A probabilistic shaping method for self-encoder fiber optic communication

Abstract

A probabilistic shaping method for optical fiber communication using an autoencoder belongs to the field of optical communication. It generates the probability of different constellation points by using a Wasserstein autoencoder and continuously updates it through an iterative training process to obtain the probability of different constellation points appearing in suitable transmission channels. The Wasserstein autoencoder automatically matches the channel environment to modulate the optical signal, reducing the impact of channel impairments that are difficult to quantitatively estimate. The probabilistic shaping method generates a shaped modulation scheme that represents the optimal distribution of the optical fiber channel, maximizing the capacity of the transmission system. A modular approach is used, where the channel model in the autoencoder is replaced according to different channel conditions; only the channel parameters need to be changed to achieve optimal optical signal tuning for different optical fiber channel environments. This invention is applicable to the field of optical communication, used to improve the capacity of optical communication systems, bringing the system capacity closer to the Shannon limit.

Description

Technical Field

[0001] This invention relates to a probabilistic shaping method for self-encoder optical fiber communication, belonging to the field of optical communication. Background Technology

[0002] Optical fiber transmission systems widely employ the traditional Quadrature Amplitude Modulation (QAM) format. QAM uses uniformly distributed constellation points arranged in a two-dimensional space to form a constellation diagram. Since nonlinear impairments have become a major factor affecting the performance of long-distance optical fiber communication systems, constellation shaping techniques are used at the transmitting end to reduce the impairments caused by nonlinear effects in order to approach the Shannon limit capacity and improve system performance. Constellation shaping techniques include geometric shaping (GS) and probabilistic shaping (PS). Probabilistic shaping alters the probability of constellation points appearing during the modulation phase, making the probability of constellation points appearing non-uniform.

[0003] Most probabilistic shaping methods are manually generated for specific modulation formats and additive white Gaussian noise (AWGN) channels. Because constellation shaping involves numerous variables and lacks strong regularity, manual generation is limited to specific environments and has certain limitations. Furthermore, it struggles to effectively address nonlinear issues in ultra-long-distance fiber optic transmission systems. Therefore, a method that can automatically generate suitable modulation schemes based on the required channel environment is urgently needed. Summary of the Invention

[0004] Existing probabilistic shaping methods are only applicable to special environments and struggle to effectively address nonlinear issues in ultra-long-distance fiber optic transmission systems. The main objective of this invention is to provide a probabilistic shaping method for optical fiber communication using an autoencoder. Based on a Wasserstein autoencoder, this method generates probabilistically shaped signals that conform to channel conditions within the optical communication system. This addresses the distortion at the receiver caused by channel loss, thereby increasing the capacity of the optical communication system and bringing it closer to the Shannon limit.

[0005] The objective of this invention is achieved through the following technical solution:

[0006] This invention discloses a probabilistic shaping method for optical fiber communication using an autoencoder. The method generates the probability of different constellation points by using a Wasserstein autoencoder and continuously updates the probability through an iterative training process. After the Wasserstein autoencoder is trained, the probability of different constellation points appearing in a suitable transmission channel is obtained. A sampler constructs a transmit bit sequence that satisfies the probability distribution and maps it to the transmit constellation. Impairment is added to the transmit signal through the optical fiber channel. The received signal is restored to a bit sequence by a decoder, reconstructing the low-dimensional information back into a high-dimensional expression, thereby improving the capacity of the optical communication system and bringing it close to the Shannon limit.

[0007] This invention discloses a probabilistic shaping method for self-encoder optical fiber communication, comprising the following steps:

[0008] Step 1: Construct the probability generator and demodulator;

[0009] The probability generator is a three-layer neural network: the first layer is a fixed one-dimensional vector as input signal, the second layer is a hidden layer with m nodes where m is the modulation order, and the third layer is the output layer with m nodes. Linear connections are used between the first and second layers, and between the second and third layers, and Leaky ReLU is used as the activation function. The output of the nodes in the third layer is normalized by Softmax to obtain the probability distribution p of the constellation points.

[0010] The demodulator is a four-layer neural network. The first layer consists of two nodes, whose inputs are the IQ signals after passing through the channel. The second and third layers are hidden layers with 2m and 128 nodes, respectively. The fourth layer is the output layer with log2m nodes. The layers of the demodulator are connected by linear connections. The activation functions of the second and third layers are LeakyReLU, and the activation function of the fourth layer is Sigmoid.

[0011] Step 2: The probability generator generates the probability distribution of constellation points, and the sampler samples according to the probability distribution of constellation points.

[0012] Based on the probability distribution p of constellation points, the sampler uses the Gumbel-Softmax technique to generate an m-dimensional vector. As shown in equation (1):

[0013]

[0014] Where, p i g represents the probability of the i-th symbol appearing. i These are independent and identically distributed samples drawn from the standard Gumbel distribution; τ is a positive parameter called temperature. It is an approximation of the one-hot vector s, satisfying A one-hot vector *s* is an m-dimensional vector where all elements except one are set to 0. As the temperature *τ* approaches zero, the Gumbel-Softmax method generates... They are closer to one-hot vectors s, and their distribution is closer to the probability distribution p.

[0015] Step 3: Perform power normalization and modulate the circuit.

[0016] The modulator first normalizes the power of constellation point c according to the probability distribution p of constellation point occurrence, thus obtaining the normalized constellation point. As shown in equation (2):

[0017]

[0018] Among them, c i and These are the constellation point and normalized constellation point corresponding to the i-th symbol. The modulator uses the normalized constellation point... Map the one-hot vector s to the corresponding constellation point, where the one-hot vector s is derived from... This is obtained through a pass-through estimator, allowing the use of the true one-hot vectors s for forward propagation during training, and the use of approximate one-hot vectors. Perform backward propagation.

[0019] Step 4: The modulator output is combined into an IQ signal, transmitted through the channel, and noise is added. The channel model is replaced according to different channel conditions, thereby achieving optimal optical signal tuning for different fiber optic channel environments;

[0020] Step 5: Input the noisy signal into the demodulator to obtain the demodulated output, which is in the form of log-likelihood ratio;

[0021] Step Six: Construct the Wasserstein autoencoder;

[0022] The demodulator output constructed in step one is compared with the training bit sequence. The bit cross-entropy with added MMD regularization term is used as the loss function Loss of the neural network for gradient backpropagation to update the network weights.

[0023] The bit cross-entropy with added MMD regularization term is used as the loss of the neural network, as shown in equation (3):

[0024]

[0025] Among them, D KL Kullback-Leibler (KL) divergence is the difference between two posterior probabilities, used to measure the difference between two distributions of the same variable. For the true posterior distribution, Mapping defined for the demodulator; For the generalized mutual information (GMI) of the channel, and These represent the input and output before and after the channel, respectively; λ is a hyperparameter controlling the size of the MMD regularization term, and D... x This is the MMD regularization term, used to measure the distribution Q of constellation points. x and prior distribution Px The difference between them; H(p) is the entropy, as shown in equation (4):

[0026]

[0027] For probabilistically shaped signals, the bit cross-entropy changes with the probability of constellation points appearing;

[0028] Step 7: Train the Wasserstein autoencoder;

[0029] Gradient backpropagation is performed, and the constructed neural network is trained based on the calculated loss. Steps two through five are repeated. During the iterative training process, the loss of the neural network gradually converges, the bit mutual information tends to be maximized, and the relative entropy of the encoder and decoder tends to be minimized. The Wasserstein autoencoder training is complete.

[0030] Step 8: Based on the Wasserstein autoencoder trained in Step 7, obtain the probability of each constellation point output by the probability generator to obtain the optimal transmission modulation scheme under a given channel environment. Applying the obtained modulation scheme to the corresponding channel can reduce the impact of noise on the signal during transmission and improve the capacity of the transmission system.

[0031] Beneficial effects:

[0032] 1. The present invention discloses a probabilistic shaping method for optical fiber communication using an autoencoder, which employs a Wasserstein autoencoder to automatically match the channel environment and modulate the optical signal, thereby reducing the impact of channel impairments that are difficult to quantitatively estimate.

[0033] 2. The present invention discloses a probabilistic shaping method for self-encoder optical fiber communication. The probabilistic shaping method generates a shaping modulation scheme that is the optimal distribution of the optical fiber channel, which can maximize the capacity of the transmission system.

[0034] 3. The self-encoder optical fiber communication probabilistic shaping method disclosed in this invention adopts a modular approach. The channel model in the autoencoder is replaced according to different channel conditions. Only the channel parameters need to be changed to achieve optimal optical signal tuning for different optical fiber channel environments. Attached Figure Description

[0035] Figure 1 This is a flowchart of a self-encoder optical fiber communication probability shaping method disclosed in this invention;

[0036] Figure 2 This is a schematic diagram of the structure of the automatic encoder constructed in the embodiment;

[0037] Figure 3 This is the 32QAM constellation diagram output by the modulator in the embodiment;

[0038] Figure 4 The diagram shows the 32QAM constellation output of the modulator at different transmission distances and different transmit powers in the embodiment.

[0039] Figure 5 This is a comparison chart of the bit error rates of two modulation schemes under different transmission powers and a transmission distance of 1600km in the example.

[0040] Figure 6 This is a comparison chart of the bit error rates of two modulation schemes under different transmission powers and a transmission distance of 2400km in the example. Detailed Implementation

[0041] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. The technical problems solved by the present invention and its beneficial effects are also described. It should be noted that the described embodiments are only intended to facilitate understanding of the present invention and do not constitute any limitation thereof.

[0042] This embodiment describes the optical signal generation process under optical fiber transmission links with transmission distances of 1600km and 2400km. The transmitted optical signal is selected as 32QAM, and the transmitted power is -3 to 2dBm. A probabilistic shaping method for optical fiber communication disclosed in this invention is applied to achieve probabilistic shaping of the optical signal. Figure 1 As shown, it includes the following steps:

[0043] Step 1: Construct the probability generator and demodulator;

[0044] In the embodiments, such as Figure 2 As shown, the probability generator is a three-layer neural network: the first layer is a fixed one-dimensional vector as input signal, the second layer is a hidden layer with m nodes, where m is the modulation order, and the third layer is the output layer with m nodes; the first and second layers, as well as the second and third layers, are connected by linear connections and Leaky ReLU is used as the activation function. The output of the nodes in the third layer is normalized by softmax to obtain the probability distribution p of the constellation points.

[0045] In the embodiments, such as Figure 2 As shown, the demodulator is a four-layer neural network. The first layer consists of two nodes, whose inputs are the IQ signals after passing through the channel. The second and third layers are hidden layers with 2m and 128 nodes, respectively. The fourth layer is the output layer with log2m nodes. The layers of the demodulator are connected by linear connections. The activation functions of the second and third layers are Leaky ReLU, and the activation function of the fourth layer is Sigmoid.

[0046] Step 2: The probability generator generates the probability distribution of constellation points, and the sampler samples according to the probability distribution of constellation points.

[0047] Based on the probability distribution p of constellation points, the sampler uses the Gumbel-Softmax technique to generate an m-dimensional vector. As shown in equation (1):

[0048]

[0049] Where, p i g represents the probability of the i-th symbol appearing. i These are independent and identically distributed samples drawn from the standard Gumbel distribution; τ is the temperature parameter. It is an approximation of the one-hot vector s. As the temperature τ approaches zero, the Gumbel-Softmax method generates... They are closer to one-hot vectors s, and their distribution is closer to the probability distribution p.

[0050] During training, a corresponding number of m-dimensional vectors are generated based on the number of training batches. Its distribution becomes closer to the probability distribution p as the temperature τ decreases.

[0051] Step 3: Perform power normalization and modulate the circuit.

[0052] The modulator first normalizes the power of constellation point c according to the probability distribution p of constellation point occurrence, thus obtaining the power-normalized constellation point. As shown in equation (2):

[0053]

[0054] Among them, c i and These are the constellation points corresponding to the i-th symbol and the normalized constellation points. The modulator uses the normalized constellation points... Map the one-hot vector s to the corresponding constellation point, where the one-hot vector s is derived from... This is obtained through a pass-through estimator, allowing the use of the true one-hot vectors s for forward propagation during training, and the use of approximate one-hot vectors. Perform backward propagation.

[0055] Step 4: Combine the output of the modulator into an IQ signal, transmit it through the channel, and add noise;

[0056] Step 5: Input the noisy signal into the demodulator to obtain the demodulated output, which is in the form of log-likelihood ratio;

[0057] Step Six: Construct the Wasserstein autoencoder;

[0058] The demodulator output constructed in step one is compared with the training bit sequence. The bit cross-entropy with added MMD regularization term is used as the loss function Loss of the neural network for gradient backpropagation to update the network weights.

[0059] The bit cross-entropy with added MMD regularization term is used as the loss of the neural network, as shown in equation (3):

[0060]

[0061] Among them, D KL The Kullback-Leibler (KL) divergence between two posterior probabilities; For the true posterior distribution, Mapping defined for the demodulator; For the generalized mutual information (GMI) of the channel; and λ represents the input and output before and after the channel, respectively; λ is a hyperparameter controlling the size of the MMD regularization term; D x This is the MMD regularization term, used to measure the distribution Q of constellation points. x and prior distribution P x The difference between them is represented by a Gaussian distribution as the prior distribution P. x H(p) is the entropy, as shown in equation (4):

[0062]

[0063] For probabilistically shaped signals, the bit cross-entropy changes with the probability of constellation points appearing;

[0064] Step 7: Train the Wasserstein autoencoder;

[0065] Gradient backpropagation is performed, and the constructed neural network is trained based on the calculated loss. Steps two to five are repeated. During the continuous iterative training process, the loss of the neural network gradually converges, the bit mutual information tends to be maximized, and the relative entropy of the encoder and decoder tends to be minimized. The Wasserstein autoencoder training is completed.

[0066] Step 8: Based on the Wasserstein autoencoder trained in Step 7, obtain the probability of each constellation point output by the probability generator. The output probabilities are as follows: Figure 3 As shown, the optimal transmission modulation scheme is obtained under a channel environment with a transmission distance of 1600km and a transmit power of 2dBm; the optimal modulation schemes under other channel conditions are as follows. Figure 4 As shown, Figure 4(a)-(c) are modulation schemes generated under channel conditions with a transmission distance of 1600km and transmit powers of -2dBm, 0dBm and 2dBm, respectively; Figure 4 (d)-(f) are modulation schemes generated under channel conditions with a transmission distance of 2400km and transmit powers of -2dBm, 0dBm and 2dBm respectively. In the modulation schemes generated under different conditions, the probability of each constellation point appearing in the modulation after probability shaping is represented by different gray levels and bar chart heights.

[0067] In the embodiments, such as Figure 5 and Figure 6 As shown, the modulation scheme obtained by using the self-encoder fiber optic communication probabilistic shaping method has achieved significant improvement in bit error rate at transmission distances of 1600km and 2400km and transmit power of -3 to 2dBm. Compared with the traditional uniform 32QAM modulation scheme, it has reduced the bit error rate by up to 33%, effectively reducing the impact of channel noise on the signal during transmission and improving the transmission system capacity.

[0068] This invention introduces channel information into the Wasserstein autoencoder and optimizes the modulation format separately for each channel environment, replacing the fixed modulation format in traditional methods. Since the autoencoder is optimized according to the minimum bit cross-entropy with the addition of MMD regularization terms, the probability of occurrence of different constellation points minimizes the error between the received and transmitted information. The modulation format determined by the method of this invention minimizes the impact of noise during transmission, reduces the bit error rate, and improves system capacity.

[0069] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A probabilistic shaping method for self-encoder optical fiber communication, characterized in that: Includes the following steps, Step 1: Construct the probability generator and demodulator; Step 2: The probability generator generates the probability distribution of constellation points, and the sampler samples according to the probability distribution of constellation points. Step 3: Perform power normalization and modulate the circuit. Step 4: Combine the output of the modulator into an IQ signal, transmit it through the channel, and add noise. The channel model is replaced according to different channel conditions, thereby achieving optimal optical signal tuning for different fiber optic channel environments; Step 5: Input the noisy signal into the demodulator to obtain the demodulated output, which is in the form of log-likelihood ratio; Step 6: Construct the Wasserstein autoencoder; The implementation method for step six is ​​as follows: The demodulator output constructed in step one is compared with the training bit sequence. The bit cross-entropy with added MMD regularization term is used as the loss function Loss of the neural network for gradient backpropagation to update the network weights. The bit cross-entropy with added MMD regularization term is used as the loss of the neural network, as shown in equation (3): （3） in, The Kullback-Leibler divergence between two posterior probabilities is used to measure the difference between two distributions of the same variable. For the true posterior distribution, Mapping defined for the demodulator; For the generalized mutual information of the channel, and These represent the input and output before and after the channel, respectively. The hyperparameters that control the size of the MMD regularization terms, This is the MMD regularization term, used to measure the distribution of constellation points. and prior distribution The differences between them; The entropy is shown in equation (4): （4） For probabilistically shaped signals, the bit cross-entropy changes with the probability of constellation points appearing; Step 7: Train the Wasserstein autoencoder; The implementation method for step seven is as follows: Gradient backpropagation is performed, and the constructed neural network is trained based on the calculated loss. Steps two through five are repeated. During the iterative training process, the loss of the neural network gradually converges, the bit mutual information tends to be maximized, and the relative entropy of the encoder and decoder tends to be minimized. The Wasserstein autoencoder training is completed. Step 8: Based on the Wasserstein autoencoder trained in Step 7, obtain the probability of each constellation point output by the probability generator to obtain the optimal transmission modulation scheme under a given channel environment. Apply the obtained modulation scheme to the corresponding channel to reduce the impact of noise on the signal during transmission and improve the capacity of the transmission system.

2. The self-encoder optical fiber communication probabilistic shaping method as described in claim 1, characterized in that: The implementation method for step one is as follows: The probability generator is a three-layer neural network: the first layer takes a fixed one-dimensional vector as input, the second layer is a hidden layer with m nodes, where m is the modulation order, and the third layer is the output layer with m nodes. Linear connections are used between the first and second layers, and between the second and third layers, with Leaky ReLU as the activation function. The outputs of the nodes in the third layer are normalized using Softmax to obtain the probability distribution of constellation points. ; The demodulator is a four-layer neural network. The first layer consists of two nodes, whose input is the IQ signal after passing through the channel. The second and third layers are hidden layers with 2m and 128 nodes respectively. The fourth layer is the output layer with [number of nodes missing]. The demodulator layers are connected by linear connections; the activation functions for the second and third layers are LeakyReLU, and the activation function for the fourth layer is Sigmoid.

3. The self-encoder optical fiber communication probabilistic shaping method as described in claim 2, characterized in that: The implementation method for step two is as follows: Based on the probability distribution of constellation points The sampler uses the Gumbel-Softmax technique to generate an m-dimensional vector. As shown in equation (1): （1） in, Let be the probability of the i-th symbol appearing; These are independent and identically distributed samples drawn from the standard Gumbel distribution; It is a positive parameter called temperature; It is a one-hot vector The approximation satisfies one-hot vector It is an m-dimensional vector where all elements are set to 0 except for one element which is set to 1; with temperature... Approaching zero, the Gumbel-Softmax method generates Closer to a one-hot vector Furthermore, their distribution is closer to the probability distribution. .

4. The self-encoder optical fiber communication probabilistic shaping method as described in claim 3, characterized in that: The implementation method for step three is as follows: The modulator first determines the probability distribution of constellation points. According to the constellation Power normalization is performed to obtain normalized constellation points. As shown in equation (2): （2） in, and These are the constellation points and normalized constellation points corresponding to the i-th symbol; the modulator uses the normalized constellation points... one-hot vector Mapped to the corresponding constellation points, where the one-hot vector Depend on Obtained through a pass-through estimator, thus using the true one-hot vector during training. Perform a forward pass and use an approximate one-hot vector. Perform backward propagation.

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