End-to-end combined constellation shaping and pulse shaping coding method based on auto-encoder

Abstract

The invention discloses an end-to-end combined constellation shaping and pulse shaping coding method based on an auto-encoder, and the method comprises the steps: normalizing the maximum expression of generalized mutual information based on a trainable parameter, and obtaining an optimal probability shaping factor; initializing a probabilistic shaping neural network by using the factor, and realizing gradient-derivable continuous processing according to a sampler to obtain a continuous differentiable vector; the continuous differentiable vector passes through a straight-through estimator and then is sent to a geometric shaping coding end for joint optimization, a learnable pulse shaping filter is introduced to carry out time domain waveform optimization and complete modulation, and a modulated signal is obtained; transmitting the modulated signal through a channel to obtain a receiving signal y; the received y signal is sent to a neural network decoder module, and an output signal is obtained through reconstruction; according to the method, triple joint optimization of constellation probability distribution, geometric structure and time domain waveform is realized, self-adaptive updating of the system is completed, larger shaping gain is obtained, and the nonlinear effect and large capacity of the system are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of communication coding and modulation, and particularly relates to a coding method based on an end-to-end joint constellation shaping and pulse shaping of an autoencoder. Background Art

[0002] With the rapid development of global communication technology, the sixth-generation mobile communication system (The 6 th Generation, 6G) has gradually become the focus of research. The development of the terahertz frequency band is a crucial part of 6G technology. The terahertz frequency band (0.1 THz - 10 THz) has the transmission capabilities of ultra-high speed, intelligence, and high reliability, and will provide strong support for many future application scenarios. With the increasing demand for terahertz communication (0.1 - 10 THz) in 6G, how to overcome the high-frequency channel non-linearity and approach the Shannon limit has become a key challenge.

[0003] In recent years, probability shaping (PCS) and geometric shaping (GCS) technologies have significantly improved the spectral efficiency of optical communication systems by optimizing the symbol probability distribution and constellation structure, approaching the shaping gap (πe / 6) of the Shannon limit by 1.53 dB. However, existing technologies such as probability amplitude shaping (PAS) and parallel distributed matching (PDM) usually independently optimize the probability or geometric dimension, and pulse shaping mostly uses fixed filters, having the following key problems: dimension splitting causes conflicts in optimization objectives (such as PAS reducing the entropy rate but increasing the peak-to-average ratio); step-by-step optimization leads to a performance ceiling; static design cannot dynamically adapt to channel changes. Summary of the Invention

[0004] Object of the Invention: The object of the present invention is to provide a coding method based on an end-to-end joint constellation shaping and pulse shaping of an autoencoder to obtain shaping gain, improve the non-linear effect and large-capacity problem of the system. The present invention proposes a geometric-probability-pulse three-dimensional joint shaping technology based on an autoencoder, which synchronously optimizes the symbol probability, constellation position, and time-domain waveform through end-to-end training, and at the same time endows the physical layer with dynamic programmable capabilities, and can adjust parameters in real time according to the channel state, providing a solution for the next-generation elastic optical network.

[0005] Technical Solution: A coding method based on an end-to-end joint constellation shaping and pulse shaping of an autoencoder of the present invention includes the following steps:

[0006] Step 1, initialize the source coding weight, and obtain a discrete and non-differentiable probability vector through the output of the source PCS encoder;

[0007] Step 2, quantize the discrete probability distribution through a sampler to obtain a continuous and differentiable vector P;

[0008] Step 3: Send batch P into the GCS encoder for training and reconstruction to obtain the jointly optimized signal constellation points;

[0009] Step 4: Normalize the power of the signal constellation points, perform pulse shaping, complete modulation, and obtain the modulated signal;

[0010] Step 5: After transmitting the modulated signal through different channels, obtain the received signal y;

[0011] Step 6: Send the received y signal into the neural network decoder module to obtain the output signal.

[0012] Step 7: Update the model parameters by backpropagation according to the loss function and function parameters. Finally, obtain the jointly optimized probability distribution constellation points at different SNRs. And compare the model performance through indicators such as GMI and BER.

[0013] Furthermore, Step 1 is specifically as follows: Initialize the encoder weights according to the Maxwell - Boltzmann distribution and the estimation formula for maximizing GMI. The MB distribution is:

[0014] where λ ∈ [0,1] is the shaping factor, x

[0015]

[0016] is the square of the constellation point amplitude, M represents M - QAM, and P(x i ) is the constellation point symbol probability; i ) is the constellation point symbol probability;

[0017] By calculating the constellation diagrams under different probability shaping factors and substituting them into the GMI calculation formula, obtain the shaping factor corresponding to the maximum GMI. The GMI estimation formula is:

[0018]

[0019] where H is the constellation diagram entropy, X is the set of M - QAM modulation symbols, b k,i ∈ {0,1} is the i - th bit of the k - th transmitted symbol, represents the set of all symbols in the M - QAM symbol whose i - th bit value is b k,i ;

[0020] Obtain the discrete and non - differentiable probability vector p s through the NN encoding end of PCS, and then use a differentiable quantization sampler to output the differentiable signal probability distribution vector.

[0021] Further, step 2 is specifically as follows: feeding the discrete and non-differentiable probability vector into the Gumbel-Max sampler to quantize the discrete probability distribution, and using the Gumbel-SoftMax estimator to output the differentiable signal probability distribution vector, that is, there is the following formula:

[0022]

[0023] where g represents the noise sampled from the standard Gumbel distribution, g ∼ Gumbel(0,1), τ is the temperature parameter, and p s represents the probability distribution vector of the discrete distribution. P represents the continuous and differentiable probability distribution vector.

[0024] Further, step 3 is specifically as follows: passing the continuous differentiable signal through the STE straight-through estimator to generate a discrete one-hot vector to represent the signal symbol, inputting it to the NN encoding end of the GCS, and sharing parameters with the constellation encoding to complete the GCS processing, and outputting the transmitted signal S after PCS-GCS hybrid shaping GP .

[0025] Further, step 4 is specifically as follows: successively passing the transmitted signal through the probability distribution and constellation distribution weighted power normalization after joint shaping, upsampling by inserting several zero values between symbols, and a trainable pulse shaping filter to complete the pulse shaping.

[0026] Further, step 5 is specifically as follows: after transmitting the signal through the channel, obtaining the received signal y and sending it to the receiving decoding module for decoding processing.

[0027] Further, step 6 is specifically as follows: after downsampling the received signal, passing it through parallel processing with a sliding window and then sending it to the decoding end DNN neural network to complete the decoding.

[0028] Further, step 7 is specifically as follows: backpropagating to jointly optimize and update the model parameters. To obtain the optimal analysis, a loss function is defined as shown in the following formula:

[0029]

[0030] where represents the cross-entropy loss between the encoder output and the discrete symbol s, which is used to ensure the symbol reconstruction accuracy, H(p) is the entropy of the symbol distribution, is the pulse shaping loss.

[0031] The present invention also discloses an end-to-end joint constellation shaping and pulse shaping coding system based on an autoencoder, including a parameter training module, a probability initialization module, a signal reconstruction module, a pulse shaping module, a channel transmission module, a receiving decoding module, and an adaptive update module;

[0032] The parameter training module obtains the initial parameters at the PCS encoding end based on the maximum expression of the trainable parameter GMI and the MB distribution;

[0033] The probability initialization module quantifies the discrete probability distribution through a Gumbel - Max sampler to obtain a continuously differentiable probability distribution;

[0034] The signal reconstruction module inputs the continuously differentiable probability distribution into the STE, obtains discrete one - hot vector symbols, and sends them to the auto - encoder for training and reconstruction to obtain jointly optimized signal constellation points;

[0035] The pulse shaping module normalizes the power of the signal, performs pulse shaping, and passes it through a low - pass filter to complete the modulation process;

[0036] The channel transmission module transmits the signal through the channel, obtains the received signal y, and sends it to the receiving and decoding module for processing;

[0037] The receiving and decoding module sends the received y signal to the neural network decoder module to obtain the output signal.

[0038] The adaptive update module realizes the real - time update of the weights of the encoding and decoding module NNs during the back - propagation process to maximize the system performance parameter GMI.

[0039] The present invention also discloses a computer device, including a memory, a processor, and a computer program stored on the memory. The processor executes the computer program to implement the steps of the method of the present invention.

[0040] The present invention also discloses a computer - readable storage medium, on which a computer program / instructions are stored. When the computer program / instructions are executed by the processor, the steps of the method of the present invention are implemented.

[0041] Advantageous effects: Compared with the prior art, an end - to - end hybrid constellation shaping and pulse shaping joint optimization coding scheme based on a deep neural network auto - encoder proposed by the present invention can obtain a larger shaping gain, reduce the non - linear effect of the signal, obtain a shaping gain, improve the non - linear effect and large - capacity problem of the system. The present invention proposes a geometric - probability - pulse three - dimensional joint shaping technology based on the auto - encoder, synchronously optimizes the symbol probability, constellation position, and time - domain waveform through end - to - end training, and at the same time endows the physical layer with dynamic programmable capabilities, which can adjust parameters in real time according to the channel state, providing a solution for the next - generation elastic optical network. Description of the Drawings

[0042] Figure 1 is the module block diagram adopted in the specific embodiment of the present invention;

[0043] Figure 2 This is the detailed flowchart of the end-to-end joint optimization of hybrid constellation shaping and pulse shaping based on the deep neural network autoencoder of the present invention;

[0044] Figure 3 This is the comparison between the present invention and the traditional model and the pulse shaping that only uses constellation shaping;

[0045] Figure 4 This is the constellation diagram after joint hybrid shaping and adding noise;

[0046] Figure 5 This is the comparison diagram of the bit error rate between the solution of the present invention and other reference solutions under the AWGN channel;

[0047] Figure 6 This is the comparison diagram of the GMI between the solution of the present invention and other reference solutions under the AWGN channel. Specific implementation mode

[0048] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0049] In this embodiment, MATLAB is used to write code for simple simulation to verify the effect of joint optimization. The source signal is 256-QAM. In the AWGN channel, the relevant parameters of the parameter training module S1 are SNR = 30dB. According to the Maxwell-Boltzmann (MB) distribution, that is:

[0050]

[0051] λ ∈ [0, 1] is the shaping factor. The constellation points corresponding to different shaping factors are obtained and substituted into the GMI calculation formula, that is:

[0052]

[0053] The best shaping factor λ = 0.0095 under this condition is obtained.

[0054] In this embodiment, the probability initialization module S2 substitutes the best shaping factor output by the parameter training module S1 to obtain the corresponding probability shaping constellation diagram, and generates the input constellation symbols according to the constellation diagram probability.

[0055] In this embodiment, the signal reconstruction module S3 modulates the digital signal by QAM and then sends it to the GCS neural network terminal for training and reconstruction, and outputs the signal after hybrid shaping.

[0056] In this embodiment, the pulse shaping module S4 first increases the signal sampling rate by 50 times through upsampling, where the carrier frequency is 1 GHz and the sampling frequency is 50 GHz. Then, it passes through a symmetric Hamming window with a length of 21, and the length u of the window function is obtained by minimizing the mean square error loss function after the reconstruction of a set of input signals through an autoencoder training. Next, the signal is sent into a raised cosine filter, and the signal power is normalized to obtain the transmitted signal.

[0057] In this embodiment, the signal transmission module S5 transmits the above-mentioned transmitted signal through an AWGN channel, and the signal-to-noise ratio is set to 30 dB.

[0058] In this embodiment, the receiving and decoding module S6 first downsamples the signal, reducing the sampling rate by 50 times. Then, it estimates the transmitted symbols through the deep neural network (DNN) at the decoding end. The DNNs at the decoding end and the encoding end can form an autoencoder to jointly optimize the mutual information and calculate evaluation parameters such as GMI and BER.

[0059] In this embodiment, the adaptive optimization module S7 has pre-trained the parameters of the receiving end and the decoding end, and substitutes them into the model for encoding, decoding, and signal processing.

[0060] Figure 3 It is a comparison diagram of pulse shaping between the present invention and other models, which are respectively the comparison of the learned pulse shape and the received pulse of the trainable FIR filter. It can be seen that the curve fitting between the learned pulse and the received pulse in the hybrid shaping is almost perfect.

[0061] Figure 4 It is the hybrid shaping constellation diagram obtained through the autoencoder in the AWGN channel. It can be seen from the figure that in addition to the change in the position of the constellation points, the probability of the symbols also tends to be in the middle, and the probability of the high-energy symbols around is relatively low. The influence of the nonlinear effect can be reduced through the learned probability distribution, and the transmission capacity of the system can be improved.

[0062] Figure 5 and Figure 6 It is the performance comparison between the present invention and other reference schemes under different signal-to-noise ratio conditions of 256QAM in the AGWN channel, and the comparison indicators are the bit error rate and GMI respectively. It can be seen from the figure that in a relatively large signal-to-noise ratio range, the present invention has a certain shaping gain compared with other models.

[0063] The specific embodiments described above further elaborate on the purpose, technical solutions, and beneficial effects of this application. It should be understood that the above description is only the specific embodiments of this application and is not used to limit the protection scope of this application. Any modifications, equivalent replacements, improvements, etc. made on the basis of the technical solutions of this application should be included within the protection scope of this application.

Claims

1. An encoding method based on end-to-end joint constellation shaping and pulse shaping by an autoencoder, characterized in that, It includes the following steps: Step 1: Initialize the source coding weight, and obtain the discrete and non-differentiable probability vector ps through the output of the source PCS encoder; Step 2: Quantize the discrete probability distribution through a sampler to obtain a continuous and differentiable vector P; Step 3: Feed batch P into the GCS encoder for training and reconstruction to obtain the jointly optimized signal constellation points S GP ; Step 4: Pulse-shape the signal constellation points, normalize the power, complete modulation, and obtain the modulated signal; Step 5: Transmit the modulated signal through the channel to obtain the received signal y; Step 6: Send the received y signal into the neural network decoder module to obtain the output signal; Step 7: Update the autoencoder AE and function model parameters by backpropagation according to the loss function, and finally obtain the jointly optimized probability distribution constellation points at different SNRs.

2. The encoding method based on end-to-end joint constellation shaping and pulse shaping using an autoencoder according to claim 1, characterized in that, Step 1 is specifically: Initialize the encoder weight according to the Maxwell-Boltzmann distribution and the estimation formula for maximizing GMI, that is: Among them, λ ∈ [0, 1] is the shaping factor, x i is the square of the amplitude of the constellation point, M represents M-QAM, and P(x i ) is the symbol probability of the constellation point; By calculating the constellation diagram under different MB distribution probability shaping factors, substitute it into the GMI calculation formula to obtain the shaping factor λ corresponding to the maximum GMI. The GMI estimation formula is: Among them, H is the entropy of the constellation diagram conforming to the MB distribution under different signal-to-noise ratios, X is the set of M-QAM modulation symbols, and b k,i ∈ {0, 1} is the i-th bit of the k-th transmitted symbol, denotes the set of all symbols in the M-QAM symbol where the i-th bit value is b k,i ; Output a discrete and non-differentiable probability vector p through the PCS coding end s , and then use a differentiable quantization sampler to output a differentiable signal probability distribution vector P.

3. The encoding method based on end-to-end joint constellation shaping and pulse shaping using an autoencoder according to claim 1, characterized in that, Step 2 is specifically: Under the shaping factor at the optimal GMI, initialize the PCS coding end, send the obtained discrete and non-differentiable probability vector into the Gumbel-Max sampler for quantization, and use the Gumbel-SoftMax estimator to output the differentiable signal probability distribution vector P, that is, there is the following formula: where g represents the noise sampled from the standard Gumbel distribution, g ∼ Gumbel(0,1), τ is the temperature parameter, and p s represents the probability vector of the discrete distribution.

4. A coding method based on an autoencoder for end-to-end joint constellation shaping and pulse shaping according to claim 1, characterized in that, Step 3 is as follows: the continuous differentiable signal passes through the STE direct estimator to generate a discrete one-hot vector s to represent the signal symbol, which is input into the neural network encoding end of the GCS and shares parameters with the constellation diagram encoding to complete the GCS processing and output the transmission complex signal S after PCS-GCS hybrid shaping. GP .

5. A coding method based on end-to-end joint constellation shaping and pulse shaping by an autoencoder according to claim 1, characterized in that, Step 4 is specifically: After passing the PCS output signal through the SoftMax function, calculate the power normalization factor in combination with the constellation diagram output by the GCS coding end, normalize the signal power, and then perform upsampling, that is, insert several zero values between each symbol, depending on the sampling ratio, and then separate the real and imaginary parts and input them into the trainable pulse shaping filter for convolution to complete pulse shaping.

6. The encoding method based on end-to-end joint constellation shaping and pulse shaping using an autoencoder according to claim 1, characterized in that, Step 5 is specifically: After transmitting the signal through the channel, obtain the received signal y and send it into the receiving decoding module for decoding processing.

7. A coding method based on end-to-end joint constellation shaping and pulse shaping using an autoencoder according to claim 1, characterized in that, Step 6 is specifically: After downsampling the received signal y, send it into the decoding NN end after parallel processing through a sliding window to complete decoding; evaluate the indicators of GMI and BER through the output signal, and calculate the cross-entropy loss and distribution entropy in the loss function at the coding end for backpropagation to update the model parameters.

8. A coding method based on end-to-end joint constellation shaping and pulse shaping using an autoencoder according to claim 1, characterized in that, Step 7 is specifically: Based on the loss function, realize real-time updating of the coding end, decoding end, and pulse shaping parameters during backpropagation to maximize the system performance GMI; obtain the optimal analysis-defined loss function through the following formula; Among them, represents the cross-entropy loss between the encoder output and the discrete symbol s, which is used to ensure the symbol reconstruction accuracy. H(p) is the entropy of the symbol distribution, is the pulse shaping loss.

9. A coding system based on an autoencoder for end-to-end joint constellation shaping and pulse shaping, used to implement the method as described in claim 1, characterized in that, It includes a parameter training module, a probability initialization module, a signal reconstruction module, a pulse shaping module, a channel transmission module, a receiving decoding module, and an adaptive update module; The parameter training module obtains the initial parameters of the PCS coding end based on the maximum expression of the trainable parameter GMI and the MB distribution; The probability initialization module quantizes the discrete probability distribution through the Gumbel-Max sampler to obtain a continuous and differentiable probability distribution; The signal reconstruction module passes the continuous and differentiable probability distribution through STE to obtain a discrete one-hot vector symbol and sends it into the autoencoder for training and reconstruction to obtain the jointly optimized signal constellation points; The pulse shaping module normalizes the power of the signal, performs pulse shaping, and uses a low-pass filter to complete the modulation process; The channel transmission module transmits the signal through the channel, obtains the received signal y, and sends it to the receiving and decoding module for processing; The receiving and decoding module sends the received y signal to the neural network decoder module to obtain the output signal; The adaptive update module updates the model parameters through backpropagation according to the output signal and the loss function expression, and obtains the optimized symbol representation and transmission strategy.

10. A computer device, comprising a memory, a processor, and a computer program stored on the memory, characterized in that, The processor executes the computer program to implement the steps of the method described in claim 1.

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