Training method, generating method, demodulating method and device of four-dimensional geometric shaping modulation format generating model

Abstract

This application provides a training method, generation method, demodulation method, and device for a four-dimensional geometrically shaped modulation format generation model. The training method includes: a first stage: in the current iteration round, a random bit vector is input into the current four-dimensional geometrically shaped residual autoencoder, causing the transmitter neural network to generate four-dimensional constellation symbols, which are then transmitted through the channel module to obtain the received four-dimensional constellation symbols; the loss is calculated and the transmitter neural network parameters are optimized; a second stage: in the current iteration round, the random bit vector is processed by the transmitter neural network and the channel module to obtain the received four-dimensional constellation symbols, which are then decoded by the receiver neural network and output as a posterior bit probability vector; the loss is calculated and the receiver neural network parameters are optimized; if the optimized neural networks all satisfy the convergence condition, the current autoencoder is used as the four-dimensional geometrically shaped modulation format generation model. This application can improve the transmission quality and spectral efficiency of optical fiber links.

Description

Technical Field

[0001] This application relates to the field of optical fiber communication system technology, and in particular to a training method, generation method, demodulation method and device for a four-dimensional geometric shaping modulation format generation model. Background Technology

[0002] As the backbone of the global information infrastructure, fiber optic communication systems are constantly approaching the limits of their theoretical transmission capacity. This "capacity crisis" is driving researchers to explore advanced technologies that can further improve spectral efficiency and transmission distance. In fiber optic communication, modulation technology is one of the core means to improve capacity. Its goal is to transmit as many bits of information as possible within each symbol period under limited bandwidth and signal-to-noise ratio conditions.

[0003] Modulation format is a core concept in communication systems, determining how digital information is mapped onto analog signals for propagation in physical channels. A commonly used polarization-multiplexed M-ary Quadrature Amplitude Modulation (PM-MQAM) first uses MQAM modulation independently in each orthogonal polarization state, then combines the signals from the two polarization states into a single optical signal for transmission, increasing transmission capacity without increasing spectral bandwidth. However, traditional two-dimensional modulation utilizes only two degrees of freedom in a single polarization state. When transmitting two independent two-dimensional modulated signals in different polarization states, the lack of correlation between constellation points leads to decreased noise immunity. Summary of the Invention

[0004] In view of this, embodiments of this application provide a training method, generation method, demodulation method, and apparatus for a four-dimensional geometrically shaped modulation format generation model, in order to eliminate or improve one or more defects existing in the prior art.

[0005] One aspect of this application provides a training method for a four-dimensional geometrically shaped modulation format generation model, the training method comprising a first training phase and a second training phase; The first training phase includes: In the current iteration, a random bit vector is input into the current four-dimensional geometrically shaped residual autoencoder, so that the transmitter neural network in the four-dimensional geometrically shaped residual autoencoder generates the original four-dimensional constellation symbol corresponding to the random bit vector based on a preset modulation constellation, and the differentiable fiber channel module in the four-dimensional geometrically shaped residual autoencoder transmits the original four-dimensional constellation symbol in a preset channel environment to obtain the received four-dimensional constellation symbol. The first target loss for the current iteration round is calculated based on the random bit vector and the received four-dimensional constellation symbol, and the model parameters of the transmitter neural network are optimized based on the first target loss. The second training phase includes: In the current iteration, a random bit vector is input into the current four-dimensional geometrically shaped residual autoencoder so that the trained transmitter neural network generates the original four-dimensional constellation symbol, and the differentiable fiber channel module transmits the original four-dimensional constellation symbol to obtain the received four-dimensional constellation symbol. The receiver neural network in the four-dimensional geometrically shaped residual autoencoder decodes the received four-dimensional constellation symbol and outputs the posterior bit probability vector corresponding to the random bit vector. The second target loss for the current iteration round is calculated based on the random bit vector and the posterior bit probability vector, and the model parameters of the receiver neural network are optimized based on the second target loss. If both the optimized transmitter neural network and receiver neural network meet the preset convergence conditions, then the current four-dimensional geometrically shaped residual autoencoder will be used as the four-dimensional geometrically shaped modulation format generation model for generating the four-dimensional geometrically shaped modulation format.

[0006] In some embodiments of this application, the first target loss is a generalized mutual information loss, which is expressed by the following formula: in, This indicates the number of bits carried in the received four-dimensional constellation symbol; Indicates bit index; This represents the value of the i-th bit in each transmitted symbol; This indicates that the value received is a four-dimensional constellation symbol; Let i represent the random variable representing the i-th bit of each transmitted symbol; Represents a random variable that receives a four-dimensional constellation symbol; Let represent the posterior probability density function based on the Gaussian-assisted channel.

[0007] In some embodiments of this application, the second target loss is a binary cross-entropy loss, which is expressed by the following formula: in, This represents the number of samples in each training batch; Represented as the first K The input bit sequence of each training sample; Indicates the index of the input bit sequence; This represents the input bit sequence of the k-th training sample; This represents the bit posterior probability vector of the k-th training sample output by the decoder.

[0008] In some embodiments of this application, the convergence condition includes a first convergence condition and a second convergence condition; wherein, the first convergence condition is that the first target loss reaches a preset first threshold or the number of iterations reaches a preset maximum value; the second convergence condition is that the second target loss reaches a preset second threshold or the number of iterations reaches a preset maximum value.

[0009] In some embodiments of this application, the transmitter neural network includes a transmitter residual neural network. The output layer of the transmitter neural network is initialized with the preset modulation constellation, and a four-dimensional residual vector is obtained through an embedding layer and multiple fully connected layers. The four-dimensional residual vector is then added to the initialized constellation points to generate the four-dimensional constellation symbol.

[0010] In some embodiments of this application, the differentiable fiber channel module includes a differentiable SSFM channel model, which is used to simulate the dispersion, nonlinear effects and transmission loss of the optical fiber, and supports gradient backpropagation.

[0011] In some embodiments of this application, the receiver neural network includes a fully connected receiver neural network, which is used to learn soft decision rules under the differentiable fiber channel module after fixing the transmitter neural network parameters.

[0012] Another aspect of this application provides a method for generating a four-dimensional geometric shaping modulation format, the method comprising: A random bit vector is input into a transmitter neural network so that the transmitter neural network outputs a four-dimensional constellation symbol corresponding to the random bit vector; wherein, the four-dimensional constellation symbol is used to be transmitted to a receiver neural network through a channel so that the receiver receives the received four-dimensional constellation symbol corresponding to the four-dimensional constellation symbol and inputs the received four-dimensional constellation symbol into the receiver neural network, thereby making the receiver neural network output a demodulation bit vector corresponding to the received four-dimensional constellation symbol. The transmitter neural network and the receiver neural network constitute a four-dimensional geometrically shaped modulation format generation model for generating a four-dimensional geometrically shaped modulation format. This four-dimensional geometrically shaped modulation format generation model is pre-trained based on the aforementioned training method for the four-dimensional geometrically shaped modulation format generation model.

[0013] A third aspect of this application provides a demodulation method for a four-dimensional geometric shaping modulation format, the demodulation method comprising: The receiver receives a received four-dimensional constellation symbol corresponding to the transmitted four-dimensional constellation symbol, and inputs the received four-dimensional constellation symbol into the receiver neural network, thereby causing the receiver neural network to output the demodulated bit vector corresponding to the received four-dimensional constellation symbol; wherein, the four-dimensional constellation symbol is output by the transmitter neural network in advance by the transmitter inputting a random bit vector into the transmitter neural network. The transmitter neural network and the receiver neural network constitute a four-dimensional geometrically shaped modulation format generation model for generating a four-dimensional geometrically shaped modulation format. This four-dimensional geometrically shaped modulation format generation model is pre-trained based on the aforementioned training method for the four-dimensional geometrically shaped modulation format generation model.

[0014] A fourth aspect of this application provides an electronic device, including a processor and a memory, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement a training method for a four-dimensional geometrically shaped modulation format generation model, a generation method for a four-dimensional geometrically shaped modulation format, or a demodulation method for a four-dimensional geometrically shaped modulation format.

[0015] A fifth aspect of this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the training method for the four-dimensional geometrically shaped modulation format generation model, the generation method for the four-dimensional geometrically shaped modulation format, or the demodulation method for the four-dimensional geometrically shaped modulation format.

[0016] The sixth aspect of this application provides a computer program product comprising a computer program that, when executed by a processor, implements the training method for the four-dimensional geometrically shaped modulation format generation model, the generation method for the four-dimensional geometrically shaped modulation format, or the demodulation method for the four-dimensional geometrically shaped modulation format.

[0017] The present application discloses a training method for a four-dimensional geometrically shaped modulation format generation model, a method for generating a four-dimensional geometrically shaped modulation format, or a method for demodulating a four-dimensional geometrically shaped modulation format. The training method includes a first training stage and a second training stage. The first training stage includes: in the current iteration round, inputting a random bit vector into the current four-dimensional geometrically shaped residual autoencoder, so that the transmitter neural network in the four-dimensional geometrically shaped residual autoencoder generates the original four-dimensional constellation symbol corresponding to the random bit vector based on a preset modulation constellation; and transmitting the original four-dimensional constellation symbol in the four-dimensional geometrically shaped residual autoencoder under a preset channel environment to obtain the received four-dimensional constellation symbol; calculating a first target loss for the current iteration round based on the random bit vector and the received four-dimensional constellation symbol, and optimizing the model parameters of the transmitter neural network based on the first target loss; the second training stage... The process includes: in the current iteration round, inputting a random bit vector into the current four-dimensional geometrically shaped residual autoencoder (4DGERC) to enable the trained transmitter neural network to generate the original four-dimensional constellation symbol; transmitting the original four-dimensional constellation symbol to the differentiable fiber channel module to obtain the received four-dimensional constellation symbol; decoding the received four-dimensional constellation symbol and outputting the posterior bit probability vector corresponding to the random bit vector in the 4DGERC; calculating the second target loss of the current iteration round based on the random bit vector and the posterior bit probability vector; and optimizing the model parameters of the receiver neural network based on the second target loss. If both the optimized transmitter neural network and the receiver neural network satisfy the preset convergence condition, the current 4DGERC is used as the four-dimensional geometrically shaped modulation format generation model for generating the four-dimensional geometrically shaped modulation format. This approach can directly learn the statistical characteristics of fiber optic nonlinear channels, achieving performance improvement while maintaining engineering feasibility and system compatibility, thereby improving the transmission quality and spectral efficiency of fiber optic links.

[0018] Additional advantages, objectives, and features of this application will be set forth in part in the description which follows, and will in part become apparent to those skilled in the art upon review of the following description, or may be learned by practice of the application. The objectives and other advantages of this application can be realized and obtained by means of the structures specifically pointed out in the specification and drawings.

[0019] Those skilled in the art will understand that the purposes and advantages that can be achieved with this application are not limited to those specifically described above, and that the above and other purposes that this application can achieve will be more clearly understood from the following detailed description. Attached Figure Description

[0020] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, do not constitute a limitation thereof. The components in the drawings are not drawn to scale but are merely for illustrating the principles of this application. For ease of illustration and description of certain parts of this application, corresponding portions in the drawings may be enlarged, i.e., may appear larger relative to other components in an exemplary device actually manufactured according to this application. In the drawings: Figure 1 This is a flowchart illustrating a training method for a four-dimensional geometric shaping modulation format generation model in one embodiment of this application.

[0021] Figure 2 This is a schematic diagram of the first flowchart of the training method for the four-dimensional geometric integer modulation format generation model in a specific example of this application.

[0022] Figure 3 This is a schematic diagram of the second process for training a four-dimensional geometric integer modulation format generation model, as illustrated in a specific example of this application.

[0023] Figure 4 This is a simplified optical fiber nonlinear channel model structure diagram illustrating a training method for a four-dimensional geometrically shaped modulation format generation model, as described in a specific example of this application.

[0024] Figure 5 This diagram illustrates the relationship between a coherent optical communication simulation system and a simplified optical fiber channel modeling method for training a four-dimensional geometrically shaped modulation format generation model, as exemplified in a specific example of this application.

[0025] Figure 6 This is a schematic diagram of a four-dimensional geometrical shaping residual autoencoder structure, which is a specific example of the training method for the four-dimensional geometrical shaping modulation format generation model in this application. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of this application clearer, the application will be further described in detail below with reference to the embodiments and accompanying drawings. Here, the illustrative embodiments and their descriptions are used to explain this application, but are not intended to limit it.

[0027] It should also be noted that, in order to avoid obscuring this application with unnecessary details, only the structures and / or processing steps closely related to the solution according to this application are shown in the accompanying drawings, while other details that are not closely related to this application are omitted.

[0028] It should be emphasized that the term "including / comprises" as used herein refers to the presence of a feature, element, step, or component, but does not exclude the presence or addition of one or more other features, elements, steps, or components.

[0029] It should also be noted that, unless otherwise specified, the term "connection" in this article can refer not only to a direct connection, but also to an indirect connection involving an intermediary.

[0030] In the following description, embodiments of the present application will be illustrated with reference to the accompanying drawings. In the drawings, the same reference numerals represent the same or similar parts, or the same or similar steps.

[0031] It should be noted that traditional 2×2D modulation structures suffer from problems such as lack of dimensional correlation, limited design space, small Euclidean distance between symbols, and limited achievable information rate (AIR). Traditional modulation format optimization methods, when transmitting two independent two-dimensional modulated signals in different polarization states, suffer from decreased noise immunity due to the lack of correlation between constellation points. Therefore, exploring higher-dimensional signal spaces is particularly important. Based on this, the inventors of this application first conceived of improving the overall system performance of achievable information rate by leveraging the powerful optimization capabilities of deep learning, building upon the concept of two-dimensional geometric shaping. By optimizing the geometry of constellation points, shaping techniques can more effectively utilize the capacity of the optical channel under nonlinear and noisy conditions. This application innovatively utilizes the four degrees of freedom of the X and Y polarization states in an optical fiber communication system to achieve true four-dimensional joint optimization, overcoming the aforementioned problems of traditional modulation structures. By introducing a differentiable distributed Fourier method (SSFM) channel model and forming an end-to-end joint optimization framework with a residual autoencoder, the statistical characteristics of fiber nonlinear channels can be directly learned, enabling the generated constellation to maintain higher GMI and transmission performance under noise and nonlinear conditions. Simultaneously, the optimized constellation has a amplitude distribution closer to a Gaussian distribution and maintains a Gray-like label structure, achieving performance improvement while maintaining engineering feasibility and system compatibility. This improves the transmission quality and spectral efficiency of fiber optic links, making it suitable for high baud rate or high-speed optical signal transmission. Furthermore, this application is not only applicable to 4D modulation but can also be extended to 8D or higher-dimensional modulation formats.

[0032] The following examples will provide a detailed description.

[0033] This application provides a training method for a four-dimensional geometric integer modulation format generation model. See [link to relevant documentation]. Figure 1 The training method includes a first training phase and a second training phase. The first training phase includes: Step 100: In the current iteration round, the random bit vector is input into the current four-dimensional geometrically shaped residual autoencoder, so that the transmitter neural network in the four-dimensional geometrically shaped residual autoencoder generates the original four-dimensional constellation symbol corresponding to the random bit vector based on the preset modulation constellation, and the differentiable fiber channel module in the four-dimensional geometrically shaped residual autoencoder transmits the original four-dimensional constellation symbol in the preset channel environment to obtain the received four-dimensional constellation symbol. In step 100, the modulation constellation can be a DP-QAM modulation constellation. The original four-dimensional constellation symbol can be a four-dimensional constellation symbol generated based on the DP-QAM modulation format; the received four-dimensional constellation symbol can be a four-dimensional constellation symbol learned by a residual autoencoder. A random bit vector is input into the current four-dimensional geometrically shaped residual autoencoder. The embedding layer of the transmitter residual neural network fine-tunes the initialized constellation points through multiple fully connected layers. The final trainable four-dimensional constellation points are the sum of the initial QAM constellation and the residual vector fine-tuned by multiple fully connected layers. For each input, the transmitter residual neural network outputs a corresponding original four-dimensional constellation symbol. The set of all original four-dimensional constellation symbols constitutes the 4D geometric constellation diagram for this iteration cycle, ensuring effective gradient propagation in the deep network. All the original four-dimensional constellation symbols are loaded onto the optical carrier and, through a differentiable fiber channel module, the received four-dimensional constellation symbol is obtained. The differentiable fiber channel module accurately simulates the dispersion and nonlinear effects of optical fibers, ensuring that the channel response is close to the real environment, thereby achieving end-to-end simulation and allowing gradient backpropagation.

[0034] Step 200: Calculate the first target loss for the current iteration round based on the random bit vector and the received four-dimensional constellation symbol, and optimize the model parameters of the transmitter neural network based on the first target loss; In step 200, the Monte Carlo estimation GMI for each training iteration, based on the random bit vector and the received 4D constellation symbol output, is used as a performance metric. The GMI is used as the first objective loss function, and the constellation point performance at the current iteration number is evaluated. The gradient of the first objective loss with respect to the transmitter encoder parameters is calculated using a backpropagation algorithm. This gradient is then propagated back through the channel layer of the differentiable fiber channel module to the transmitter neural network. During iteration, the transmitter neural network indirectly learns the nonlinear channel characteristics simulated by the differentiable fiber channel module through the received gradient signals. Based on the learned channel characteristics, the transmitter neural network continuously adjusts its parameters, thereby dynamically redesigning the bit-to-4D constellation point mapping rules. This can be iterated up to 5000 times, forming a closed-loop optimization cycle to ensure that the first objective loss converges and reaches a stable state. After training, the optimized model parameters of the transmitter neural network are obtained, which define the final 4D geometric constellation.

[0035] The second training phase includes: Step 300: In the current iteration round, input the random bit vector into the current four-dimensional geometrically shaped residual autoencoder so that the trained transmitter neural network generates the original four-dimensional constellation symbol, and the differentiable fiber channel module transmits the original four-dimensional constellation symbol to obtain the received four-dimensional constellation symbol, and the receiver neural network in the four-dimensional geometrically shaped residual autoencoder decodes the received four-dimensional constellation symbol and outputs the posterior bit probability vector corresponding to the random bit vector; In step 300, the posterior bit probability vector can be the bit probability vector output by the decoder, ranging from 0 to 1, with a number of m, for example (0.1, 0.2, 0.3, 0.5, 0.8, 0.7, 0.4). After determining the optimized model parameters of the transmitter neural network in the first training phase, the four-dimensional shaped constellation points after the transmitter training remain unchanged. The random bit vector is input into the transmitter neural network, and the generated constellation symbol is loaded onto the optical carrier. The signal propagates through the channel layer of the differentiable fiber channel module to obtain the received four-dimensional constellation symbol, and the receiver neural network in the four-dimensional geometrically shaped residual autoencoder decodes the received four-dimensional constellation symbol and outputs the posterior bit probability vector corresponding to the random bit vector.

[0036] Step 400: Calculate the second target loss for the current iteration based on the random bit vector and the posterior bit probability vector, and optimize the model parameters of the receiver neural network based on the second target loss; In step 400, the receiver neural network is trained based on the second objective loss function. The gradient of the second objective loss with respect to the parameters of the receiver neural network is calculated using the backpropagation algorithm, and the decision rules for the four-dimensional geometrically shaped constellation points in the differentiable fiber channel module are learned. This process can iterate 10,000 times, forming a closed-loop optimization loop to ensure that the second objective loss function converges and reaches a stable state.

[0037] Step 500: If both the optimized transmitter neural network and receiver neural network meet the preset convergence conditions, then the current four-dimensional geometrically shaped residual autoencoder is used as the four-dimensional geometrically shaped modulation format generation model for generating the four-dimensional geometrically shaped modulation format.

[0038] As described above, the training method for the four-dimensional geometrically shaped modulation format generation model provided in this application, by embedding a differentiable fiber channel module into a residual autoencoder framework, enables the transmitter neural network to adaptively learn the characteristics of the nonlinear fiber channel. This allows the gradient to propagate back through the channel, thereby jointly optimizing constellation points in four-dimensional space. This overcomes the inherent defects of traditional polarization-multiplexed orthogonal amplitude modulation formats, which suffer from weak dimensional correlation, poor noise resistance, and limited achievable information rate due to the independent design of two polarization states. A segmented training strategy is adopted. In the first stage, the transmitter is optimized using a preset first objective loss function to make the generated constellation amplitude distribution approximate a Gaussian distribution. In the second stage, the receiver is optimized using a preset second objective loss function to maintain a Gray code-like tag structure in the constellation, which can improve the transmission rate and reduce the bit error rate. The finally trained four-dimensional geometrically shaped modulation format generation model can output a modulation format with higher spectral efficiency and longer transmission distance in nonlinear fiber channels, thereby improving the overall performance of the optical communication system.

[0039] To further improve the transmission rate and reduce the bit error rate of optical communication systems, in a training method for a four-dimensional geometrically shaped modulation format generation model provided in this application embodiment, the first target loss is a generalized mutual information loss, which is expressed by the following formula: in, This indicates the number of bits carried in the received four-dimensional constellation symbol; Indicates bit index; This represents the value of the i-th bit in each transmitted symbol; This indicates that the value received is a four-dimensional constellation symbol; Let i represent the random variable representing the i-th bit of each transmitted symbol; Represents a random variable that receives a four-dimensional constellation symbol; Let represent the posterior probability density function based on the Gaussian-assisted channel.

[0040] In one or more embodiments of this application, in an autoencoder framework trained based on the BCE loss function, the receiver decoder typically relies on an approximate posterior probability distribution to make decisions about the received signal. Its decision model is difficult to perfectly match the conditional probability distribution of the real channel, meaning a certain degree of model mismatch is unavoidable. Under these conditions, directly using this approximate posterior probability to estimate the mutual information between the transmitted symbol and the received signal may result in a deviation from the true mutual information. Therefore, based on the above considerations, to address the model mismatch problem at the receiver, a Generalized Mutual Information (GMI) loss based on Gaussian-assisted channel posterior probability estimation is adopted as the optimization objective, and a corresponding objective function is constructed accordingly. This loss function approximates the GMI index by performing Monte Carlo statistics based on the bit sequence and four-dimensional symbols of each batch of transmitters and additive white Gaussian noise (AWGN) channels. This more robustly characterizes the system's effective information transmission capability under model mismatch conditions, enabling effective evaluation and optimization of the modulation constellation under actual channel conditions. No additional decoder neural network is introduced during GMI optimization, allowing the encoder neural network to focus more on transmitter constellation optimization. In addition, the first target loss can also be other performance metrics such as mutual information (MI), symbol error rate (SER), or minimum Euclidean distance.

[0041] Understandably, in communication systems, the receiver needs to demodulate the received signal. Demodulation is typically based on an assumed channel model to calculate the posterior probability of each bit. Real-world channels, such as fiber optic nonlinear channels, exhibit non-Gaussian characteristics at high power, meaning they suffer from nonlinear distortion. To simplify calculations, the receiver often assumes the channel is Gaussian (i.e., an assumed channel model) and calculates the posterior probability based on this assumption. However, this model mismatch between the actual channel and the receiver's assumed model leads to a model mismatch problem. When the model mismatch occurs, the posterior probability calculated by the receiver is inaccurate. If the true mutual information is directly used as the optimization objective, the optimization direction will deviate due to the inconsistency between the receiver's model and the actual channel. GMI (Gross Interaction Information) calculates the actual information transmission rate the system can achieve when using a mismatched decoder at the receiver. In the first training phase, the transmitter neural network, without knowing the specific structure of the receiver, optimizes the constellation shape by maximizing GMI, ensuring that even when the receiver uses a simple Gaussian-assumed decoder, it can achieve the highest possible information rate. In other words, although simplified fiber nonlinear channels exhibit significant non-Gaussian characteristics at high power, the GMI (Gross Mismatch Index) as the achievable information rate under mismatch decoding can still be used to effectively evaluate system performance. Therefore, the GMI objective function, which directly reflects the achievable information rate at the receiver, is more suitable for geometric optimization of the four-dimensional constellation in the encoder. Compared to autoencoders trained under AWGN channel conditions, the decision generator trained through a neural network shows almost no performance difference from traditional hard-decision methods, since optimal detection can be achieved using Euclidean distance-based hard decision in this channel.

[0042] To further improve the transmission rate and reduce the bit error rate of optical communication systems, in a training method for a four-dimensional geometrically shaped modulation format generation model provided in this application embodiment, the second target loss is a binary cross-entropy loss, which is expressed by the following formula: in, This represents the number of samples in each training batch; Represented as the first K The input bit sequence of each training sample; Indicates the index of the input bit sequence; This represents the input bit sequence of the k-th training sample; This represents the bit posterior probability vector of the k-th training sample output by the decoder.

[0043] To achieve end-to-end optimization, the trainable weights of the autoencoder are updated using a log-likelihood-based loss function and iteratively optimized using stochastic gradient descent. In one or more embodiments of this application, the second objective loss takes the form of a binary cross-entropy (BCE) loss function. The loss for a single sample symbol is the binary cross-entropy, which can be expressed as follows: in, This indicates the number of bits carried by each symbol. The true bit vector for each four-dimensional symbol. This is the bit posterior probability vector output by the decoder. In simplified fiber nonlinear channels, signals are affected by both link noise and nonlinear effects during transmission, making it difficult for traditional hard decision-making systems to fully utilize the statistical information of the signal. Therefore, the decoder is trained at the receiver using a binary cross-entropy (BCE) loss function to learn a decision boundary that better reflects the actual channel characteristics, thereby improving system performance.

[0044] To further improve the transmission rate and reduce the bit error rate of optical communication systems, in a training method for a four-dimensional geometrically shaped modulation format generation model provided in this application embodiment, the convergence conditions include a first convergence condition and a second convergence condition; wherein, the first convergence condition is that the first target loss reaches a preset first threshold or the number of iterations reaches a preset maximum value; the second convergence condition is that the second target loss reaches a preset second threshold or the number of iterations reaches a preset maximum value.

[0045] In one or more embodiments of this application, the first threshold can be the minimum value of the GMI cost function from -10 to -6; the maximum number of iterations in the first training phase can be 5000; the second threshold can be the minimum value of the BCE loss function from 0 to 0.6; and the maximum number of iterations in the first training phase can be 10000.

[0046] To further overcome the inherent defects of traditional polarization multiplexing orthogonal amplitude modulation formats, such as weak dimensional correlation, poor noise resistance, and limited achievable information rate due to the independent design of two polarization states, a training method for a four-dimensional geometrically shaped modulation format generation model is provided in this application embodiment. In this method, the transmitter neural network includes a transmitter residual neural network. The output layer of the transmitter neural network is initialized with a preset modulation constellation. A four-dimensional residual vector is obtained through an embedding layer and multiple fully connected layers. The four-dimensional residual vector is then added to the initialized constellation points to generate the four-dimensional constellation symbol.

[0047] In one or more embodiments of this application, the transmitter neural network does not relearn the entire constellation structure. Instead, it learns small offsets in a data-driven manner through fully connected layers to achieve geometric refinement of the base dual-polarization orthogonal amplitude modulation (DP-QAM) constellation. After multiple layers of nonlinear mapping, the output of the fourth fully connected layer is added to the initialized constellation points to form the corresponding four-dimensional transmit constellation points. This allows the final generated constellation to better adapt to the noise characteristics of the channel while maintaining the DP-QAM topology. Furthermore, the transmitter neural network can also employ different neural network architectures such as Transformer, fully connected networks, and convolutional structures.

[0048] To further enable the transmitter neural network to adaptively learn the nonlinear channel characteristics of optical fiber and allow the gradient to propagate back through the channel, thereby jointly optimizing constellation points in four-dimensional space, in the training method of a four-dimensional geometrically shaped modulation format generation model provided in this application embodiment, the differentiable optical fiber channel module includes a differentiable SSFM channel model. The differentiable SSFM channel model is used to simulate the dispersion, nonlinear effects and transmission loss of optical fiber and supports gradient backpropagation.

[0049] In one or more embodiments of this application, the channel model plays a crucial role in the training and performance evaluation of end-to-end networks. The nonlinear fiber optic channel model requires unified modeling of system noise and nonlinear distortion characteristics. The way the channel model characterizes nonlinear effects directly impacts the nonlinear resistance performance of the modulated four-dimensional constellation under high-power transmission conditions. This application can employ a simplified fiber optic nonlinear channel model based on the split-step Fourier method to uniformly model the fiber optic transmission channel and system noise. The constructed channel model simultaneously includes link amplifier noise and fiber nonlinear transmission effects to characterize their combined impact on signal structure and system performance. Furthermore, the differentiable SSFM split-step Fourier method channel model can also be replaced by other differentiable fiber optic channel models, including enhanced Gaussian noise (GN) models and channel simulators trained using machine learning.

[0050] To further overcome the inherent defects of traditional polarization multiplexing orthogonal amplitude modulation formats, which suffer from weak dimensional correlation, poor noise resistance, and limited achievable information rate due to the independent design of two polarization states, a training method for a four-dimensional geometrically shaped modulation format generation model is provided in this application embodiment. In this method, the receiver neural network includes a fully connected receiver neural network, which is used to learn the soft decision rules under the differentiable fiber channel module after fixing the transmitter neural network parameters.

[0051] In one or more embodiments of this application, the receiver neural network may also employ different neural network architectures such as Transformer, fully connected network, and convolutional structure.

[0052] This application also provides a method for generating a four-dimensional geometric shaping modulation format, including: Step 10: Input a random bit vector into the transmitter neural network so that the transmitter neural network outputs a four-dimensional constellation symbol corresponding to the random bit vector; wherein, the four-dimensional constellation symbol is used to be transmitted to the receiver neural network through the channel so that the receiver receives the received four-dimensional constellation symbol corresponding to the four-dimensional constellation symbol and inputs the received four-dimensional constellation symbol into the receiver neural network, thereby making the receiver neural network output a demodulation bit vector corresponding to the received four-dimensional constellation symbol. The transmitter residual encoder neural network and the receiver decoder neural network constitute a four-dimensional geometrically shaped modulation format generation model for generating a four-dimensional geometrically shaped modulation format. This four-dimensional geometrically shaped modulation format generation model is pre-trained based on the aforementioned training method for the four-dimensional geometrically shaped modulation format generation model.

[0053] This application also provides a demodulation method for a four-dimensional geometric shaping modulation format, characterized by comprising: Step 01: Receive the received four-dimensional constellation symbol corresponding to the transmitted four-dimensional constellation symbol, and input the received four-dimensional constellation symbol into the receiver neural network, thereby causing the receiver neural network to output the demodulated bit vector corresponding to the received four-dimensional constellation symbol; wherein, the four-dimensional constellation symbol is output by the transmitter neural network in advance by the transmitter inputting a random bit vector into the transmitter neural network. The transmitter neural network and the receiver neural network constitute a four-dimensional geometrically shaped modulation format generation model for generating a four-dimensional geometrically shaped modulation format. This four-dimensional geometrically shaped modulation format generation model is pre-trained based on the aforementioned training method for the four-dimensional geometrically shaped modulation format generation model.

[0054] In a specific example of the training method for the four-dimensional geometric integer modulation format generation model of this application, see [link to example]. Figure 2 and Figure 3 The training method includes the following steps: Step 1: Construct the transmitter neural network and receiver neural network. The transmitter encoder adopts a residual neural network structure, and the receiver decoder adopts a fully connected structure. The residual network is initialized using the DP-QAM modulation format in an embedded layer manner. The weights and biases of the transmitter network output layer are initialized to the constellation point coordinates of polarization multiplexed DP-QAM.

[0055] Step 2: The transmitted bit vector is input into the initialized transmitter residual neural network. The embedding layer fine-tunes the initialized constellation points through multiple fully connected layers. The final trainable 4D constellation points are obtained by adding the initial DP-QAM constellation and the residual vector fine-tuned by multiple fully connected layers. For each input, the residual network outputs a corresponding 4D symbol. The set of all output symbols constitutes the 4D geometric constellation diagram for this iteration cycle, ensuring that the gradient propagates effectively in the deep network.

[0056] Step 3: Load the constellation symbols generated in Step 2 onto the optical carrier. Using a differentiable SSFM channel model, which accurately simulates the dispersion and nonlinear effects of the optical fiber, the channel response closely approximates the real-world environment. This step achieves end-to-end simulation and allows gradient backpropagation. In this embodiment, a simplified optical fiber nonlinear channel model based on the split-step Fourier method is used to uniformly model the optical fiber transmission channel and system noise. See [link to relevant documentation]. Figure 4 The picture N sp This represents the number of fiber spans. This channel modeling method accurately characterizes the main physical effects in coherent optical transmission systems, while balancing the stability and computational complexity of end-to-end model training, reducing simulation complexity while ensuring physical rationality. The constructed channel model simultaneously incorporates link amplifier noise and fiber nonlinear transmission effects to characterize their combined impact on signal structure and system performance. Specifically, in end-to-end noise modeling, this embodiment uniformly equates the amplifier-related noise in the link to additive white Gaussian noise and superimposes it onto the optical signal with a set input optical power for modeling. By adjusting the power of the equivalent AWGN, the target optical signal-to-noise ratio (OSNR) can be directly set in the simulation, thus flexibly controlling different noise conditions within the end-to-end framework. This equivalent noise model can uniformly characterize the impact of amplifier noise using OSNR as a system-level indicator, enabling the channel model to maintain physical rationality while possessing good controllability. In fiber nonlinear modeling, targeted modeling of the fiber transmission channel is performed based on anti-nonlinear modulation design. The optical signal with link amplifier-related noise propagates in a standard single-mode fiber, and its transmission process is numerically simulated using the SSFM split-step Fourier method. Since fiber dispersion can be accurately compensated at the receiver using the inverse SSFM process, computational complexity can be further reduced. This embodiment omits the linear dispersion term in channel modeling, retaining only the Kerr nonlinearity described by the Manakov equation to highlight the impact of nonlinear effects on signal structure and system performance, and to avoid interference from linear transmission effects on the network training process. See also Figure 5 The correspondence between coherent optical communication simulation systems and simplified fiber optic channel modeling is determined by... Figure 5The dashed box indicates that the constructed coherent optical communication simulation system is used to verify the feasibility of a simplified fiber nonlinear channel model. It is understood that the aforementioned simplified fiber nonlinear channel is first used for modeling, and this channel model is embedded in the autoencoder framework as a channel module, thereby achieving differentiable end-to-end link simulation and joint optimization. The specific settings of each key component and channel parameter in the simulation system are shown in Table 1.

[0057] Table 1 SSFM-4DAE-QAM Simulation System Parameter Settings To ensure the reliability and repeatability of the experimental results, this embodiment sets the key training parameters for end-to-end learning uniformly. See Table 2 for the main training parameter settings for the model and training channel used.

[0058] Table 2 SSFM-4DAE-QAM Training Parameter Settings During model training, the simplified fiber nonlinear channel can be achieved by setting the fiber transmission distance to 5 × 100 km. Since the GMI objective function assumes a Gaussian channel, the training transmit power can be set to -1 dBm, placing it at the boundary between the linear and nonlinear regions. This satisfies the objective function assumption while reflecting the actual conditions under which fiber nonlinearity begins to manifest. Furthermore, the SSFM-4DAE-256QAM and SSFM-4DAE-1024QAM modulation formats can be set to different OSNRs, corresponding to equivalent SNRs of 18 dB and 22 dB, respectively.

[0059] Step 4: Calculate the GMI for the received 4D symbols. Based on the known transmitted bit vector and the received 4D symbols, output the Monte Carlo estimated GMI for each training iteration as a performance metric. Use the GMI as the loss function to evaluate the constellation point performance at the current iteration number. The function is shown in the following equation: in, m The number of bits carried by the four-dimensional symbol. To send bits, For the received symbols, this loss function approximates the GMI index by performing Monte Carlo statistics on the bit sequence and four-dimensional symbols from each batch transmitter, as well as the sampled results of the four-dimensional symbols received at the AWGN channel output. This allows for a more robust characterization of the system's effective information transmission capability under model mismatch conditions, enabling effective evaluation and optimization of the modulation constellation under actual channel conditions. Furthermore, no additional decoder neural network is introduced during GMI optimization, allowing the encoder neural network to focus more on transmitter constellation optimization.

[0060] Step 5: Calculate the gradient of the loss with respect to the transmitter encoder parameters using the backpropagation algorithm. This gradient is then propagated back to the transmitter through the differentiable SSFM channel layer. During the iteration process, the transmitter network indirectly learns the nonlinear channel characteristics simulated by the SSFM channel through the received gradient signals. Based on the learned channel characteristics, the transmitter network continuously adjusts its parameters, thereby dynamically redesigning the bit-to-4D constellation point mapping rules.

[0061] Step 6: Repeat steps 2 through 6 5000 times to form a closed-loop optimization cycle, ensuring that the GMI optimization function fully converges and reaches a stable state.

[0062] Step 7: After training is complete, the optimized transmitter network parameters are obtained, which define the final 4D geometric constellation.

[0063] Step 8: After determining the optimized encoder transmitter network parameters, keep the four-dimensional shaped constellation points after the transmitter training unchanged, input the transmitted bit vector into the transmitter residual neural network, and then load the generated constellation symbols onto the optical carrier. Similar to Step 3, the signal propagates through the SSFM channel layer.

[0064] Step Nine: Train the receiver decoder based on the BCE loss function. Using the backpropagation algorithm, calculate the gradient of the loss with respect to the receiver decoder parameters, and learn the decision rules for the four-dimensional geometrically shaped constellation points in the SSFM channel. The BCE loss function is expressed as follows: in, This represents the input bit sequence of the k-th training sample; Let represent the bit posterior probability vector of the k-th training sample output by the decoder. The loss for a single sample symbol is the binary cross-entropy, which can be expressed as follows: in, This indicates the number of bits carried by each symbol. The true bit vector for each four-dimensional symbol. It is the bit posterior probability vector output by its decoder.

[0065] Step 10: Repeat steps 8 to 9 10,000 times to form a closed-loop optimization cycle to ensure that the BCE loss function fully converges and reaches a stable state.

[0066] Step 11: Finally, an end-to-end four-dimensional geometric shaping modulation format generation model based on joint optimization of GMI and BCE is obtained.

[0067] In this embodiment, a four-dimensional geometrically shaped residual autoencoder training framework is constructed. A nonlinear optical fiber channel generated by the distributed Fourier method is embedded into the autoencoder structure. Joint optimization is performed using generalized mutual information and the bit cross-entropy (BCE) loss function to achieve collaborative learning of the transmitter constellation mapping and receiver soft decision. Channel characteristics are learned through deep learning methods, and constellation points are redesigned end-to-end. Through these learning methods, the learned constellation exhibits an amplitude probability distribution close to a Gaussian distribution in one dimension, while maintaining a Gray code-like tagging structure through self-optimization. This four-dimensional geometrically shaped residual autoencoder consists of a residual encoder at the transmitter containing an embedding layer and a fully connected layer, and a decoder at the receiver containing a fully connected layer. (See [link to relevant documentation]). Figure 6 The encoder's input is a sequence of symbols, with values ​​ranging from... ,in, Where m is the number of bits corresponding to a symbol, and each sequence corresponds to one symbol to be modulated. To improve training efficiency and reduce the difficulty of constellation training, the encoder uses a size of... The embedding layer completes DP-QAM residual initialization, using a traditional QAM constellation as the initial basis. The network then learns offsets based on this constellation, thus achieving a more flexible trainable constellation distribution while maintaining the original geometric structure. After initialization by the embedding layer, the encoder consists of multiple fully connected networks, and its core operations are shown in the following equation: in, For the first l The output features of the layer and These represent the learnable weight matrix and bias vector of this layer, respectively. The ReLU activation function is used. The input sequence of symbols is first processed through an embedding mapping to obtain an initial feature vector. Subsequently, through layer-by-layer transformations in multiple fully connected layers, the data is mapped to a richer high-dimensional feature representation. The last fully connected layer of the network outputs a four-dimensional vector to represent the residual correction term for the traditional PM-MQAM constellation points, as shown in the following equation: Where L represents the total number of layers in the encoder. The final trainable four-dimensional constellation points. QAM Initial Constellation With residual vector The sum can be expressed as follows: Understandably, the encoder does not relearn the entire constellation structure. Instead, it learns small offsets in a data-driven manner through fully connected layers to achieve geometric refinement of the base QAM constellation. After multiple layers of nonlinear mapping, the output of the fourth fully connected layer is added to the initialized constellation points to form the corresponding four-dimensional emission constellation points, which can be represented as follows: ,in, This represents all learnable parameters of the encoder. It enables the final generated constellation to better adapt to the noise characteristics of the channel while maintaining the QAM topology.

[0068] This application also provides an electronic device, which may include a processor, a memory, a receiver, and a transmitter. The processor is used to execute the training method for the four-dimensional geometrically shaped modulation format generation model, the generation method for the four-dimensional geometrically shaped modulation format, or the demodulation method for the four-dimensional geometrically shaped modulation format mentioned in the above embodiments. The processor and the memory can be connected via a bus or other means, taking a bus connection as an example. The receiver can be connected to the processor and the memory via wired or wireless means.

[0069] The processor can be a central processing unit (CPU). The processor can also be 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, or combinations of the above types of chips.

[0070] Memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs, non-transitory computer-executable programs, and modules, such as the program instructions / modules corresponding to the training method, generation method, or demodulation method of the four-dimensional geometrically shaped modulation format generation model described in the embodiments of this application. The processor executes various functional applications and data processing by running the non-transitory software programs, instructions, and modules stored in the memory, thereby implementing the training method, generation method, or demodulation method of the four-dimensional geometrically shaped modulation format generation model described in the above method embodiments.

[0071] The memory may include a program storage area and a data storage area. The program storage area may store the operating system and applications required for at least one function; the data storage area may store data created by the processor, etc. Furthermore, the memory may include high-speed random access memory and non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, the memory may optionally include memory remotely located relative to the processor, which can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, corporate intranets, local area networks, mobile communication networks, and combinations thereof.

[0072] The one or more modules are stored in the memory, and when executed by the processor, the training method, generation method, or demodulation method of the four-dimensional geometrically shaped modulation format generation model described in the embodiment are executed.

[0073] In some embodiments of this application, the user equipment may include a processor, a memory, and a transceiver unit. The transceiver unit may include a receiver and a transmitter. The processor, memory, receiver, and transmitter may be connected via a bus system. The memory is used to store computer instructions, and the processor is used to execute the computer instructions stored in the memory to control the transceiver unit to send and receive signals.

[0074] As one implementation method, the functions of the receiver and transmitter in this application can be implemented by transceiver circuits or dedicated transceiver chips, and the processor can be implemented by dedicated processing chips, processing circuits or general-purpose chips.

[0075] As another implementation approach, the server provided in this application embodiment can be implemented using a general-purpose computer. That is, the program code implementing the processor, receiver, and transmitter functions is stored in memory, and the general-purpose processor implements the processor, receiver, and transmitter functions by executing the code in memory.

[0076] This application also provides a computer-readable storage medium storing a computer program thereon. When executed by a processor, the computer program implements the steps of the aforementioned training method for a four-dimensional geometrically shaped modulation format generation model, the generation method for a four-dimensional geometrically shaped modulation format, or the demodulation method for a four-dimensional geometrically shaped modulation format. The computer-readable storage medium can be a tangible storage medium, such as random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, floppy disks, hard disks, removable storage disks, CD-ROMs, or any other form of storage medium known in the art.

[0077] This application also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the aforementioned training method for a four-dimensional geometrically shaped modulation format generation model, the generation method for a four-dimensional geometrically shaped modulation format, or the demodulation method for a four-dimensional geometrically shaped modulation format.

[0078] Those skilled in the art will understand that the exemplary components, systems, and methods described in conjunction with the embodiments disclosed herein can be implemented in hardware, software, or a combination of both. Whether implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application. When implemented in hardware, it can be, for example, electronic circuits, application-specific integrated circuits (ASICs), appropriate firmware, plug-ins, function cards, etc. When implemented in software, the elements of this application are programs or code segments used to perform the required tasks. The programs or code segments can be stored on a machine-readable medium or transmitted over a transmission medium or communication link via data signals carried on a carrier wave.

[0079] It should be clarified that this application is not limited to the specific configurations and processes described above and shown in the figures. For the sake of brevity, detailed descriptions of known methods are omitted here. In the above embodiments, several specific steps are described and shown as examples. However, the method process of this application is not limited to the specific steps described and shown. Those skilled in the art can make various changes, modifications, and additions, or change the order of steps, after understanding the spirit of this application.

[0080] In this application, features described and / or illustrated for one embodiment may be used in the same or similar manner in one or more other embodiments, and / or combined with or in place of features of other embodiments.

[0081] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to the embodiments of this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A training method for a four-dimensional geometric integer modulation format generation model, characterized in that, The training method includes a first training phase and a second training phase; The first training phase includes: In the current iteration, a random bit vector is input into the current four-dimensional geometrically shaped residual autoencoder, so that the transmitter neural network in the four-dimensional geometrically shaped residual autoencoder generates the original four-dimensional constellation symbol corresponding to the random bit vector based on a preset modulation constellation, and the differentiable fiber channel module in the four-dimensional geometrically shaped residual autoencoder transmits the original four-dimensional constellation symbol in a preset channel environment to obtain the received four-dimensional constellation symbol. The first target loss for the current iteration round is calculated based on the random bit vector and the received four-dimensional constellation symbol, and the model parameters of the transmitter neural network are optimized based on the first target loss. The second training phase includes: In the current iteration, a random bit vector is input into the current four-dimensional geometrically shaped residual autoencoder so that the trained transmitter neural network generates the original four-dimensional constellation symbol, and the differentiable fiber channel module transmits the original four-dimensional constellation symbol to obtain the received four-dimensional constellation symbol. The receiver neural network in the four-dimensional geometrically shaped residual autoencoder decodes the received four-dimensional constellation symbol and outputs the posterior bit probability vector corresponding to the random bit vector. The second target loss for the current iteration round is calculated based on the random bit vector and the posterior bit probability vector, and the model parameters of the receiver neural network are optimized based on the second target loss. If both the optimized transmitter neural network and receiver neural network meet the preset convergence conditions, then the current four-dimensional geometrically shaped residual autoencoder will be used as the four-dimensional geometrically shaped modulation format generation model for generating the four-dimensional geometrically shaped modulation format.

2. The method according to claim 1, characterized in that, The first target loss is the generalized mutual information loss, which is expressed by the following formula: in, This indicates the number of bits carried in the received four-dimensional constellation symbol; Indicates bit index; This represents the value of the i-th bit in each transmitted symbol; This indicates that the value received is a four-dimensional constellation symbol; Let i represent the random variable representing the i-th bit of each transmitted symbol; Represents a random variable that receives a four-dimensional constellation symbol; Let represent the posterior probability density function based on the Gaussian-assisted channel.

3. The method according to claim 1, characterized in that, The second objective loss is the binary cross-entropy loss, which is expressed by the following formula: in, This represents the number of samples in each training batch; Represented as the first K The input bit sequence of each training sample; Indicates the index of the input bit sequence; This represents the input bit sequence of the k-th training sample; This represents the bit posterior probability vector of the k-th training sample output by the decoder.

4. The method according to claim 1, characterized in that, The convergence conditions include a first convergence condition and a second convergence condition; wherein, the first convergence condition is that the first target loss reaches a preset first threshold or the number of iterations reaches a preset maximum value; the second convergence condition is that the second target loss reaches a preset second threshold or the number of iterations reaches a preset maximum value.

5. The method according to claim 1, characterized in that, The transmitter neural network includes a transmitter residual neural network. The output layer of the transmitter neural network is initialized with the preset modulation constellation. A four-dimensional residual vector is obtained through an embedding layer and multiple fully connected layers. The four-dimensional residual vector is added to the initialized constellation points to generate the four-dimensional constellation symbol.

6. The method according to claim 1, characterized in that, The differentiable fiber channel module includes a differentiable SSFM channel model, which is used to simulate the dispersion, nonlinear effects and transmission loss of the optical fiber, and supports gradient backpropagation.

7. The method according to claim 1, characterized in that, The receiver neural network includes a fully connected receiver neural network, which is used to learn soft decision rules under the differentiable fiber channel module after fixing the transmitter neural network parameters.

8. A method for generating a four-dimensional geometric shaping modulation format, characterized in that, include: A random bit vector is input into a transmitter neural network so that the transmitter neural network outputs a four-dimensional constellation symbol corresponding to the random bit vector; wherein, the four-dimensional constellation symbol is used to be transmitted to a receiver neural network through a channel so that the receiver receives the received four-dimensional constellation symbol corresponding to the four-dimensional constellation symbol and inputs the received four-dimensional constellation symbol into the receiver neural network, thereby making the receiver neural network output a demodulation bit vector corresponding to the received four-dimensional constellation symbol. The transmitter neural network and the receiver neural network constitute a four-dimensional geometrically shaped modulation format generation model for generating a four-dimensional geometrically shaped modulation format. The four-dimensional geometrically shaped modulation format generation model is pre-trained based on the training method of the four-dimensional geometrically shaped modulation format generation model according to any one of claims 1 to 7.

9. A demodulation method for a four-dimensional geometric shaping modulation format, characterized in that, include: The receiver receives a received four-dimensional constellation symbol corresponding to the transmitted four-dimensional constellation symbol, and inputs the received four-dimensional constellation symbol into the receiver neural network, thereby causing the receiver neural network to output the demodulated bit vector corresponding to the received four-dimensional constellation symbol; wherein, the four-dimensional constellation symbol is output by the transmitter neural network in advance by the transmitter inputting a random bit vector into the transmitter neural network. The transmitter neural network and the receiver neural network constitute a four-dimensional geometrically shaped modulation format generation model for generating a four-dimensional geometrically shaped modulation format. The four-dimensional geometrically shaped modulation format generation model is pre-trained based on the training method of the four-dimensional geometrically shaped modulation format generation model according to any one of claims 1 to 7.

10. An electronic device, characterized in that, It includes a processor and a memory; when the processor executes the running program stored in the memory, it implements the training method of the four-dimensional geometrically shaped modulation format generation model as described in any one of claims 1 to 7, the generation method of the four-dimensional geometrically shaped modulation format as described in claim 8, or the demodulation method of the four-dimensional geometrically shaped modulation format as described in claim 9.

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