Encoding method based on end-to-end joint constellation shaping and pulse shaping with autoencoder

Abstract

The application discloses an encoding method based on end-to-end joint constellation shaping and pulse shaping of a self-encoder, and comprises the following steps: obtaining an optimal probability shaping factor based on a maximum expression of trainable parameter normalized generalized mutual information; initializing a probability shaping neural network by using the factor, realizing gradient-derivable continuous processing according to a sampler, and obtaining a continuous differentiable vector; sending the continuous differentiable vector to a geometric shaping encoding end after passing through a straight-through estimator to perform joint optimization, introducing a learnable pulse shaping filter to perform time-domain waveform optimization and complete modulation, and obtaining a modulated signal; transmitting the modulated signal through a channel to obtain a received signal y; sending the received signal y to a neural network decoder module to reconstruct an output signal; and the application realizes triple joint optimization of constellation probability distribution, geometric structure and time-domain waveform, completes adaptive updating of the system, obtains greater shaping gain, and improves nonlinear effects and large capacity problems of the system.

Description

Technical Field

[0001] This invention belongs to the field of communication coding and modulation technology, and particularly relates to a coding method based on end-to-end joint constellation shaping and pulse shaping using an autoencoder. Background Technology

[0002] With the rapid development of global communication technology, the sixth-generation mobile communication system (The 6G) has emerged. th Terahertz (6G) technology is gradually becoming a research focus, with the development of the terahertz band being a crucial component. The terahertz band (0.1 THZ to 10 THz) offers ultra-high speed, intelligent, and highly reliable transmission capabilities, providing strong support for numerous future applications. As 6G increases its demands for terahertz communication (0.1-10 THz), overcoming high-frequency channel nonlinearity and approaching the Shannon limit becomes a key challenge.

[0003] In recent years, probabilistic shaping (PCS) and geometric shaping (GCS) techniques have significantly improved the spectral efficiency of optical communication systems by optimizing symbol probability distribution and constellation structure, approaching the Shannon limit of 1.53 dB shaping gap (πe / 6). However, existing techniques such as probabilistic amplitude shaping (PAS) and parallel distributed matching (PDM) typically optimize the probability or geometric dimension independently, and pulse shaping often uses fixed filters, resulting in the following key problems: dimensional fragmentation causes conflicting optimization objectives (e.g., PAS reduces entropy rate but increases peak-to-average power ratio); step-by-step optimization leads to performance ceilings; and static design cannot dynamically adapt to channel changes. Summary of the Invention

[0004] Purpose of the Invention: The purpose of this invention is to provide a coding method based on end-to-end joint constellation shaping and pulse shaping using an autoencoder to obtain shaping gain and improve the nonlinear effects and large capacity of the system. This invention proposes a geometric-probabilistic-pulse three-dimensional joint shaping technique based on an autoencoder. Through end-to-end training, it synchronously optimizes symbol probability, constellation position, and time-domain waveform, while simultaneously endowing the physical layer with dynamic programmability, allowing parameters to be adjusted in real time according to channel conditions, thus providing a solution for next-generation resilient optical networks.

[0005] Technical solution: The present invention provides an encoding method based on end-to-end joint constellation shaping and pulse shaping of an autoencoder, comprising the following steps:

[0006] Step 1: Initialize the source coding weights 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 using a sampler to obtain a continuously 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, shape the pulses, and complete the modulation to obtain the modulated signal;

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

[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 through backpropagation based on the loss function and function parameters, ultimately obtaining the jointly optimized probability distribution constellation points under different SNRs. Then, compare the model performance using metrics such as GMI and BER.

[0013] Furthermore, step 1 specifically involves: using the Maxwell-Boltzmann distribution and the formula for maximizing GMI...

[0014] The encoder weights are initialized using the formula, and the MB distribution is as follows:

[0015]

[0016] Where λ∈[0,1] is the integer factor, x i The square of the constellation point amplitude, M represents M-QAM, P(x i () represents the probability of the constellation point sign;

[0017] By calculating the constellation diagram under different probability shaping factors, and substituting it into the GMI calculation formula, the shaping factor corresponding to the maximum GMI is obtained. The GMI estimation formula is as follows:

[0018]

[0019] Where H is the constellation diagram entropy, 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. This indicates that the value of the i-th bit in the M-QAM symbol is b. k,i The set of all symbols.

[0020] The discrete and non-differentiable probability vector p is obtained through the NN encoder of PCS. s Then, a differentiable sampler is used to output a differentiable signal probability distribution vector.

[0021] Furthermore, step 2 specifically involves feeding the discrete and non-differentiable probability vector into a Gumbel-Max sampler to quantize the discrete probability distribution, and using a Gumbel-SoftMax estimator to output a differentiable signal probability distribution vector, as shown in 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 Let P represent the probability distribution vector of a discrete distribution. P represents a continuously differentiable probability distribution vector.

[0024] Further, step 3 specifically involves: passing the continuously differentiable signal through the STE direct-through estimator to generate a discrete one-hot vector representing the signal symbol, inputting this vector into the NN encoding end of the GCS, and sharing parameters with the constellation diagram encoding to complete the GCS processing, outputting the transmitted signal S after PCS-GCS hybrid shaping. GP .

[0025] Further, step 4 specifically involves: after the transmitted signal is subjected to joint shaping, the probability distribution and constellation distribution are weighted and normalized, and several zero values ​​are inserted between symbols for upsampling, thus completing the pulse shaping filter.

[0026] Furthermore, step 5 specifically involves: transmitting the signal through the channel to obtain the received signal y and sending it to the receiving decoding module for decoding processing.

[0027] Furthermore, step 6 specifically involves: after downsampling the received signal, processing it in parallel through a sliding window, and then feeding it into the DNN neural network at the decoding end to complete the decoding.

[0028] Furthermore, step 7 specifically involves backpropagation to jointly optimize and update the model parameters. To obtain the optimal analysis, the loss function is defined as follows:

[0029]

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

[0031] The present invention also discloses an encoding system based on end-to-end joint constellation shaping and pulse shaping of 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 of the PCS encoder based on the maximum expression of the trainable parameter GMI and the MB distribution.

[0033] The probability initialization module quantizes the discrete probability distribution using a Gumbel-Max sampler to obtain a continuously differentiable probability distribution.

[0034] The signal reconstruction module inputs a continuously differentiable probability distribution into the STE to obtain discrete one-hot vector symbols, which are then fed into the autoencoder for training and reconstruction to obtain jointly optimized signal constellation points.

[0035] The pulse shaping module performs power normalization, pulse shaping, and low-pass filtering on the signal to complete the modulation process.

[0036] The channel transmission module transmits the signal through the channel to obtain the received signal y and sends it to the receiving 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 updates the weights of the encoding / decoding modules (NNs) in real time during backpropagation 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 in the memory, wherein 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 having a computer program / instructions stored thereon, which, when executed by a processor, implements the steps of the method of the present invention.

[0041] Beneficial Effects: Compared with existing technologies, the coding scheme proposed in this invention, which combines end-to-end hybrid constellation shaping and pulse shaping based on a deep neural network autoencoder, achieves greater shaping gain, reduces signal nonlinearity, and improves system nonlinearity and capacity. This invention proposes a geometric-probabilistic-pulse three-dimensional joint shaping technique based on an autoencoder. Through end-to-end training, it synchronously optimizes symbol probability, constellation position, and time-domain waveform, while simultaneously endowing the physical layer with dynamic programmability, allowing parameters to be adjusted in real time according to channel conditions, providing a solution for next-generation resilient optical networks. Attached Figure Description

[0042] Figure 1 This is a block diagram of the modules used in a specific embodiment of the present invention;

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

[0044] Figure 3 This invention is compared with traditional models and pulse shaping that uses constellation shaping alone;

[0045] Figure 4 It is a constellation image after joint hybrid shaping and noise addition;

[0046] Figure 5 This is a comparison chart of the bit error rate of the present invention's solution under an AWGN channel and other reference solutions;

[0047] Figure 6 This is a comparison chart of the GMI of the present invention under an AWGN channel and other reference schemes. Detailed Implementation

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

[0049] In this embodiment, MATLAB code is used to perform a simple simulation to verify the effect of joint optimization. The source signal is 256-QAM, and the parameter training module S1 is in an AWGN channel with a relevant parameter of SNR = 30dB, according to the Maxwell-Boltzmann (MB) distribution:

[0050]

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

[0052]

[0053] The optimal shaping factor λ = 0.0095 was obtained under this condition.

[0054] In this embodiment, the probability initialization module S2 substitutes the optimal shaping factor output by the parameter training module S1 to obtain the corresponding probability-shaped constellation diagram, and generates the input constellation symbol based on the probability of the constellation diagram.

[0055] In this embodiment, the signal reconstruction module S3 modulates the digital signal with QAM and sends it to the GCS neural network for training and reconstruction, and outputs the hybrid shaped signal.

[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 the signal through a symmetrical Hamming window of length 21. The length u of the window function is obtained by minimizing the mean square error loss function after a set of input signals is reconstructed through training with an autoencoder. Next, the signal is fed 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 transmission signal through the AWGN channel, and the signal-to-noise ratio is set to 30dB.

[0058] In this embodiment, the receiving decoding module S6 first downsamples the signal, reducing the sampling rate by 50 times, and then estimates the transmitted symbol 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 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 receiver and decoder, which are then substituted into the model for encoding, decoding, and processing signals.

[0060] Figure 3 This is a comparison diagram of pulse shaping between the present invention and other models, showing the comparison between the learning pulse shape and the received pulse of the trainable FIR filter. It can be seen that the learning pulse and the received pulse curve fit almost perfectly in the hybrid shaping.

[0061] Figure 4 This is a hybrid shaped constellation diagram obtained through an autoencoder in an AWGN channel. As can be seen from the diagram, besides the change in the positions of constellation points, the probability of symbols also tends to be more central, with lower probabilities for higher-energy symbols in the surrounding areas. The learned probability distribution can reduce the impact of nonlinear effects and improve the system's transmission capacity.

[0062] Figure 5 and Figure 6 This figure compares the performance of the present invention with other reference schemes under different signal-to-noise ratios (SNRs) in the AGWN channel using 256QAM. The comparison metrics are bit error rate (BER) and GMI. As can be seen from the figure, the present invention exhibits a certain shaping gain compared to other models over a relatively large SNR range.

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

Claims

1. A coding method based on end-to-end joint constellation shaping and pulse shaping of an autoencoder, characterized in that, Includes the following steps: Step 1: Initialize the source coding weights and obtain a discrete and non-differentiable probability vector from the output of the source PCS encoder. ; Step 1 specifically involves initializing the encoder weights based on the Maxwell-Boltzmann distribution and the estimation formula for maximizing GMI, i.e.: P = / ； in, As a shaping factor, The square of the amplitude of the constellation point. Indicates M-QAM, P( () represents the probability of the constellation point sign; By calculating the constellation diagram under different MB distribution probability shaping factors, and substituting it into the GMI calculation formula, the shaping factor λ corresponding to the maximum GMI is obtained. The GMI estimation formula is: GMI ; Where H represents the entropy of the constellation diagram conforming to the MB distribution under different signal-to-noise ratios. It is a set of K-QAM modulation symbols. ∈{0,1} is the nth bit of the nth transmitted symbol. This indicates that the value of the nth bit in the 𝑀-QAM symbol is... The set of all symbols; The discrete and non-differentiable probability vector is obtained by outputting the PCS encoder. Then, a differentiable sampler is used to output a differentiable signal probability distribution vector P; Step 2: Based on discrete and non-differentiable probability vectors By quantizing the discrete probability distribution through a sampler, a continuously differentiable vector P is obtained; Step 3: Feed batch P into the GCS encoder for training and reconstruction to obtain the jointly optimized signal constellation points. ; Step 4: Perform pulse shaping on the signal constellation points, normalize the power, complete the 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 signal y into the neural network decoder module to obtain the output signal; Step 7: Based on the output signal, update the autoencoder AE and function model parameters through backpropagation according to the loss function, and finally obtain the jointly optimized probability distribution constellation points under different SNR.

2. The encoding method based on end-to-end joint constellation shaping and pulse shaping of an autoencoder according to claim 1, characterized in that, Step 2 specifically involves: initializing the PCS encoder under the optimal GMI shaping factor, feeding the obtained discrete and non-differentiable probability vector into the Gumbel-Max sampler for quantization, and using the Gumbel-SoftMax estimator to output the differentiable signal probability distribution vector P, as shown in the following formula: ； Where g represents the noise sampled from the standard Gumbel distribution, g ~ Gumbel(0,1), For temperature parameters, A probability vector representing a discrete distribution.

3. The encoding method based on end-to-end joint constellation shaping and pulse shaping of an autoencoder according to claim 1, characterized in that, Step 3 specifically involves: passing the continuously differentiable signal through the STE direct-through estimator to generate a discrete one-hot vector s to represent the signal symbol, inputting it into the neural network encoding end of the GCS, and sharing parameters with the constellation diagram encoding to complete the GCS processing, outputting the transmitted complex signal after PCS-GCS hybrid shaping. .

4. The encoding method based on end-to-end joint constellation shaping and pulse shaping of an autoencoder according to claim 1, characterized in that, Step 4 specifically involves: passing the PCS output signal through the SoftMax function, calculating the power normalization factor in conjunction with the constellation diagram output from the GCS encoder, normalizing the signal power, then upsampling, i.e., inserting several zero values ​​between each symbol, depending on the sampling rate, and then inputting the real and imaginary parts separately into a trainable pulse shaping filter for convolution to complete pulse shaping.

5. The encoding method based on end-to-end joint constellation shaping and pulse shaping of an autoencoder according to claim 1, characterized in that, Step 5 specifically involves transmitting the signal through the channel to obtain the received signal y, which is then sent to the receiving decoding module for decoding processing.

6. The encoding method based on end-to-end joint constellation shaping and pulse shaping of an autoencoder according to claim 1, characterized in that, Step 6 specifically involves: downsampling the received signal y, processing it in parallel through a sliding window, and then sending it to the decoding NN end to complete the decoding; evaluating the GMI and BER metrics through the output signal, and calculating the cross-entropy loss and distribution entropy in the loss function with the encoding end, and then performing backpropagation to update the model parameters.

7. The encoding method based on end-to-end joint constellation shaping and pulse shaping of an autoencoder according to claim 1, characterized in that, Step 7 specifically involves: based on the loss function, updating the encoder, decoder, and pulse shaping parameters in real time during backpropagation to maximize system performance GMI; obtaining the optimal analytical loss function using the following formula; ； in, This represents the cross-entropy loss between the encoder output and the discrete symbol s, used to ensure the accuracy of symbol reconstruction. It is the entropy of the symbol distribution. This is the pulse shaping loss.

8. A coding system based on end-to-end joint constellation shaping and pulse shaping using an autoencoder, for implementing 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 receiver decoding module, and an adaptive update module; The parameter training module obtains the initial parameters of the PCS encoder based on the maximum expression of the trainable parameter GMI and the MB distribution. The probability initialization module quantizes the discrete probability distribution using a Gumbel-Max sampler to obtain a continuously differentiable probability distribution. The signal reconstruction module passes the continuously differentiable probability distribution through STE to obtain discrete one-hot vector symbols, which are then fed into the autoencoder for training and reconstruction to obtain jointly optimized signal constellation points. The pulse shaping module performs power normalization, pulse shaping, and low-pass filtering on the signal to complete the modulation process. The channel transmission module transmits the signal through the channel to obtain the received signal y and sends it to the receiving 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 by backpropagation based on the output signal and the loss function expression, thereby obtaining an optimized symbolic representation and transmission strategy.

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

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