Offset minimum and LDPC code decoding algorithm based on model-driven neural network

Abstract

The invention discloses an offset minimum sum LDPC (Low Density Parity Check) code decoding algorithm based on a model-driven neural network, and relates to an offset minimum sum LDPC code decoding algorithm. The invention aims to solve the problem that a traditional LDPC decoding algorithm is insufficient in convergence speed, calculation complexity, flexibility and the like. The method comprises the following steps: step 1, constructing a model-driven offset minimum sum algorithm network model, wherein the network model comprises an input layer, a check node layer, a variable node layer and an output layer; step 2, an input layer calculates a receiving channel LLR by using the receiving signal y to carry out initialization; step 3, the check node layer calculates the LLR value of the CN-to-VN; step 4, the variable node layer calculates the LLR value of the VN-to-CN; and step 5, calculating final decoding output by an output layer. The invention belongs to the technical field of decoding.

Description

Technical Field

[0001] The invention relates to a minimum deviation and LDPC code decoding algorithm, belonging to the technical field of decoding. Background Art

[0002] In modern communication systems, channel coding is an important technology to ensure reliable data transmission. Channel coding adds redundant information to the transmitted data so that the receiver can correct errors caused by noise, interference, and signal attenuation. Common channel coding schemes include convolutional codes, turbo codes, and low-density parity-check codes (LDPC codes). LDPC codes are an effective channel coding method with performance close to the Shannon limit. The encoding and decoding process of LDPC codes is described by graph theory, especially using sparse graphs (bit graphs and check graphs) to represent them. Their key features include: 1) Sparsity: There are only a small number of non-zero elements in the rows and columns of the LDPC matrix, which reduces the computational complexity of encoding and decoding. 2) Scalability: LDPC codes can adjust the length and code rate according to requirements to adapt to different application scenarios.

[0003] Traditional LDPC decoding algorithms mainly include the belief propagation (BP) algorithm and the minimum sum algorithm (Min-Sum). The belief propagation algorithm is based on an iterative method that gradually updates the confidence of each bit by passing messages between the bitmap and the check map. This method has superior performance, but may converge slowly in a high signal-to-noise ratio environment. The minimum sum algorithm is a simplified belief propagation algorithm that reduces computational complexity by selecting the minimum value, but there will be some compromise in 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) Physical knowledge integration: By combining domain knowledge and data-driven methods, the performance and reliability of the model are improved. 2) Network architecture design: Design a neural network architecture that can capture channel characteristics, usually including convolutional layers, recurrent layers, etc., to adapt to channel changes and interference characteristics. Researchers have begun to use deep learning methods to decode LDPC codes, mainly including: 1) Neural network decoder: The neural network decoder 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: The network is trained using a dataset generated by simulation to enhance its robustness in the actual channel environment.

[0005] Existing traditional LDPC decoding algorithms usually require multiple iterations to converge, especially in low signal-to-noise ratio (SNR) environments. Slow convergence may cause decoding delays, affecting the performance of real-time systems. And in the high-complexity iteration process, especially when the code length increases, the computational overhead will increase significantly. The belief propagation algorithm involves a lot of message passing and calculations, resulting in high latency. Finally, although the traditional algorithm performs well in many cases, its performance may be limited under certain extreme conditions and cannot reach performance close to the Shannon limit.

[0006] In general, the traditional LDPC decoding algorithm has certain shortcomings in terms of convergence speed, computational complexity, and flexibility. The application of model-driven neural networks in LDPC code decoding combines the advantages of traditional channel coding and the flexibility of modern deep learning. By combining these two technologies, 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 the innovation of the next generation of communication technology. Summary of the invention

[0007] The present invention aims to solve the problems that traditional LDPC decoding algorithms have deficiencies in terms of convergence speed, computational complexity, flexibility, etc., and further proposes an offset minimum and LDPC code decoding algorithm based on a model-driven neural network.

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

[0009] Step 1: construct a model-driven minimum-drift-sum algorithm network model, wherein the network model includes an input layer, a check node layer, a variable node layer, and an output layer;

[0010] Step 2: The input layer uses the received signal y to calculate the received channel LLR for initialization;

[0011] Step 3: The verification node layer calculates the LLR value of CN-to-VN;

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

[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 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, V j represents the set of column positions of '1' in the jth row, Vj\i represents V that does not contain the variable node VNi j .

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

[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 include the check node CNj.

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

[0024]

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

[0026] The beneficial effects of the present invention are:

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

[0028] 2. Although neural network training may require more computing resources in the early stages, in the inference stage, neural networks can be processed efficiently in parallel, thereby greatly reducing the computational complexity of real-time decoding;

[0029] 3. Through training, neural networks can learn various channel characteristics and have stronger adaptability. They can be fine-tuned under different channel conditions to provide better performance;

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

[0031] 5. The design and training process of neural networks is relatively complex, but once the training is completed, the implementation and optimization of the inference process are relatively simple and can be easily deployed using modern deep learning frameworks. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a diagram of the LDPC decoding structure proposed by the present invention;

[0033] Figure 2 It is the signal flow chart of the model of the present invention;

[0034] Figure 3 It is a simulation diagram of the number of iterations of the model of the present invention;

[0035] Figure 4 It is a simulation diagram of the bit error rate performance of the model of the present invention. DETAILED DESCRIPTION

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

[0037] Step 1: construct a model-driven minimum-drift-sum algorithm network model, wherein the network model includes an input layer, a check node layer, a variable node layer, and an output layer;

[0038] Step 2: The input layer uses the received signal y to calculate the received channel LLR for initialization; the calculation formula is as follows:

[0039]

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

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

[0042]

[0043] In formula (2), α represents the correction factor, V j represents the set of column positions of '1' in the jth row, Vj\i represents V that does not contain the 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, σ(x)=(1+e -x ) -1 and the activation function σ(x)=(1+sgn(x)) / 2.

[0050] Among them, the task of the LDPC decoder is to estimate the transmitted information bits The detailed signal flow chart of the receiving end of the decoding network is as follows Figure 2 As shown in Figure 2, the iterative decoding algorithm is expanded 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 different correction factors α in each iteration. ij and β ji , which 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 receiving channel corresponding to bit i, then the CN-to-VN message L(rji) and VN-to-CN message L(qij) are propagated and iteratively updated.

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

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

[0053] Secondly, in the lth hidden layer, in order to calculate the CN-to-VN message L(rji), the data set L(qi'j) connected to CNj is extracted from L(qij) through Wv2c, where Wv2c is the row weight information of the check matrix H, and L(rji) is calculated by the neurons of the CN layer;

[0054] Third, to calculate the VN-to-CN message L(qij), extract the data set L(rj′i) from L(rji) through Wc2v, where L(rj′i) connects VNi except CNj, where Wc2v comes from the column weight information of the check matrix H;

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

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

[0057]

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

[0059] Example

[0060] The proposed LDPC decoding network is trained and tested using the Tensorflow framework. The LDPC code is designed according to the IEEE802.16e standard, with a code block length of 576, a code rate of 3 / 4, and randomly selected codewords. The training data is generated under multiple signal-to-noise ratios (SNRs) from 0dB to 5dB. The network is trained using the min-batch gradient descent method. Each mini-batch contains 120 data blocks, and each SNR has the same proportion in a mini-batch. The Adaptive Moment Estimation (Adam) optimization method with a learning rate of 0.001 is used to search for the optimal network parameters.

[0061] Figure 3 The BER performance is analyzed from the perspective of the number of network layers. Within a certain range of network layers, the BER performance improves as the number of network layers increases. It must be pointed out that deeper network layers consume more multiplication and summation operations, and the improvement in bit error rate performance comes at the cost of computational complexity. When the number of network layers reaches a certain depth, the decoder bit error performance will not be greatly improved, which is also in line with the nature of conventional LDPC decoding. Therefore, considering the trade-off between performance and complexity, we recommend choosing 10 iterations in a 22-layer network.

[0062] Figure 4 The traditional OMS algorithm and NOMS network model are compared. When the network model is iterated 15 times, the bit error rate of the proposed model can reach 10 -8 , and the performance of the NOMS model proposed by others can be improved by 0.5dB. This is because the present invention adaptively optimizes the OMS algorithm and has better performance in the model-driven deep learning method.

[0063] The above is only a preferred embodiment of the present invention and does not limit the present invention in any form. Although the present invention has been disclosed as a preferred embodiment as above, it is not used to limit the present invention. Any technician familiar with this profession can make some changes or modify the technical contents disclosed above into equivalent embodiments without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent replacement and improvement made to the above embodiments without departing from the content of the technical solution of the present invention, based on the technical essence of the present invention, within the spirit and principles of the present invention, still fall within the protection scope of the technical solution of the present invention.

Claims

1. A minimum-shift LDPC code decoding algorithm based on a model-driven neural network, characterized in that: Specifically include: Step 1: construct a model-driven minimum-drift-sum algorithm network model, wherein the network model includes an input layer, a check node layer, a variable node layer, and an output layer; Step 2: The input layer uses the received signal y to calculate the received channel LLR for initialization; Step 3: The verification node layer calculates the LLR value of CN-to-VN; Step 4: The variable node layer calculates the LLR value of VN-to-CN; Step 5: The output layer calculates the final decoded output.

2. The method of claim 1, wherein the minimum deviation and LDPC code decoding algorithm based on a model-driven neural network is characterized in that: The calculation formula in step 2 is as follows: In formula (1), σ 2 represents the noise variance under additive white Gaussian noise channel conditions.

3. The method of claim 1, wherein the minimum deviation and LDPC code decoding algorithm based on a model-driven neural network is characterized in that: The calculation formula in step 3 is as follows: In formula (2), α represents the correction factor, V j represents the set of column positions of '1' in the jth row, Vj\i represents V that does not contain the variable node VNi j .

4. The method of claim 1, wherein the minimum deviation and LDPC code decoding algorithm based on a model-driven neural network is characterized in that: The calculation formula in step 4 is: 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 include the check node CNj.

5. The method of claim 1, wherein the minimum deviation and LDPC code decoding algorithm based on a model-driven neural network is characterized in that: The calculation formula in step 5 is: In formula (4), l is the number of iterations, and lmax is the maximum number of iterations. In the output neuron, σ(x)=(1+e -x ) -1 and the activation function σ(x)=(1+sgn(x)) / 2.

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