing phases respectively adopt σ(x)=(1+e -x ) -1 And the activation function σ(x)=(1+sgn(x)) / 2.

[0026] The beneficial effects of this invention are:

[0027] 1. The decoding process proposed in this invention, through a deep learning model, can usually converge faster, especially with the support of a large amount of training data;

[0028] 2. Although neural network training may require a lot of computing resources in the early stages, neural networks can efficiently process data in parallel during the inference stage, thereby significantly reducing the computational complexity of real-time decoding.

[0029] 3. Through training, neural networks can learn various channel characteristics, exhibiting greater adaptability. They can be fine-tuned under different channel conditions, providing better performance;

[0030] 4. Neural networks can learn complex nonlinear mappings to approximate the optimal decoding strategy, thereby achieving better decoding performance under specific conditions and approaching or exceeding the performance limits of traditional algorithms.

[0031] 5. The design and training process of neural networks is relatively complex, but once training is complete, the implementation and optimization of the inference process is relatively simple and can be easily deployed using modern deep learning frameworks. Attached Figure Description

[0032] Figure 1 This is a diagram of the LDPC decoding structure proposed in this invention;

[0033] Figure 2 This is a signal flow diagram of the model of the present invention;

[0034] Figure 3 This is a simulation diagram showing the number of iterations of the model in this invention;

[0035] Figure 4 This is a simulation diagram of the bit error rate performance of the model of this invention. Detailed Implementation

[0036] Specific implementation method one: as follows Figures 1 to 4 As shown, a model-driven neural network-based offset-minimum LDPC code decoding algorithm specifically includes:

[0037] Step 1: Construct a model-driven offset minimum sum algorithm network model, which includes an input layer, a check node layer, a variable node layer, and an output layer;

[0038] Step 2: The input layer initializes the received channel LLR using the received signal y; the calculation formula is as follows:

[0039]

[0040] In formula (1), σ 2 This represents the noise variance under additive white Gaussian noise channel conditions;

[0041] Step 3: Calculate the LLR value of CN-to-VN at the verification node layer; the calculation formula is as follows:

[0042]

[0043] In formula (2), α represents the correction factor, and V j Vj represents the set of column positions of '1' in the j-th row, and Vj\i represents the set of V that does not contain variable node VNi. j ;

[0044] Step 4: Calculate the LLR value of VN-to-CN at the variable node layer; the calculation formula is:

[0045]

[0046] In formula (3), Ci represents the set of row positions of '1' in the i-th column (representing the set of CNs connected to VNi), and Ci\j represents Ci that does not contain the check node CNj;

[0047] Step 5: The output layer calculates the final decoded output; the calculation formula is:

[0048]

[0049] In formula (4), l is the number of iterations, and lmax is the maximum number of iterations. In the output neuron, the training and testing phases respectively adopt σ(x)=(1+e -x ) -1 And the activation function σ(x)=(1+sgn(x)) / 2.

[0050] The task of the LDPC decoder is to estimate the transmitted information bits. The detailed signal flow diagram of the receiver end of the decoding network is as follows: Figure 2 As shown, the iterative decoding algorithm is unfolded into a forward propagation network. In the Tanner graph, the parity check matrix H determines the edges connecting CNs and VNs. The messages between the CN layer and the VN layer are multiplied by a different correction factor α in each iteration. ij and β ji This is equivalent to adding weight parameters in each iteration. The process of calculating CN-to-VN messages and VN-to-CN messages is implemented by the CN layer and VN layer in the neural network, respectively. Let L(ui) represent the log-likelihood ratio of the received channel corresponding to bit i. Then, CN-to-VN messages L(rji) and VN-to-CN messages L(qij) are propagated and iteratively updated.

[0051] Among them, such as Figure 2 The LDPC decoding network shown;

[0052] First, the received data L(ui) is fed into the LDPC decoding network through the input layer as the initialization data L(qij);

[0053] Secondly, in the l-th hidden layer, in order to compute the CN-to-VN message L(rji), the dataset L(qi'j) connected to CNj is extracted from L(qij) through Wv2c, where Wv2c is the row weight information of the verification matrix H, and L(rji) is computed through the neurons of the CN layer.

[0054] Third, in order to calculate the VN-to-CN message L(qij), the dataset L(rj′i) is extracted from L(rji) by Wc2v, where L(rj′i) connects VNi except CNj. Here, Wc2v comes from the column weight information of the verification matrix H.

[0055] L(qij) is computed in neurons of the VN layer. Similarly, the number of iterations can be easily increased by adding more CN and VN layers in the hidden layers. For (N,k)LDPC codes, T iterations are expanded into a deep neural network with 2lmax+2 layers, including lmax CN layers, lmax VN layers, 1 input layer and 1 output layer.

[0056] Finally, we train the proposed network using the cross-entropy loss function, which measures the error between the neural network output o and the transmitted codeword u, and is defined as:

[0057]

[0058] In formula (5), ui and oi are the i-th transmitted information bit and the network soft estimate, respectively.

[0059] Example

[0060] The proposed LDPC decoding network was trained and tested using the TensorFlow framework. LDPC codes were designed according to the IEEE 802.16e standard, with a block length of 576, a code rate of 3 / 4, and randomly selected codewords. Training data was generated at multiple signal-to-noise ratios (SNRs) ranging from 0dB to 5dB. The network was trained using a min-batch gradient descent method. Each mini-batch contained 120 data blocks, with each SNR representing an equal proportion within a mini-batch. The optimal network parameters were searched using the Adaptive Moment Estimation (Adam) optimization method with a learning rate of 0.001.

[0061] Figure 3 The BER performance was analyzed from the perspective of network layer count. Within a certain range of network layers, BER performance improves with increasing network layer count. It must be noted that deeper network layers consume more multiplication and summation operations; the improvement in BER performance comes at the cost of computational complexity. When the network layer count reaches a certain depth, the decoder's BER performance does not improve significantly, which is consistent with the nature of conventional LDPC decoding. Therefore, considering the trade-off between performance and complexity, we recommend selecting 10 iterations in a 22-layer network.

[0062] Figure 4 The traditional OMS algorithm and the NOMS network model were compared. The proposed model achieves a bit error rate of 10% after 15 iterations. -8 Furthermore, the performance of this invention is 0.5 dB higher than that of the NOMS model proposed by others. This is because the OMS algorithm is adaptively optimized in this invention, resulting in better performance in model-driven deep learning methods.

[0063] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent substitutions, and improvements made to the above embodiments without departing from the scope of the present invention, based on the technical essence of the present invention and within the spirit and principles of the present invention, shall still fall within the protection scope of the present invention.

Claims

1. A model-driven neural network-based offset-minimum LDPC code decoding algorithm, characterized in that, Specifically, it includes: Step 1: Construct a model-driven offset minimum sum algorithm network model, which includes an input layer, a check node layer, a variable node layer, and an output layer; Step 2: The input layer initializes the received channel LLR using the received signal y; the calculation formula is as follows: （1）， In formula (1), This represents the noise variance under additive white Gaussian noise channel conditions; Step 3: Calculate the LLR value of CN-to-VN at the verification node layer; the calculation formula is as follows: （2）， In formula (2), Indicates the correction factor. Vj represents the set of column positions of '1' in the j-th row, and Vj\i represents the set of columns that do not contain variable nodes VNi. ; Step 4: Calculate the LLR value of VN-to-CN at the variable node layer; the calculation formula is: （3）， In formula (3), Ci represents the set of row positions of '1' in the i-th column (representing the set of CNs connected to VNi), and Ci\j represents Ci that does not contain the check node CNj; Step 5: The output layer calculates the final decoded output; the calculation formula is: （4）， In formula (4), l is the number of iterations, and lmax is the maximum number of iterations. In the output neuron, the training and testing phases respectively adopt... and The activation function.

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