Concealed communication system based on generative diffusion model

Abstract

The invention discloses a covert communication system based on a generative diffusion model, and belongs to the technical field of covert communication. In order to solve the problems of insufficient concealment and poor anti-noise performance in the prior art, hidden transmission and reliable recovery of information are realized by constructing a diffusion generation and classification discrimination module. The sending end carries out noise addition and shaping on the original bit waveform by using a forward diffusion process to form a noise-like hidden signal; and a receiving end recovers a signal structure through a reverse denoising process, and accurately judges bit information through a classifier. According to the method, a Gaussian approximation hidden waveform library is constructed by adopting a signal pair training model which is consistent in statistics but distinguishable in structure, and random sampling mapping and boundary smooth splicing are combined, so that transmission signals are difficult to distinguish from noise in a frequency domain and a feature space; therefore, the avoidance capability, the anti-interference robustness and the information recovery accuracy under the low signal-to-noise ratio of the detection means are remarkably improved.

Description

Technical Field

[0001] This invention relates to covert communication technology, and particularly to covert communication technology based on a generative diffusion model. Background Technology

[0002] Existing covert communication technologies aim to embed information into publicly available carrier signals for transmission without the knowledge of unauthorized parties. These technologies are diverse, primarily including steganography, which utilizes carrier signal redundancy to hide information, and spread spectrum communication, which disperses information energy by broadening the signal spectrum or altering the signal's time-frequency characteristics. In recent years, the development of deep learning technology has provided a new paradigm for covert communication. For example, the TripartiteGAN (Generative Adversarial Network) optimizes the amplitude and phase of the covert signal through a generator, making its distribution approximate pure noise when superimposed with the legitimate signal. Generative text steganography methods, based on Variational Autoencoders (VAEs), embed secret information into the latent feature space of an image, achieving peak signal-to-noise ratio (PSNR) indistinguishable from the natural image through distribution alignment. These studies demonstrate that models such as Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs) have been used to construct carrier signals with controllable statistical properties and achieve covert information transmission through implicit encoding during the generation process.

[0003] Current covert communication technologies generally face several key shortcomings, especially in complex channel environments and high-impact application scenarios. First, the covert signals generated by existing methods often contain detectable traces in their statistical characteristics or structure. Whether it's traditional spread spectrum techniques based on fixed codebooks or steganography that modifies the carrier signal, the embedded information signal, after sophisticated spectral analysis, energy detection, or machine learning-based feature analysis, may reveal differences from the pure carrier signal, leading to a failure of covertness. Second, these technologies generally lack robustness against channel noise interference. In low signal-to-noise ratio environments, noise severely disrupts the structure of the embedded information, making it difficult for the receiver to accurately recover the information from the noisy background, resulting in a rapid increase in the bit error rate. Furthermore, existing covert communication methods based on generative models also have limitations; the generated signals may be sensitive to channel disturbances, and their generation process typically does not explicitly model the impact of noise on the signal, making it difficult to stably recover information in noisy environments. Therefore, existing covert communication technologies face significant bottlenecks in balancing high covertness and noise robustness, making it difficult to meet the requirements for reliable covert communication in environments with high interference and high detection risk. Summary of the Invention

[0004] The technical problem to be solved by this invention is to address the issue that existing covert communication has weak anti-interference ability and is easily detected in noisy channels. The invention proposes a covert communication scheme that constructs a forward diffusion and reverse denoising process to enable communication information to be carried by the generated and constructed covert waveform and to recover the information in a noisy environment.

[0005] The technical solution adopted by this invention to solve the above-mentioned technical problems is a covert communication system based on a generative diffusion model, comprising:

[0006] The transmitting end's diffusion generation module maps the communication bitstream to be transmitted into a hidden signal waveform with noise-like characteristics and transmits it. The receiving end's classification and discrimination module performs inverse diffusion denoising on the received signal and restores the original communication bitstream. The diffusion generation module's operation includes: constructing two pairs of original signals that are consistent in key statistics but distinguishable in structural features, and labeling them as bits 0 and 1 respectively; performing a forward diffusion process on the two pairs of original signals using a diffusion model to generate a hidden waveform library corresponding to each bit, with statistical characteristics approximating a Gaussian distribution but retaining distinguishable structural differences; randomly selecting waveform segments from the corresponding waveform library according to the bitstream to be transmitted, mapping them, and forming the transmitted signal after splicing and boundary smoothing. The classification and discrimination module's operation includes: slicing the received noisy signal into fixed-length slices, performing an inverse diffusion process on each slice to restore the signal structure, and then using a trained classifier to make bit decisions, ultimately restoring the bitstream.

[0007] Accordingly, a covert communication method based on a generative diffusion model is proposed and applied to the above system, including the following steps:

[0008] Sending steps:

[0009] S1. Construct and train the diffusion model: Generate two statistically consistent and structurally distinguishable pairs of original signals as training sets, and train the diffusion model to learn its forward diffusion and reverse denoising processes;

[0010] S2. Construct a hidden waveform library: Using the trained diffusion model, perform forward diffusion sampling on the two types of original signals respectively to generate a hidden waveform library corresponding to bits 0 and 1;

[0011] S3. Generate and send covert signals: Based on the bit stream to be transmitted, randomly select waveform segments from the corresponding waveform library, splice and smooth the boundaries, and then send them through the channel;

[0012] Receiving end steps:

[0013] S4. Receive and slice: Receive signals that have been disturbed by the channel and slice them into fixed lengths;

[0014] S5. Denoising and Decision: Perform a reverse diffusion process on each slice to recover the signal, then input it into the classifier for bit decision to restore the original bit stream.

[0015] This invention fully utilizes the advantages of diffusion models in Gaussian perturbation modeling and probability distribution reconstruction to achieve covert information transmission, accurate recovery, and enhanced communication security.

[0016] The system consists of a diffusion generation module at the transmitting end and a classification and discrimination module at the receiving end, responsible for the concealed representation and accurate reconstruction of communication bits, respectively. At the transmitting end, the original bit-carrying waveform is shaped by adding noise through a forward diffusion process to generate a signal with noise-like characteristics as the transmission carrier, thereby achieving concealment of the communication process. The receiving end uses a unified denoising receiver, and achieves signal reconstruction and information discrimination through a reverse denoising process, forming a communication mechanism centered on signal reconstruction and information discrimination.

[0017] The core of covert communication lies in using signals with statistical consistency and structural distinctiveness to train a diffusion network, constructing a library of covert waveforms in intermediate diffusion states, and achieving bit-level information mapping and highly covert encoding. The core generation and denoising network of the diffusion model adopts a lightweight temporal signal processing architecture, possesses symmetrical feature encoding-decoding capabilities, and retains key structural information at multiple scales through cross-scale feature fusion mechanisms (such as skip connections) to balance the dual requirements of "noise prediction accuracy" and "resource-constrained deployment" in covert communication scenarios.

[0018] By modeling and selecting samples at the distribution level using a diffusion model, the system can carry communication information with the constructed concealed waveform and achieve accurate recovery in an interference environment, thereby significantly improving communication concealment, noise robustness, information recovery accuracy, and system deployability.

[0019] Specifically, regarding communication concealment, this invention constructs a concealed waveform library with Gaussian approximation characteristics by using structurally different but statistically indistinguishable signal pairs as basic data and combining them with a forward diffusion process under an improved cosine scheduling strategy. Simulations show that the generated concealed waveforms highly overlap with the power spectral density of standard white noise in the frequency domain and are difficult to distinguish from real Gaussian noise samples in the t-SNE feature embedding space, thus significantly enhancing the ability to evade traditional detection methods such as spectrum analysis and energy detection.

[0020] The beneficial effects of this invention are that, through the accurate modeling of signal distribution and noise adaptation capabilities of the diffusion model, the system possesses anti-interference robustness and signal undetectability, effectively solving the core problem in the field of covert communication where it is difficult to balance the concealment of information transmission with noise resistance reliability. Attached Figure Description

[0021] Figure 1 For application scenarios;

[0022] Figure 2 This refers to the model architecture content;

[0023] Figure 3 This is a schematic diagram of the forward perturbation in the diffusion model;

[0024] Figure 4 A library of hidden waveforms in the intermediate state of diffusion. Construct a mechanism diagram;

[0025] Figure 5 A flowchart illustrating the mapping and splicing of information bits to hidden waveform segments;

[0026] Figure 6 This is a flowchart of bit reconstruction based on diffusion denoising and classification.

[0027] Figure 7 The time-domain difference of the inverted signal and its power spectral density are compared with random noise;

[0028] Figure 8 The t-SNE feature space embedding distribution map;

[0029] Figure 9 The system bit error rate under different SNR conditions. Detailed Implementation

[0030] This invention proposes a covert communication system based on a generative diffusion model, with application scenarios such as... Figure 1 As shown. Communication parties A and B, to bypass eavesdropping, achieve covert communication through waveform mapping and diffusion / de-diffusion. The sending end (communication party A) first prepares a basic waveform library (storing characteristic waveforms corresponding to "0" and "1") and a covert waveform library (used to hide the signal); the bits to be transmitted (such as "110…010") are mapped to a mixed signal of the corresponding waveform through diffusion shaping. Figure 1 (The yellow / blue waveform segments correspond to "1" and "0" respectively). The mixed signal is transmitted in the channel, simultaneously superimposed with signals from the hidden waveform library, making the overall signal appear as noise (reducing the probability of being detected by the eavesdropping party). The receiving end (communicating party B) performs inverse diffusion denoising on the received noise-like signal: first, it is segmented into groups, then the original waveform segments are restored through a classifier, and finally, "110…010" is recovered through bit mapping. During the communication between the two parties, the eavesdropping party can only receive the noise signal mixed with the hidden waveform and cannot identify the valid bits within it.

[0031] The core of the communication process is to achieve concealment by using "waveform mapping + diffusion / reverse diffusion": making the valid signal disguised as noise, so that only the legitimate communicator can recover the information.

[0032] The overall communication process of the system is as follows: Figure 2 As shown, the main stages include the construction of the original waveform carrier and dataset, the generation of the hidden waveform, bit mapping and waveform construction, signal reception and segmentation, as well as the inverse denoising and classification stages. Each stage will be described in detail below.

[0033] (I) Construction stage of original waveform carrier and dataset:

[0034] The process of constructing the original dataset used to train the diffusion model focuses on building labeled data with structural boundary features through signal pairs, so that the model can learn effective structural mappings during the diffusion and denoising process.

[0035] 1. Rules for generating original waveform carriers

[0036] Let the original signal pair be , where a single signal , The length of the signal segment. Representing the real number domain, both types of signals are generated through randomization: they can be generated based on random sampling from Gaussian or uniform distributions, or constructed using regular functions (such as periodic functions or random amplitude modulation functions) combined with random parameters. This ensures that the time-domain waveform and amplitude variations of each type of signal are random, and that there are no fixed correlation constraints between the two types of signals during generation; they only need to meet the core condition of statistical consistency—that is... and Maintaining consistency in key statistical quantities such as energy, mean, and frequency distribution is crucial for constructing a statistically indistinguishable input distribution that meets the requirements of covert communication for pseudo-randomness of carrier signals.

[0037] 2. Signal-to-structure differentiation design logic

[0038] To ensure that the two randomly generated signals possess structural differences that can be learned by the model, it is necessary to... and The structural features are designed to be distinctive, with the core objective of providing support for subsequent bit tag mapping and classification by differentiating the structural dimensions while maintaining consistent statistical properties. The structural distinctiveness design can be implemented flexibly, such as using strategies based on signal phase reversal, symbol flipping, and local timing reconstruction, to ensure that there are clear and stable differences in the structural features of the two types of signals in the time or frequency domains, and that these differences can be captured and learned by the diffusion model.

[0039] For a given pair of signal sequences, assign bit tags to it. :

[0040] ;

[0041] The dataset size can be set according to the actual communication bit rate, for example, 5000 groups are generated for each class, for a total of 10000 sample pairs.

[0042] (II) Diffusion Modeling and Hidden Waveform Generation Stage

[0043] This stage is the core of the system, and its goal is to construct a generative diffusion process that can converge stably and has high structural discriminativeness, thereby forming waveform segments that can be used for covert communication.

[0044] 1. Forward Diffusion Modeling Process

[0045] The forward process of the diffusion model is based on a Markov chain with added Gaussian noise, and its mathematical model is as follows:

[0046] Given the original signal The forward diffusion process gradually adds noise to it. Its recursive relation is:

[0047] ;

[0048] in, For from the first The generation signal of the step to the first The probability of generating a signal in a step. It follows a Gaussian distribution. middle Let be a Gaussian distributed random variable. The mean of a Gaussian distribution is given. Let V be the variance of the Gaussian distribution. It is the identity matrix. It is the first To control the noise intensity of a step, a linear or cosine scheduling strategy is typically employed.

[0049] Through accumulation, it can be and The relationship is displayed as follows:

[0050] ;

[0051] in, , . For the front The cumulative product of step noise figures, For the first The scaling factor of the step. The value ranges from 1 to .

[0052] like Figure 3 As shown, the noise data generated at each step still has a linear correlation with the original data, thus ensuring that the intermediate state is recoverable.

[0053] 2. Noise Dispatch Strategy Design

[0054] This invention employs an improved cosine scheduling strategy, following the definition proposed by the Improved-DDPM denoising diffusion probability model. For diffusion time steps, It is a very small offset constant, used to prevent Noise intensity when =0 Too small:

[0055] ;

[0056] in, This is a truncation function used to truncate the target function. Numerical range constraints will be applied; inputs exceeding the specified range will be assigned the minimum value. Or the maximum value is 0.999, where It is a very small positive number. This is an improved cosine annealing scheduling function. Compared to linear scheduling, this strategy results in a smoother diffusion process, better preserves the classifiable structure of the generated intermediate waveforms, and enhances discriminative learning.

[0057] 3. Hidden Waveform Sampling and Library Construction

[0058] By analyzing each type of raw signal , Apply randomly initialized noise and execute. Step forward diffusion, generating at time step Multiple sets of diffusion intermediate state samples. Samples were taken separately for each class. Subsequently, the following hidden waveform library was constructed. and :

[0059] ;

[0060] in, Indicates the original signal Apply randomly initialized noise and execute. The first step forward diffusion obtained Secondary sampling.

[0061] based on Hidden waveform library The construction process is as follows Figure 4 As shown, the statistical characteristics of the data in the waveform library approximate a Gaussian distribution, but exhibit weak but learnable structural differences in the time domain, which form the basis for subsequent bit embedding and discriminative classification.

[0062] 4. Structural Preservation Assessment

[0063] Define each class mean between samples With covariance matrix for:

[0064] ;

[0065] Among them, category number Or 1, This indicates transpose.

[0066] The separability of its distribution was analyzed using a combination of KL divergence and Mahalanobis distance:

[0067]

[0068] ;

[0069] and All 2D multivariate Gaussian distribution , , for arrive Regarding the covariance matrix The square of the Mahalanobis distance, Let be the order of the covariance matrix. To find the trace of the matrix, It is the inverse of the matrix.

[0070] The core objective of structural retention assessment is to determine two types of signals after diffusion: Corresponding bit 0, For bit 1, we need to determine whether they possess both statistical concealment and retain classifiable structural differences. Therefore, we need to determine the threshold range around this contradictory balance.

[0071] The lower threshold can be determined in conjunction with the performance verification of the classifier: for example, by calculating the KL divergence and Mahalanobis distance using samples from the training or validation set, find the distance value corresponding to when the classifier accuracy first stably reaches the target value (such as 90%), and set it as the lower threshold.

[0072] The upper limit of the threshold needs to be determined in conjunction with the concealment verification index. The upper limit of the threshold can be set by calculating the fluctuation range of the KL divergence / Mahanobis distance of white noise in the public channel.

[0073] (III) Bit mapping mechanism and continuous waveform construction stage

[0074] This stage aims to stably map any bitstream into a sequence of diffused samples, achieving a transmission waveform that is approximately continuous in form and statistically hidden. The mapping and splicing process is as follows: Figure 5 As shown:

[0075] 1. Bit mapping mechanism

[0076] Suppose the bit stream to be transmitted for:

[0077] ;

[0078] in, For the i-th bit, the bit stream Total 1 bit;

[0079] Definition of the first Mapping function for each sample segment :

[0080] ;

[0081] in, For sampling index, To ensure uniform distribution, Indicates from 1 to One integer is randomly selected with equal probability from the set of integers; that is, for each bit... Randomly sample one from its corresponding waveform library This strategy prevents fixed mappings from exposing patterns.

[0082] 2. Stitching strategy and boundary smoothing

[0083] Will The sampled segments are spliced ​​together in sequence. :

[0084] ;

[0085] The entire sequence after splicing have The elements are denoted as To prevent abrupt changes at the splicing boundary from causing detection or spectral leakage, an overlapping window fusion mechanism is introduced to update the previous... The values ​​of the elements:

[0086] ;

[0087] in It is the fusion coefficient, the spliced ​​sequence after boundary fusion. It can guarantee stability and detection avoidance capabilities.

[0088] 3. Modulation intensity control and power spectrum optimization

[0089] To enhance concealment, control the spliced ​​waveform. Its power spectrum approximates a white noise distribution, i.e., in the target frequency band. Internally maintained power spectral density Approximately a constant , .

[0090] If certain frequency components are prominent in the actual spectrum, the segment energy can be adjusted or phase perturbation can be added during the splicing process to maintain overall flatness and further enhance the anti-detection capability.

[0091] (iv) Channel disturbance and slice reception stage

[0092] This section describes the disturbance modeling process of the noisy channel and the method for deconstructing the concealed signal at the receiver.

[0093] 1. Channel Model Construction

[0094] Considering a typical additive white Gaussian noise (AWGN) channel, the received signal is modeled. for:

[0095] ;

[0096] Furthermore, theoretically, it can be extended to multipath fading channels like Rayleigh or models with channel equalizers, expanding application scenarios:

[0097] ;

[0098] in This represents the impulse response of a random channel.

[0099] 2. Segmentation and slicing mechanism

[0100] The receiving end uses the pre-set segment length. right Perform slicing, the first slice Represented as:

[0101] ;

[0102] The slicing mechanism requires the waveform structure to have a synchronization flag or fixed timing to ensure that errors do not propagate.

[0103] (V) Reverse diffusion reduction and classification stage

[0104] The reverse diffusion reduction and classification module, such as Figure 6 As shown, the core design of this module is to recover information from a noisy environment and complete bit decoding through a neural network.

[0105] 1. Reverse diffusion process

[0106] Inverse diffusion modeling is a sampling process that gradually denoises the data from a Gaussian distribution to a data distribution, starting from the first... Step-by-step signal generation To the Step-by-step signal generation :

[0107] ;

[0108] in, To predict noise neural networks, To predict noise, the neural network uses the input step number. and the Step-by-step signal generation Output prediction noise, For the first The standard deviation of residual noise in the step; ,Right now It follows a vector with a mean of 0 and a covariance of the identity matrix. The multivariate standard normal distribution; For the front The cumulative product of step noise figures, For the first The scaling factor of the step;

[0109] Here The input slice of the backdiffusion in the corresponding classifier After gradually denoising through a reverse diffusion process, the initial data is finally obtained. (i.e., the result of reverse diffusion reduction of the slice).

[0110] Then, by minimizing the prediction noise and real noise The differences are used to update the model parameters. Objective optimization function Choose from the following:

[0111] ;

[0112] This loss function uses mean squared error as a metric and guides... Learning the patterns of predicting real noise from noisy signals provides gradient guidance for the de-diffusion denoising process. Describing the L2 norm, Expressing expectations, This means taking all possible initial data. All possible diffusion steps All possible real noise All of these factors are taken into account when calculating the expected value.

[0113] 2. Classification and discriminant structure

[0114] Reverse diffusion reduction results Perform bit-based decision-making to obtain the decision result. :

[0115] ;

[0116] in As a classification discriminator, it adopts a temporal feature classification network architecture. Its core function is to extract features and classify the one-dimensional temporal signal after inverse diffusion reconstruction. Figure 6 As shown, the optimization objective is cross-entropy loss. :

[0117] .

[0118] The specific communication method of the present invention includes the following steps:

[0119] Step 1: Construction of a Randomly Distinguished Signal Dataset

[0120] Two sets of one-dimensional time-series signal samples of equal length and with consistent key statistics (energy, mean, frequency distribution, etc.) are generated. They are then subjected to structural differentiation processing to form stable differences that can be captured by the model. The two sets of signals correspond to bit labels 0 and 1, respectively. This type of signal sample pair is generated to form the training set of the diffusion model.

[0121] Step 2: Communication Bit Mapping and Covert Waveform Construction

[0122] Input the two original waveforms mentioned above into the diffusion model and execute... Parallel Step forward diffusion to generate time steps intermediate state sequence and ,in Because noise sampling during the diffusion process is random, the results generated each time are independent of each other, resulting in a large set of sequences with similar distributions but different waveform structures, which are then labeled with bits 0 and 1 respectively.

[0123] The transmitting end randomly selects sequence segments based on bit tags from the information bit stream for mapping. For example, for the bit stream "0101", from... Selected from ,from Selected from This forms a corresponding waveform sequence. , (Indicates the sample index).

[0124] Multiple waveform segments selected by bit mapping are sequentially spliced ​​together and their boundaries are smoothed to form the final transmitted signal: , , , ,… The processed waveform will be transmitted to the receiving end via the channel as a covert communication carrier.

[0125] Step 3: Building the Hidden Waveform Library

[0126] During the construction of the concealed waveform, a sequence set can be synchronously stored and added to the concealed waveform library. This waveform library is statistically close to a Gaussian distribution, but retains enough structural information to recover the tag. It is used for recording concealed waveform carriers, which facilitates subsequent measurement of their concealment, or can be used as a selection library for subsequent bit mapping carriers, improving the processing efficiency of the transmitting end.

[0127] Step 4: Receiver signal slicing

[0128] The receiver receives a continuous signal after channel disturbance. According to the original length of each segment Slice to obtain This is to recover the communication bits corresponding to each segment.

[0129] Step 5: Diffusion Denoising and Decision

[0130] Each noisy segment The input diffusion model is subjected to t-step backsampling to reconstruct the estimated waveform. Then input it into the trained binary classifier. Output category labels This enables bit-level decoding.

[0131] The above communication strategies can achieve bit representation without directly embedding explicit information, and have high concealment, high noise resistance and flexible adaptability.

[0132] The network input is a single-channel one-dimensional waveform sequence. (L is the set sequence fragment length) and diffusion time step (T represents the total number of steps in the diffusion model). The main body of the network includes feature downsampling paths, multi-scale feature fusion layers, and feature upsampling paths, and fuses features of different resolutions through skip connections.

[0133] The diffusion generation module is configured as follows: The model contains 3 scale levels, with the number of channels increasing sequentially. Multiplier expansion, with a base number of 96 channels, corresponding to the number of channels per layer as follows: Each downsampling and upsampling layer contains two residual blocks. The convolutional kernel size is 3. Most convolutions in the main network are configured with kernel_size=3, stride=1, and padding=1 to maintain the signal length. Convolutional modules are used for feature compression in the downsampling path, while upsampling restores the original length through interpolation and convolution, maintaining an overall encoder-decoder symmetric structure. The model uses Group Normalization (32 groups per layer) and the SiLU activation function. The time-step information of the diffusion process is encoded into a high-dimensional vector with a dimension set to the number of basic channels * 4. This vector is then converted into a temporal embedding vector suitable for injection into the residual blocks through a fully connected layer and injected into the residual blocks in a scale-shift mode. Downsampling uses a one-dimensional convolution with stride=2 (conv_resample=True), and upsampling uses nearest-neighbor interpolation combined with convolution. The model outputs two channels to predict the diffusion residuals. With logarithmic variance term It conforms to the structural configuration of IDDPM. The diffusion process controls the amount of noise added at each step. The scheduling strategy uses cosine scheduling, and the diffusion time step is set to 500 steps, which helps to improve the signal recovery stability at high time steps.

[0134] The classifier section is used to recover bit information and adopts a temporal feature classification network architecture to perform bit-level decisions on the signal after de-diffusion reconstruction. The network input is a one-dimensional temporal waveform segment of the de-diffusion output. The front end completes the initial feature encoding through a temporal feature extraction layer. The middle section improves the discriminative power of the features through feature enhancement units (such as residual connection units) and suppresses the impact of noise interference on the classification results. The back end outputs the class probability of the corresponding communication bit (0 or 1) through global feature aggregation (such as global pooling) and fully connected mapping.

[0135] The classification and discrimination module is configured as follows: the front-end convolutional layer is adjusted to accept... The input is a one-dimensional time-series waveform, and the output layer is reconstructed into a fully connected layer that maps to two categories, performing bit-level discrimination. Cross-entropy loss and the Adam optimizer are used during training, with the initial learning rate set to [value missing]. The batch size is 32, and the training rounds are 50. The training data consists of the reconstructed waveforms output by the diffusion model and their corresponding bit labels. This structure can be trained independently or jointly with the diffusion module to achieve covert embedding and high-precision recovery of communication bits.

[0136] The overall system architecture is lightweight, making it suitable for deployment in resource-constrained communication terminals and edge devices. It has good concealment, robustness and scalability, and can be widely used for covert data transmission tasks in secure communication, satellite links and low-power IoT scenarios.

[0137] like Figure 7 As shown, a comparative analysis of the power spectral density (PSD) of the original signal, the inverted signal, and white noise is performed. With the original signal sampling rate set to 1kHz, within the frequency range of 0Hz to 500Hz, the PSD curves of the original signal (blue solid line) and the inverted signal (red dashed line) are highly similar and essentially overlap, indicating statistical consistency in their frequency domain energy distribution. Crucially, the overall trend and main peak / valley positions of the PSD curves of these two signals show high consistency with the standard white noise (green dotted line), and their power values ​​are... to The waveforms fluctuate and intertwine within the dB / Hz range, lacking clearly distinguishable significant energy differences. This strongly demonstrates that the hidden waveform generated by this invention is highly similar to white noise in the frequency domain, making it difficult to be effectively identified by detection methods based on spectral energy characteristics. Simultaneously, the time-domain waveform comparison in the figure intuitively shows the inverse relationship between the original signal (blue solid line) and the inverted signal (red dashed line), exhibiting equal amplitude but opposite signs. This structural difference lays the foundation for subsequent model recovery and discrimination.

[0138] Furthermore, to assess the indistinguishability of signals at the feature space level, the t-SNE (t-distributed random neighborhood embedding) algorithm was employed to reduce the dimensionality of the original signal, its inverse signal, and independent random noise samples (original time-domain data containing small perturbations) to a two-dimensional space for visualization. t-SNE aims to preserve the local similarity structure of data in high-dimensional space; theoretically, if signals are distinguishable, their low-dimensional embeddings should form clusters separated by category.

[0139] However, as Figure 8 The t-SNE results show that within the formed clusters, samples from the original signal, the inverted signal, and white noise are highly mixed and cannot be clearly separated. Sample points from different categories intermingle without clear boundaries. This reveals that it is difficult to effectively distinguish these signals in the feature space based solely on the original waveform features of the signal using this method.

[0140] From the perspective of feature space analysis, these results strongly corroborate the concealment of the signal in this invention. Its characteristics are highly similar to or mixed with random noise, significantly increasing the difficulty for non-cooperative parties to identify and classify it, thereby enhancing the signal's concealment effect. This, along with the conclusions obtained from the aforementioned power spectral density analysis, constitutes the key technical advantage of this invention.

[0141] Secondly, this invention demonstrates significant advantages in noise robustness and bit-level information recovery. It employs an improved diffusion model (Improved-DDPM) as the core generation and reverse recovery mechanism, combined with a random sampling coding strategy using a hidden waveform library. This ensures that each communication bit is carried by a different diffusion intermediate waveform sample, enhancing anti-analysis capabilities and guaranteeing the concealment of information embedding. The receiving end performs inverse diffusion denoising on the noisy signal to recover the signal structure. Despite channel noise interference, the diffusion model effectively reconstructs the signal, preserving the original bit-discriminative features. The decoding end uses a trained classifier to perform bit-by-bit decision-making on the denoised signal. Under typical simulation conditions, this classifier achieves a classification accuracy of over 90%, effectively guaranteeing the reliability of information recovery. Figure 9 As shown, simulation results of the system of the present invention in an additive white Gaussian noise (AWGN) channel demonstrate that even in interference environments with a signal-to-noise ratio as low as -10dB, the system can still achieve better performance than... The low bit error rate fully demonstrates the excellent noise resistance performance of the proposed method after integrating robust denoising and high-precision classification decision, which significantly improves the communication reliability under interference environment.

[0142] Finally, regarding system deployability and scalability, this invention adopts a modular design, and both the diffusion model and the discriminator are implemented using lightweight network structures. For example, the diffusion model uses a lightweight one-dimensional generator network, and the classification discriminator uses a modified one-dimensional residual network structure. These lightweight network structures include, but are not limited to, one-dimensional convolutional networks with fewer than 1M parameters, thus effectively adapting to resource-constrained application environments such as mobile devices and edge devices. Furthermore, since the communication process is based on standard waveform processing procedures, the technical framework of this invention can be naturally extended to covert communication scenarios involving multiple modalities such as images, audio, and time-series data, providing a unified and highly scalable technical solution for secure communication in multiple fields in the future.

[0143] In summary, this invention not only significantly improves communication concealment and robustness, but also takes into account deployability and adaptability, possessing good theoretical value and promising prospects for practical engineering applications.

Claims

1. A covert communication system based on a generative diffusion model, characterized in that, include: The diffusion generation module at the transmitting end is used to map the communication bit stream to be transmitted into a hidden signal waveform with noise-like characteristics and then transmit it. The classification and discrimination module at the receiving end is used to perform inverse diffusion denoising on the received signal and restore the original communication bitstream. The diffusion generation module's operation includes: constructing two pairs of original signals that are consistent in key statistics but distinguishable in structural features, and labeling them as bits 0 and 1 respectively; performing a forward diffusion process on the two pairs of original signals using a diffusion model to generate a hidden waveform library corresponding to each bit, whose statistical characteristics approximate a Gaussian distribution but retain distinguishable structural differences; randomly selecting waveform segments from the corresponding waveform library according to the bitstream to be transmitted, mapping them, and forming the transmitted signal after splicing and boundary smoothing; the classification and discrimination module's operation includes: slicing the received noisy signal into fixed-length slices, performing an inverse diffusion process on each slice to restore the signal structure, and then using a trained classifier to make bit decisions, ultimately restoring the bitstream.

2. The covert communication system based on a generative diffusion model according to claim 1, characterized in that, The construction of the original signal pair specifically involves generating two types of one-dimensional time-series signals, each of length L, as the original signal pair. The two types of signals are consistent in key statistics such as energy, mean, and frequency distribution, but they form structural differences through at least one of phase reversal, sign reversal, or local time series reconstruction.

3. The covert communication system based on a generative diffusion model according to claim 1, characterized in that, The forward diffusion process is based on the stepwise addition of Gaussian noise to a Markov chain, and its recursive relationship is as follows: ； in, For from the first The generation signal of the step to the first The probability of generating a signal in a step. It follows a Gaussian distribution. middle Let be a Gaussian distributed random variable. The mean of a Gaussian distribution is given. Let V be the variance of the Gaussian distribution. It is the identity matrix. It is the first The noise intensity of the step is set using an improved cosine scheduling strategy.

4. The covert communication system based on a generative diffusion model according to claim 3, characterized in that, The function definition of the improved cosine scheduling strategy is: ； in, This is a truncation function used to truncate the target function. Numerical range constraints will be applied; inputs exceeding the specified range will be assigned the minimum value. Or the maximum value is 0.

999. For an improved cosine annealing scheduling function, For diffusion time steps, This is an offset constant.

5. The covert communication system based on a generative diffusion model according to claim 1, characterized in that, The specific process of generating the hidden waveform library involves: for each type of original signal... Category number =0,1, apply randomly initialized noise and execute Step forward diffusion, repeated sampling Next, a hidden waveform library corresponding to this bit is constructed. ,in, Indicates the original signal Apply randomly initialized noise and execute. The first step forward diffusion obtained Secondary sampling.

6. The covert communication system based on a generative diffusion model according to claim 1, characterized in that, The bit mapping and waveform construction specifically include: For length of bitstream , For the i-th bit, its carrier waveform mapping function ,in, For sampling index, Indicates 1 to Uniform distribution; This means for bits The corresponding original signal In the Step 1 Secondary sampling.

7. The covert communication system based on a generative diffusion model according to claim 1, characterized in that, The reverse diffusion process from the noisy signal Gradually denoise and recover the original signal Its recursive relation is: ; in, To predict noise neural networks, To predict noise, the neural network uses the input step number. and the Step-by-step signal generation Output prediction noise, For the first The standard deviation of residual noise in the step; ,Right now It follows a vector with a mean of 0 and a covariance of the identity matrix. The multivariate standard normal distribution; For the front The cumulative product of step noise figures, For the first The scaling factor of the step, where, , , For the front The cumulative product of step noise figures, For the first The scaling factor of the step. For the first The scaling factor of the step. The step number takes a value from 1 to... ; It is the first The noise intensity of the step.

8. The covert communication system based on a generative diffusion model according to claim 1, characterized in that, The classifier in the classification and discrimination module is a temporal feature classification network. Its input is a one-dimensional waveform segment recovered by inverse diffusion, and its output is a bit decision result. It is trained by minimizing the cross-entropy loss function.

9. The covert communication system based on a generative diffusion model according to any one of claims 1 to 8, characterized in that, The diffusion generation module employs a lightweight one-dimensional convolutional neural network architecture, which includes a symmetrical feature encoding-decoding path and performs cross-scale feature fusion through skip connections; the classifier in the classification and discrimination module adopts a lightweight one-dimensional residual network structure.

10. A covert communication method based on a generative diffusion model, applied to the system as described in any one of claims 1 to 9, characterized in that, Includes the following steps: Sending steps: S1. Construct and train the diffusion model: Generate two statistically consistent and structurally distinguishable pairs of original signals as training sets, and train the diffusion model to learn its forward diffusion and reverse denoising processes; S2. Construct a hidden waveform library: Using the trained diffusion model, perform forward diffusion sampling on the two types of original signals respectively to generate a hidden waveform library corresponding to bits 0 and 1; S3. Generate and send covert signals: Based on the bit stream to be transmitted, randomly select waveform segments from the corresponding waveform library, splice and smooth the boundaries, and then send them through the channel; Receiving end steps: S4. Receive and slice: Receive signals that have been disturbed by the channel and slice them into fixed lengths; S5. Denoising and Decision: Perform a reverse diffusion process on each slice to recover the signal, then input it into the classifier for bit decision to restore the original bit stream.

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