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Article

DeepChaos+: Signal Detection Quality Enhancement of High-Speed DP-16QAM Optical Fiber Communication Based on Chaos Masking Technique with Deep Generative Models

by
Dao Anh Vu
1,
Nguyen Khoi Hoang Do
2,
Huyen Ngoc Thi Nguyen
2,
Hieu Minh Dam
3,
Thuy Thanh Thi Tran
1,
Quyen Xuan Nguyen
4 and
Dung Cao Truong
1,*
1
Department of Electronic Engineering, Post and Telecommunications Institute of Technology, Hanoi 152638, Vietnam
2
Department of Information Technology, Post and Telecommunications Institute of Technology, Hanoi 152638, Vietnam
3
Department of Computer Science, Swinburne University of Technology, Hanoi 100000, Vietnam
4
School of Electrical and Electronic Engineering, Hanoi University of Science and Technology, Hanoi 100000, Vietnam
*
Author to whom correspondence should be addressed.
Photonics 2024, 11(10), 967; https://doi.org/10.3390/photonics11100967
Submission received: 2 August 2024 / Revised: 8 September 2024 / Accepted: 14 September 2024 / Published: 15 October 2024
(This article belongs to the Special Issue Machine Learning Applied to Optical Communication Systems)
Browse Figures
Figure 1
<p>Conceptual Conceptional diagram of the COC and CFOC channels in the long-haul WDM optical communication system using the <math display="inline"><semantics> <mrow> <mi>D</mi> <mi>P</mi> <mo>−</mo> <mn>16</mn> <mi>Q</mi> <mi>A</mi> <mi>M</mi> </mrow> </semantics></math> modulation scheme.</p> "> Figure 2
<p>Overview of the DeepChaos+ framework. The framework introduces two key models: the Variational Autoencoder (VAE) and the lightweight Informer Network. The VAE is trained to generate interpolated data from the set <math display="inline"><semantics> <mi mathvariant="script">X</mi> </semantics></math>. The generated data are then combined with the dataset <math display="inline"><semantics> <mi mathvariant="script">D</mi> </semantics></math> and used to iteratively retrain the VAE. The lightweight Informer Network, with fewer parameters but functionality equivalent to the VAE’s decoder, is trained to predict a set <math display="inline"><semantics> <mover accent="true"> <mi mathvariant="script">X</mi> <mo>˜</mo> </mover> </semantics></math> that minimizes the bit error rate <math display="inline"><semantics> <mrow> <mi mathvariant="script">B</mi> <mo>(</mo> <mover accent="true"> <mi mathvariant="script">X</mi> <mo>˜</mo> </mover> <mo>,</mo> <mi mathvariant="script">X</mi> <mo>)</mo> </mrow> </semantics></math>. Knowledge Distillation is employed to ensure the Informer achieves similar performance to the decoder while enabling faster inference time.</p> "> Figure 3
<p>The training performance of DeepChaos+ in the 60% dataset is shown in the <b>left</b> figure, while the learning performance of the student model is depicted for different sizes in the <b>right</b> figure. The red line in the right figure represents the training time, indicating that, as the size of the student model increases, the training time also lengthens.</p> "> Figure 4
<p>The figure on the <b>left</b> illustrates the performance of DeepChaos+ on the testing set of training datasets of 20%, 40%, 60%, and 80%. The figure on the <b>right</b> displays the BER (bit error rate) of DeepChaos compared to the other methods, particularly on the 60% and 80% datasets.</p> ">
Review Reports Versions Notes

Abstract

:
In long-haul WDM (wavelength division multiplexing) optical communication systems utilizing the DP-16QAM modulation scheme, traditional methods for removing chaos have exhibited poor performance, resulting in a high bit error rate of 10 − 2 between the original signal and the removed chaos signal. To address this issue, we propose DeepChaos+, a machine learning-based approach for chaos removal in WDM transmission systems. Our framework comprises two key points: (1) DeepChaos+ automatically generates a dataset that accurately reflects the features of the original signals in the communication system, which eliminates the need for time-consuming data simulation, streamlining the process significantly; (2) it allows for the training of a lightweight model that provides fast prediction times while maintaining high accuracy. This allows for both efficient and reliable signal reconstruction. Through extensive experiments, we demonstrate that DeepChaos+ achieves accurate reconstruction of the original signal with a significantly reduced bit error rate of approximately 10 − 5 . Additionally, DeepChaos+ exhibits high efficiency in terms of processing time, facilitating fast and reliable signal reconstruction. Our results underscore the effectiveness of DeepChaos+ in removing chaos from WDM transmission systems. By enhancing the reliability and efficiency of chaotic secure channels in optical fiber communication systems, DeepChaos+ holds the potential to improve data transmission in high-speed networks.

1. Introduction

In the field of communication, for several decades recently, the wavelength division multiplexing (WDM) technique has been widely applied in optical transmission systems for both high-speed backbone and access systems, up to 400 Gbps per wavelength, aiming to utilize the huge bandwidth of optical fiber [1,2,3,4] in order to respond to the huge requirement of broadband services, e.g., broadband mobile access service, data mining, cloud computing, augmented reality, and virtual reality experiments. To enhance the capacity of communication channels, we can combine the WDM technique with several different methods, such as spatial division multiplexing [5], multi-carrier [6], super-channel [7], advanced multilevel modulation format [8], etc. This is due to the linear independence of such mentioned formats from the wavelength. Lots of optical fiber WDM communication systems use advanced modulation schemes such as quadrature amplitude modulation (QAM) [9,10] or phase shift keying (PSK) [11] techniques in combination with a dual polarization scheme to increase the significant spectral efficiency by mean of maximization of wavelength bandwidth. For example, if an optical fiber transmission migrates from the mono polarization-QPSK format to the dual polarization-QPSK format, the capacity of the channel will double, while the bit error rate of the optical link will be negligibly affected [11].
In high-security communication systems, such as military communication, banking communication, and government communication systems [12], advanced and complicated encryption systems have been used to encode communication bit streams, such as FPGA-based hardware [13], RSA [14,15], DES [16], alternatively interleaved AES [16,17,18], etc. However, these methods have some drawbacks, such as: (i) requiring complex electronic circuits for encoding and decoding, which are costly; (ii) increasing information processing delays; and (iii) being vulnerable to brute-force algorithms due to the development of computer-supported algorithms [19,20]. Therefore, an economical approach increasingly used in physical layer security is the use of chaotic techniques [21,22,23] due to the superior characteristics of chaotic features, such as random pseudo-noise and spread spectrum [24]. On the other hand, chaos is also a deterministic phenomenon, so data can be decrypted if the synchronization process can be controlled. Information data are mixed with chaotic sequences through mechanisms such as scrambling, modulation, and encryption in order to enhance security so that eavesdroppers cannot successfully detect the encrypted information [17,25,26]. Nowadays, the chaos phenomenon is applied in various applications, such as wireless and radio communication [27], free-space optical communication [25], short-range chaotic optical communication [28,29], visible light communication (VLC) [30,31], underwater communication [32,33,34], automatic control [35], sensors [36], etc. Some related works have proposed utilizing the chaos effect arising from the dynamic properties of semiconductor laser systems for high-intensity applications in intensity-modulated direct detection (IM-DD) systems. However, generating chaotic laser beams with significant amplitude variations for WDM IM-DD systems remains challenging [37,38]. In addition, chaotic techniques have not been widely applied in fiber optic communication systems due to the lack of research on the chaos phenomenon in wideband optical fiber communication systems, such as WDM systems.
One of the most significant technological advancements in recent years is artificial intelligence (AI). In particular, deep learning (DL) models [39] have brought new dimensions to many fields, such as human–machine interaction [40], robotics [41], natural language processing [42,43], etc. Recently, deep learning models have been applied in the field of information by effectively representing them through deep autoencoders for optical information signals to reduce nonlinearity and nonlinear balance. Specifically, in chaotic optical communication systems, the Informer model is utilized to improve the BER performance quality of chaos shift keying (CSK) modulation communication systems due to a deep understanding of the dynamic behaviors of chaos through data-driven analysis [44].
In this study, we introduce DeepChaos+, a novel framework designed to address the chaos problem to enhance the performance of high-speed DP-16QAM optical fiber communication systems. This framework tackles the chaos challenge in WDM systems, which previously caused high bit error rates, by using deep learning models to reduce the bit error rate to approximately 10 − 5 . Furthermore, with the use of advanced machine learning techniques, namely, data augmentation and knowledge distillation, reduction in both training time and inference time is achieved. This offers a reliable and efficient solution for enhancing the quality of optical fiber communications, which is critical for the advancement of high-speed networks.

2. Background and Problem Setting

2.1. Long-Haul WDM Optical Communication System Using DP-16QAM Modulation Scheme

The conceptual diagram of the chaotic optical communication with two wavelength multiplexed channels using DP-16QAM for each channel is exhibited and described in Figure 1. In this diagram, one channel is for chaotic optical communication (COC), and another is for conventional fiber optic communication (CFOC). Each channel, defined by the wavelength of its carrier wave, is coupled into the same optical fiber in DP-16QAM data format [45,46]. The chaos cryptography technique encrypts some crucial information at a given WDM channel λ c . In this paper, the chaos sequence is created by a logistic map using a retrieval rule as follows [17]:
z n + 1 = 4 z n 1 − z n ,
where n = 1 , 2 , 3 … is a positive integer, and z 0 = [ 0 , 1 ] is a starting real number between 0 and 1. Therefore, it is easy to see that z n always satisfies 0 < z n < 1 . The chaotic function has a probability distribution density as follows:
p ( z ) = 1 π z ( 1 − z ) for 0 < z < 1 .
In this proposed system, both the laser diode transmitter (LDT) and the laser diode receiver (LDR) are constructed from a single-mode semiconductor laser with an external reflector and the same configuration. Both the COC channel and the CFOC channel are (de)multiplexed by means of a wavelength (de)multiplexer in the C-band of the third telecom window. The transmitter laser (LDT) of the COC channel emits a chaotic carrier, and an optical isolator (ISO) is used to ensure unidirectional transmission. The original message is superimposed on a chaotic carrier by the chaos masking sequence (CMS). As seen in Figure 1, the chaotic signal is implemented by simply adding the CMS signal to the output of the conventional 16QAM modulated signal. On the receiver side, the chaotic signal is decoded by simply subtracting the received COC signal and a CMS signal that is synchronized to the form of the transmitter side.
Information propagating along the long-haul optical fiber link is greatly affected by fiber loss, dispersion, and nonlinear effects. We place an erbium-doped fiber amplifier (EDFA) for the fiber loss compensation and a dispersion compensating fiber (DCF) for the dispersion compensation.
The EDFA amplifier has the gain coefficient G, determined by the formula G = α L . Here, α is the fiber loss coefficient, L is the total length of the transmission link, and L D C F is the length of the DCF fiber. On the receiver, the optical signal is de-multiplexed by the wavelength de-multiplexer (DEMUX) and photodetector after propagating over a long-haul section.
The dynamic behaviors of a couple of transmitters and receivers that are set up in a COC system can be described by well-known Lang–Kobayashi rate equations, with optical feedback and injection terms [29,45] as follows:
d E T , R ( t ) d t = 1 2 ( 1 + i ψ ) G N T , R ( t ) − N 0 1 + ε E T , R ( t ) 2 E T , R ( t ) , + k T , R E T , R ( t − τ ) exp ( − i ω τ ) + k irj E ext ( t ) ,
where E and N correspond the slowly varying complex electric field amplitudes and the carrier density in the laser cavity, respectively; T and R stand for transmitter and receiver; ω is the angle frequency of the free operation laser; τ is the round-trip time; and E est is the transmission link. Then, the COC signal is decoded, and the DP-16QAM signal is also demodulated to recover the baseband signals of the external electric field amplitude at the input of the receiver. For the proposed COC and CFOC parallel transmission system, we consider a two-channel WDM system (each subscript denotes the channel number). The light propagation through the fiber is described in terms of the well-known nonlinear Schrödinger (NLS) equation [46]:
d N T , R ( t ) d t = I T , R q V − 1 τ n N T , R ( t ) − G N T , R ( t ) − N 0 1 + ε E T , R ( t ) 2 E T , R ( t ) 2 .
Here, E j and E k are slowly varying complex electric field amplitudes of the j-th and k-th channels; equally α is the fiber loss coefficient; β 2 is the second-order dispersion coefficient of optical fiber; and γ is the nonlinear coefficient. In this implementation, we use non-zero dispersion shifted fiber (NZ-DSF) following the ITU-T G.655 recommendation, and these typical parameters are determined as α = 0.2 dB / km , β 2 = 5.1 ps 2 · km − 1 / km , and γ = 1.5 W − 1 · km − 1 . Other hyperparameters are listed in Table 1.

2.2. Problem Definition

In our objective to employ a deep learning-based approach for eliminating the chaos introduced at the transmitter side from the received signal in a long-haul WDM optical communication system utilizing the DP-16QAM modulation scheme, our main goal is to minimize the bit error rate (BER) as a critical performance metric in communication systems [48]. To achieve this, we aim to find a mapping function F θ parameterized by θ . The mapping function F θ should be capable of removing the chaos from the received signal, denoted as X † , and recovering the original signal, denoted as X . We define the set of original signals in the system as X ∈ { 0 , 1 } ( 1 × d ) , where d represents the length of the original sampled signals. The chaos adding function is denoted as I, such that X † = I ( X ) . The mapping function F θ : X † → X ˜ can be optimized by finding the optimal parameters θ * for F θ that minimize the expected BER, expressed as:
θ * : = arg min θ B ( X ˜ , X ) .
Here, B ( X ˜ , X ) represents the BER between the reconstructed signal X ˜ from the received signal with added chaos ( X † ) and the original signal ( X ). By optimizing the θ parameters of the mapping function F θ , we aim to train a model that can effectively eliminate the chaos from the received signal. This deep learning-based approach offers the advantage of faster noise removal compared to traditional methods. Additionally, the trained model can generalize well to handle unseen signals with similar properties, providing robust chaos elimination in a wide range of scenarios.

3. Related Work

Recently, the prominent advantages of deep neural networks as well as the advancement of algorithms and deep learning models have become very attractive for viable applications thanks to their ability to automatically learn feature representations from input data without the need for human intervention. Deep neural networks and deep learning models have been able to automatically extract important features from input signals effectively, thereby improving the quality and accuracy of digital signal processing in fiber optic information systems and chaotic-modulated optical information systems. For example, the digital back-propagation through DNNs has been applied to eliminate the nonlinear effect limit in order to enhance the quality of digital signal processing in amplified fiber optic communication systems, as demonstrated by the work of Q. Fan et al. [49]. Similarly, deep learning models have been effectively used to address the challenges of dispersion and nonlinearity compensation in high-speed wavelength division multiplexing (WDM) fiber optic communication systems employing multilevel modulation channels like 64QAM, as demonstrated in [50,51,52,53,54,55]
For chaotic communication systems, recently, a multi-carrier chaos shift keying (DL-IM-MCDCSK) system utilizing deep learning (DL) and index mapping (IM) techniques to mitigate the information leakage risk associated with conventional MC-DCSK systems has been proposed [56]. The proposed system operates without a reference signal and utilizes a two-dimensional reshaping (TDR) index mapping structure to equalize the chaotic signals in both frequency and time domains. The offline-trained DNN classifier can significantly improve the bit error rate (BER) performance during information recovery without requiring conventional maximum likelihood estimation (MLE). In addition, a chaos synchronization that does not require hardware implementations [57] or reference chaotic sequences [58] can be achieved via deep learning models to provide high-level physical layer security for optical communications. For another actual implementation, very recently, a high-speed chaotic receiver with up to 32 Gb/s messages hidden in a wideband chaotic optical carrier has been experimentally demonstrated over a 20 km fiber link, showing a significant simplification while still guaranteeing security [59]. These promising potentials prove that both deep neural networks and deep learning models are effective and viable performance quality enhancements for solving signal detection and signal processing problems in chaotic secure communication systems as well as in high bit rate optical fiber communication systems.

4. Our Solution: DeepChaos+

This section presents DeepChaos+, a framework designed to enhance the performance of high-speed DP-16QAM optical fiber communication systems. We first provide an overview of the framework and then introduce its end-to-end learning objective.

4.1. Overview Process of DeepChaos+

Let us define E ( X ˜ ) as the set of incorrect predictions (error bits) made by the model F θ given the true label X (transmitted bits). In our system, we employ the bit error rate (BER) metric, similar to the approach proposed by Dao et al. [60], defined as follows:
B ( X ˜ , X ) = | E ( X ˜ ) | | X | .
Generating a large dataset X to train the model F θ is time-consuming, and balancing the training X t r a i n ∈ X and testing sets X t e s t ∈ X ∖ X t r a i n is challenging. Too much training data may cause overfitting, while too little can lead to underfitting, both increasing the BER B ( X ˜ , X ) .
DeepChaos+ (as depicted in Figure 2) combines a Variational Autoencoder (VAE) F θ and a lightweight Informer Network f s t u d e n t ω to optimize communication system performance while using limited original signal data X t r a i n . The VAE is first trained on X t r a i n to generate synthetic data X g , which is combined with X t r a i n to form an augmented dataset D . This process continues iteratively, refining the VAE until it can minimize the BER on X t e s t . Optionally, chaos can be added to X g to better represent original signal characteristics.
In parallel, the Informer Network f s t u d e n t ω is trained using the augmented dataset D , with fewer parameters than the VAE’s decoder but with similar functionality. Knowledge Distillation is used to transfer knowledge from the VAE to f s t u d e n t ω by training it to mimic the output of the VAE’s decoder, enabling it to achieve comparable performance while enabling faster inference.

4.2. End-to-End Learning Objective

Mathematically, we further decompose the Variational Autoencoder (VAE) model F θ into two models: the encoder denoted as G ψ and the decoder denoted as M ϕ . Formally, we have:
F θ = G ψ ∘ M ϕ ,
X t r a i n = F θ ( X t r a i n ) = M ϕ G ψ ( X t r a i n ) = M ϕ ( Z ) .
The encoder G ψ maps X t r a i n to a latent space Z , and the decoder M ϕ reconstructs X t r a i n from Z . The VAE assumes a latent variable Z ∈ R 1 × v , with v as the latent space dimension. This latent variable captures the features of the original signal and follows a latent distribution p ϕ ( Z ) . The complete generative process can be described by:
p ϕ ( Z ∣ X ) = p ϕ ( X ∣ Z ) p ϕ ( Z ) p ϕ ( X ) .
To approximate the intractable posterior distribution p ϕ ( Z ∣ X ) , the model G p s i learns a simpler distribution q ψ ( Z ∣ X ) . The objective is to have p ϕ ( Z ∣ X ) ≈ q ψ ( Z ∣ X ) , which is achieved by minimizing the KL divergence D K L ( q ψ ∥ p ϕ ) . This is equivalent to maximizing the evidence lower bound objective (ELBO):
L ELBO = E q ψ log p ϕ ( X ∣ Z ) − E q ψ log q ψ ( Z ∣ X ) p ϕ ( Z ) .
The ELBO includes the expected reconstruction error log p ϕ ( X ∣ Z ) learned by the decoder model. The DeepChaos+ framework introduces a student model f ω student trained on augmented data D generated by the VAE (teacher model). The student model is trained using a mean squared error (MSE) loss, defined as:
L MSE = 1 N ∑ i = 1 N X ˜ ( i ) − X ^ ζ ( i ) 2 2 ,
where N is the number of samples in the dataset D . The overall objective function for training the student model combines the ELBO loss and the MSE loss:
L total = λ L ELBO + ( 1 − λ ) . L MSE
Here, λ is a hyperparameter that balances the trade-off between the ELBO and MSE losses. By optimizing this combined loss function, DeepChaos+ effectively learns from the synthetic data, enhancing the student model’s ability to predict the original signals. This approach addresses the challenge of limited original signal data by generating synthetic data that capture the essential features of the original signals, leading to more accurate predictions by the student model.

5. Experiment

In this section, we present a comprehensive evaluation of the performance of our proposed DeepChaos+ framework in removing chaos from simulated original signals in long-haul WDM optical communication systems utilizing the DP-16QAM modulation scheme. We conduct experiments under various settings to assess the effectiveness of DeepChaos+. We begin by describing the experiment setup, which includes the selection of hyperparameters, dataset description, and comparison methods. Hyperparameters such as the learning rate, batch size, and network architecture are carefully chosen to ensure the optimal performance of DeepChaos+. Additionally, we compare the performance of DeepChaos+ with traditional methods to establish its superiority.

5.1. Experiment Setup

Our objective is to evaluate the bit error rate (BER), as defined in Equation (6), and the time efficiency of DeepChaos+. Regarding BER, we aim to demonstrate that DeepChaos+ achieves competitive performance even with a limited amount of training data. To accomplish this, we divided the dataset X into different proportions for training and testing: 20%, 40%, 60%, and 80%. For the second term, we analyze the training time and inference time of DeepChaos+ and compare it with other machine learning-based methods.
Hardware Configuration. In order to run our framework efficiently, the following hardware requirements should be met. A GPU is recommended for faster training and inference, with a minimum of an NVIDIA GTX 1060 (6GB VRAM), though more powerful options like the NVIDIA RTX 3090 or A100 are ideal for larger datasets. A minimum of 8GB of RAM is required, but 16GB or more is recommended for on larger datasets. Additionally, a multi-core CPU (quad-core or higher) is beneficial for data preprocessing and managing overall system performance. Our experiments is run on a system equipped with Intel Core i7 Processor, a NVIDIA GTX 4090i (24GB VRAM) and 64GB of RAM.
Comparison Methods And Metrics. We compare DeepChaos+ with several comparison methods, including BiLSTM [61], Informer [62], GRU-D [63], and the chaos-solving module proposed within the system. For convenience, we denote the chaos-solving module in our system as TDiS. These machine learning-based methods were chosen as they represent state-of-the-art approaches in the field of time series analysis and chaos-based modeling. The comparison is based on two metrics: bit error rate and inference time (in seconds).
Dataset. The dataset used in our experiment was collected by simulating the COC (chaos on carrier) and CFOC (chaos frequency on carrier) channels in a long-haul WDM (wavelength division multiplexing) optical communication system using the DP-16QAM modulation scheme. We generated a sequence of 1,000,000 bits and passed them through the communication system. At the transmitter side, the generated sequence was combined with chaos, resulting in a chaotic-modulated signal. At the receiver side, the received signal was subjected to noise removal, resulting in a de-noised signal. It is important to note that this de-noised signal is used to evaluate the performance of the proposed TDiS (chaos-solving module) method.
Hyperparameter Settings. The detailed hyperparameters used for training the model are provided in Table 1. As mentioned earlier, we employ a Knowledge Distillation technique to reduce the model size while preserving accuracy for faster inference. The student model, which is obtained through Knowledge Distillation, is partitioned into different sizes: tiny, with a total of 240,712 parameters; small, with 461,283 parameters; medium, with 920,784 parameters; and large, with 1,911,365 parameters. These variations in model size allow us to evaluate the trade-off between model complexity and performance, enabling us to select the most suitable configuration based on our specific requirements. The learning rates for the VAE (0.0003) and student (0.001) models ensure stable convergence, and the Adam optimizer is selected for its adaptive learning rate benefits. A total of 8 epochs per update and an update time step of 600 allow the model to learn effectively over time, while the mini-batch size of 128 balances speed and memory efficiency. The aggregation model uses the Informer, incorporating attention and convolution for capturing long-range dependencies, and ELU is chosen as the activation function for the VAE to prevent vanishing gradients. The VAE–student coefficient λ is set to 0.6 for optimal knowledge transfer, and a gradient norm of 0.5 prevents gradient explosion during training.

5.2. Training Efficiency Analysis

In Figure 3 (left), it is evident that DeepChaos+ (medium size) achieves fast convergence to a BER of approximately 2 × 10 − 5 in X t e s t . However, the other learning models, such as GRU-D and BiLSTM, also exhibit fast convergence, but the only reach a BER of around 2 × 10 − 3 . Despite utilizing 60% of the original signal set X and having larger model sizes compared to DeepChaos+, they do not attain the same level of accuracy. This highlights the superiority of DeepChaos+ in effectively capturing the underlying patterns and optimizing the BER, even with a smaller proportion of training data. The key factor behind this phenomenon is the ability of DeepChaos+ to generate additional data variants that effectively represent the original data using only 60% of the original data. It selectively learns from the best-performing generated data, resulting in the lowest BER for the X t e s t set. Over time, DeepChaos+ autonomously generates data that accurately capture the underlying features of the remaining 40% of the data, further enhancing its performance and ultimately achieving the lowest BER among the three methods.
On the other hand, in Figure 3 (right), an interesting observation is made when experimenting with different sizes of the student model for the remaining 40% subset. It is noted that DeepChaos+ did not converge to 100% accuracy on the test set with the tiny and small sizes. This suggests that these smaller-sized models would have a higher bit error rate (BER). However, starting from the medium-sized model and above, DeepChaos+ achieved nearly 100% fit with a recorded BER of 2.3 × 10 − 4 . This observation emphasizes the significance of model size in attaining higher accuracy. Larger-sized models, such as medium and above, possess the ability to effectively capture and represent the underlying dynamics of the data, leading to better convergence and lower BER. Additionally, it is worth noting the training time (red line in the figure), which significantly increases with each model size. In our experiments, the medium-sized student model proved to be the most suitable choice, as it offered a balance between fast training time and achieving accuracy comparable to the large-sized model.

5.3. Inference Efficiency Analysis

We have implemented a prediction model using batch processing with a batch size of 128 data points at a time. This ensures that the model predicts 128 data points in parallel, thereby increasing the prediction speed. It is important to note that setting the batch size hyperparameter depends on the GPU configuration. Note that if we use a dataset consisting of 20% of the original sampling signal for training, the remaining 80% of the data points need to be predicted. The more data we use for training, the fewer test points we have for prediction. The total time required for predicting the entire dataset can be calculated by multiplying the batch size by the number of batches. Since the model predicts 128 data points simultaneously (due to the batch size of 128), the model only needs to predict a certain number of batches. The overall prediction time of the model is then divided by the total number of data points to obtain the average prediction time per data point. By organizing and optimizing the prediction process in batches, we can leverage parallel processing and enhance the prediction speed, especially when dealing with large datasets [64].
Based on Table 2, we can analyze the effectiveness of DeepChaos+ compared to other methods. Note that DeepChaos + t i n y , DeepChaos + s m a l l , DeepChaos + m e d i u m , and DeepChaos + l a r g e are referred to as student models in this context. Looking at the runtime performance, both BiLSTM and GRU-D exhibit increasing runtime values as the percentage of the original data increases. However, the DeepChaos+ models consistently show significantly lower runtimes across different data percentages. Even the largest student model, DeepChaos + l a r g e , has remarkably lower runtimes compared to BiLSTM and GRU-D. As the model size increases from tiny to small, medium, and large, the DeepChaos+ models have slower execution times as the number of parameters increases.

5.4. Quantitative Analysis

We compared the effectiveness of DeepChaos+ on test sets of 20%, 40%, 60%, and 80%, as shown in Figure 4 (left). For all test sets, DeepChaos+ was able to generate data and learn until achieving near 100% accuracy on the 40%, 60%, and 80% sets. However, on the 20% set, the model only achieved about 84% accuracy due to the initial lack of data, which was insufficient for effective inference and generation of samples. The remaining competing methods showed significantly lower effectiveness, as they could not infer features like DeepChaos+, especially on the 40% dataset, where DeepChaos+ achieved an accuracy of nearly 95%. Methods like BiLSTM only reached around 67%, and GRU-D reached 72%. The traditional approach also achieved accuracy similar to that of DeepChaos+ across all four datasets. However, when it comes to BER (discussed in the following section), this method yields a lower performance compared to DeepChaos+.
Regarding the BER of the test sets (Figure 4, right), we only show the results for the 60% and 80% sets since DeepChaos+ has not yet reached 100% accuracy on the other two sets, resulting in higher BER. DeepChaos+ clearly has the best performance, as seen in the 60% set where its BER falls within the range of 2.3 × 10 − 4 . The remaining methods have BER ranging from approximately 1.9 × 10 − 3 to 3 × 10 − 3 . For the 80% set, DeepChaos+ demonstrates superior performance, with a BER of around 1.5 × 10 − 4 . This can be explained by the fact that, as DeepChaos+ has more datasets, the interpolation for generating data becomes more accurate. However, when reaching a certain threshold, the other methods also start to generalize and narrow the gap slightly compared to DeepChaos+.

5.5. Discussion

While the experimental results presented effectively demonstrate the prowess of the DeepChaos+ framework in reducing the bit error rate in WDM optical fiber communication systems, it is important to acknowledge the limitations associated with the use of simulated datasets. The simulated environment, although carefully designed to mimic real-world conditions, may not fully capture the inherent complexities of actual optical communication systems. To address this limitation, future research should focus on validating the DeepChaos+ framework using actual experimental data obtained from real-world optical communication systems. This approach will assess the robustness and generalizability of our model under more complicated conditions. Additionally, incorporating real-world data will provide deeper insights into the practical applications of DeepChaos+ for reliably improving the performance of optical fiber communication systems, ensuring that the proposed solutions can be effectively implemented in practical, large-scale deployments.

6. Conclusions

In this study, we addressed the challenge of removing chaos in long-haul WDM optical communication systems utilizing the DP-16QAM modulation scheme. DeepChaos+ introduced two key components to enhance the performance of chaos removal. Through extensive experiments, we demonstrated the effectiveness of DeepChaos+ in accurately reconstructing the original signal with a significantly reduced bit error rate. The achieved bit error rate of approximately 10 − 5 highlighted the superiority of DeepChaos+ compared to traditional methods. Additionally, DeepChaos+ exhibited high efficiency in terms of processing time, enabling fast signal reconstruction. By enhancing the reliability and efficiency of chaotic secure channels in optical fiber communication systems, DeepChaos+ has the potential to significantly improve data transmission in high-speed networks.

Author Contributions

Conceptualization, D.A.V., Q.X.N. and D.C.T.; methodology, D.A.V., D.C.T. and N.K.H.D.; data collection, H.N.T.N., T.T.T.T. and D.A.V.; software, T.T.T.T., H.N.T.N., H.M.D. and N.K.H.D.; validation, D.A.V., T.T.T.T., N.K.H.D., Q.X.N. and D.C.T.; formal analysis, H.N.T.N., H.M.D. and N.K.H.D.; investigation, D.A.V., T.T.T.T., H.N.T.N. and H.M.D.; resources, D.C.T. and Q.X.N.; data curation, T.T.T.T., N.K.H.D., H.N.T.N. and H.M.D.; writing—original draft preparation, D.A.V., T.T.T.T., H.M.D. and H.N.T.N.; writing—review and editing, H.M.D., H.N.T.N. and D.C.T.; visualization, T.T.T.T. and H.N.T.N.; supervision, D.C.T. and Q.X.N.; project administration, D.C.T.; funding acquisition, D.A.V. and D.C.T. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Statement

The simulation dataset used in our experiments is publicly available at: https://drive.google.com/drive/folders/1PwM4Z79csBFITiqdQcsq_gdbEwMzloxd.

Conflicts of Interest

The authors declare no conflicts of interest.

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Photonics 11 00967 g001
Figure 1. Conceptual Conceptional diagram of the COC and CFOC channels in the long-haul WDM optical communication system using the D P − 16 Q A M modulation scheme.
Figure 1. Conceptual Conceptional diagram of the COC and CFOC channels in the long-haul WDM optical communication system using the D P − 16 Q A M modulation scheme.
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Figure 2. Overview of the DeepChaos+ framework. The framework introduces two key models: the Variational Autoencoder (VAE) and the lightweight Informer Network. The VAE is trained to generate interpolated data from the set X . The generated data are then combined with the dataset D and used to iteratively retrain the VAE. The lightweight Informer Network, with fewer parameters but functionality equivalent to the VAE’s decoder, is trained to predict a set X ˜ that minimizes the bit error rate B ( X ˜ , X ) . Knowledge Distillation is employed to ensure the Informer achieves similar performance to the decoder while enabling faster inference time.
Figure 2. Overview of the DeepChaos+ framework. The framework introduces two key models: the Variational Autoencoder (VAE) and the lightweight Informer Network. The VAE is trained to generate interpolated data from the set X . The generated data are then combined with the dataset D and used to iteratively retrain the VAE. The lightweight Informer Network, with fewer parameters but functionality equivalent to the VAE’s decoder, is trained to predict a set X ˜ that minimizes the bit error rate B ( X ˜ , X ) . Knowledge Distillation is employed to ensure the Informer achieves similar performance to the decoder while enabling faster inference time.
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Figure 3. The training performance of DeepChaos+ in the 60% dataset is shown in the left figure, while the learning performance of the student model is depicted for different sizes in the right figure. The red line in the right figure represents the training time, indicating that, as the size of the student model increases, the training time also lengthens.
Figure 3. The training performance of DeepChaos+ in the 60% dataset is shown in the left figure, while the learning performance of the student model is depicted for different sizes in the right figure. The red line in the right figure represents the training time, indicating that, as the size of the student model increases, the training time also lengthens.
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Figure 4. The figure on the left illustrates the performance of DeepChaos+ on the testing set of training datasets of 20%, 40%, 60%, and 80%. The figure on the right displays the BER (bit error rate) of DeepChaos compared to the other methods, particularly on the 60% and 80% datasets.
Figure 4. The figure on the left illustrates the performance of DeepChaos+ on the testing set of training datasets of 20%, 40%, 60%, and 80%. The figure on the right displays the BER (bit error rate) of DeepChaos compared to the other methods, particularly on the 60% and 80% datasets.
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Table 1. Hyperparameters for the DeepChaos+ framework include the VAE model, the student model, and the Informer Aggregation model.
Table 1. Hyperparameters for the DeepChaos+ framework include the VAE model, the student model, and the Informer Aggregation model.
HyperparameterValue
Learning rate for the VAE model0.0003
Learning rate for the student model0.001
Optimizer Adam [47]
Total epochs per update8
Update time step600
Mini-batch size128
Aggregation model for VAE and student modelsInformer (Attention and Convolution)
Activation function for the VAE modelELU
VAE–student coefficient λ 0.6
Gradient norm0.5
Table 2. Comparing the inference time of DeepChaos+ with other state-of-the-art (SOTA) models across different training set and testing set ratios of 20%, 40%, 60%, and 80% for training.
Table 2. Comparing the inference time of DeepChaos+ with other state-of-the-art (SOTA) models across different training set and testing set ratios of 20%, 40%, 60%, and 80% for training.
Model20%40%60%80%Each Data Point (Average)
BiLSTM 3.2984 s 2.4752 s 1.5684 s 0.6956 s 0.0054 s
GRU-D 5.6874 s 3.315 s 2.1064 s 1.1896 s 0.0092 s
DeepChaos + t i n y 0.051 s 0.03388 s 0.02464 s 0.01248 s 0.00007 s
DeepChaos + s m a l l 0.102 s 0.06776 s 0.04928 s 0.02496 s 0.00016 s
DeepChaos + m e d i u m 0.153 s 0.10164 s 0.07392 s 0.03744 s 0.00025 s
DeepChaos + l a r g e 0.204 s 0.13552 s 0.09856 s 0.04992 s 0.00034 s
DeepChaos+ 2.5764 s 1.0248 s 0.5596 s 0.2804 s 0.0021 s
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MDPI and ACS Style

Vu, D.A.; Do, N.K.H.; Nguyen, H.N.T.; Dam, H.M.; Tran, T.T.T.; Nguyen, Q.X.; Truong, D.C. DeepChaos+: Signal Detection Quality Enhancement of High-Speed DP-16QAM Optical Fiber Communication Based on Chaos Masking Technique with Deep Generative Models. Photonics 2024, 11, 967. https://doi.org/10.3390/photonics11100967

AMA Style

Vu DA, Do NKH, Nguyen HNT, Dam HM, Tran TTT, Nguyen QX, Truong DC. DeepChaos+: Signal Detection Quality Enhancement of High-Speed DP-16QAM Optical Fiber Communication Based on Chaos Masking Technique with Deep Generative Models. Photonics. 2024; 11(10):967. https://doi.org/10.3390/photonics11100967

Chicago/Turabian Style

Vu, Dao Anh, Nguyen Khoi Hoang Do, Huyen Ngoc Thi Nguyen, Hieu Minh Dam, Thuy Thanh Thi Tran, Quyen Xuan Nguyen, and Dung Cao Truong. 2024. "DeepChaos+: Signal Detection Quality Enhancement of High-Speed DP-16QAM Optical Fiber Communication Based on Chaos Masking Technique with Deep Generative Models" Photonics 11, no. 10: 967. https://doi.org/10.3390/photonics11100967

APA Style

Vu, D. A., Do, N. K. H., Nguyen, H. N. T., Dam, H. M., Tran, T. T. T., Nguyen, Q. X., & Truong, D. C. (2024). DeepChaos+: Signal Detection Quality Enhancement of High-Speed DP-16QAM Optical Fiber Communication Based on Chaos Masking Technique with Deep Generative Models. Photonics, 11(10), 967. https://doi.org/10.3390/photonics11100967

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