Learning-type non-linear compensation with physical information neural networks for data access

Abstract

A system and computer-implemented method for data communication using a Physical Information Neural Network (PINN) is provided. At a transmitter, the method is configured to obtain source data to be transmitted, encode the source data into a codeword based on a Forward Error Correction (FEC) code, map the codeword to amplitude symbols, modify the mapped amplitude symbols to pre-equalized symbols including pre-distorted channel impairment symbols based on a predetermined physical model, and transmit the modified pre-equalized symbols to a receiver. And transmitting the digital data of the pre-balanced symbols as channel data through a channel. At a receiver, the method is configured to receive and demodulate channel data from a channel to produce an initial estimate of bits of the received channel data, mitigate channel noise and waveform distortion in the channel data based on the initial estimate, channel data composed of shaped non-uniform symbols is converted into a de-shaped bit sequence as a uniform data sequence, the de-shaped bit sequence is decoded to correct a residual error in the converted channel data, and the corrected channel data is stored in a data sink.

Description

Technical Field

[0001] The present invention relates generally to the field of waveform equalization for data communications, and more particularly to a method and system for learning-based nonlinear compensation based on an artificial neural network employing a physical model. Background Art

[0002] In digital communication and data storage systems, the transmitted signal waveform is often distorted by many factors including hardware defects, channel media and signal imperfections. For example, optical fiber communications often suffer from amplified spontaneous emission noise, shot noise, thermal noise, Kerr fiber nonlinearity, dispersion, polarization multiplexing, self-phase modulation, cross-phase modulation, Raman scattering, carrier offset, linewidth, timing jitter, etc. Many linear and nonlinear equalization or denoising methods have been proposed, such as decision feedback equalization, turbo equalization, maximum likelihood sequence estimation, etc. However, these methods are highly dependent on simple signal models that are mathematically tractable, such as linear dispersion models, autoregressive models, Volterra series, regular perturbation models, nonlinear Schrodinger equations, Maxwell equations, Helmholtz equations, delay Doppler angle spectrum, etc. Model-based methods have some disadvantages: i) It is numerically difficult or complex to construct an accurate signal model; ii) Model mismatch is inevitable; iii) The interaction of unknown physical phenomena cannot be well modeled; iv) The model is highly sensitive to uncertain physical parameters.

[0003] Recently, data-driven learning-based methods, mainly based on deep neural networks (DNNs), have become an alternative solution to model-based methods. For example, convolutional neural networks, recurrent neural networks, and other network architectures have performed well as nonlinear equalizers to compensate for signal distortion. In general, DNNs are configured with a large number of trainable parameters, such as weights and biases of affine transformations, and the trainable parameters are optimized by stochastic gradient methods based on training data. Such over-parameterized DNNs have higher capabilities and can more accurately approximate almost arbitrary functions. However, data-driven learning methods using over-parameterized DNNs have some defects and challenges themselves: i) sufficient high-quality training data is required; ii) large amounts of data training require high computing power, resources, and storage; iii) the interpretability and certifiability of the training model are poor; iv) finding a suitable DNN architecture is not easy.

[0004] Therefore, there is a need and requirement to effectively address these challenges of signal waveform equalization in data communication and storage systems. Summary of the invention

[0005] Some embodiments of the present invention are based on the recognition that data communication and storage systems often suffer from signal distortion due to channel noise, device nonlinearity, and signal processing imperfections. The present invention provides a method for improving data quality by using a physical information neural network. The present invention solves some challenges of existing methods in terms of effective training and interpretability. In some embodiments, the optical fiber physics governed by the nonlinear Schrodinger equation is modeled using Koopman operators, Volterra expansion, split-step Fourier methods, conventional perturbations, and Runge-Kutta integration. Model parameters such as Kerr nonlinearity, fiber attenuation, dispersion, etc. are adaptively trained. In order to mitigate residual model mismatch errors, another embodiment uses additional DNNs on top of the learned physical model. Another embodiment uses joint time / frequency / space domain physics. Impairments are mitigated by designing transmitters and receivers via models based on differentiable digital twins (e.g., joint transmitter / receiver filtering, joint modulation / demodulation, and joint pre-distortion / post-distortion). The present invention makes it possible to implement joint design at relay points (e.g., at programmable amplifiers, repeaters, switches, multiplexers, and routers). Physical information models include hidden layers based on diffusion, equilibrium, quantum physics, and molecular physics.

[0006] The present invention is based on the recognition that fully data-driven DNN models have difficulty interpreting learned parameters, and over-parameterized general DNN models require a large amount of high-quality training data. In addition, the present invention is based on the recognition that signal distortion in communication and storage systems is potentially dominated by physical models of channel links (mediums) (such as Maxwell equations and nonlinear Schrodinger equations for electromagnetics, optics, and circuits). The present invention implements an interpretable and effectively trainable DNN model by integrating data-based methods and physical information models to compensate for signal waveform distortion in data communication and storage systems. Physical information DNN models can provide non-obvious benefits in reducing redundant and irrelevant parameters and interpretable adjustments of physically related parameters. At the same time, the present invention provides a way to adjust the tradeoff between model accuracy and complexity by mixing data-driven DNN models and physical information mathematical models.

[0007] In some embodiments, fiber physics governed by nonlinear Schrodinger equations are incorporated into DNN models, including but not limited to neural Koopman operators, neural Volterra expansions, neural split-step Fourier methods (SSFM), neural canonical perturbations (RP), neural Runge-Kutta (RK) integration, neural ordinary differential equations (ODE), neural diffusion models, neural equilibrium models, collocation models, exponential integrators, etc. In some embodiments, model parameters such as Kerr nonlinear factors, fiber attenuation, dispersion factors, etc. can be trained online or offline to adapt to a given training data set. In addition, incremental parameters such as phase correction, gain correction, and phasor correction are provided to generalize the physical model.

[0008] In some embodiments, multiple physical information models are used at once, for example, RP and SSFM are combined. In addition, the residual DNN model is used to correct the residual error of model mismatch. Another embodiment uses joint time / frequency / space domain physics to combine, for example, time domain neural kernel and frequency domain neural kernel are mixed.

[0009] In some embodiments, signal impairments are mitigated by jointly designing the transmitter and receiver ends via a digital twin-based model that is differentiable to achieve gradient-based optimization (e.g., joint transmitter / receiver filter design, joint encoder / decoder design, joint modulation / demodulation design, joint pre-distortion / post-distortion design, etc.). In addition to the transmitter / receiver end through differentiable operational graphs in the system, some embodiments jointly design multiple relay points, such as at programmable amplifiers, repeaters, switches, multiplexers, routers, etc.

[0010] In some embodiments, the physical information model includes hidden layers based on other differentiable computations, such as diffusion, equilibrium, photon, quantum physics, and molecular physics, and has trainable parameters. In some embodiments, the integrated physical information DNN model is applied to audio / visual signal processing, biological signal processing, data storage reading / writing, radio communication, wired communication, etc.

[0011] Thus, some embodiments disclose a method for reliably transmitting data from a transmitter to a receiver over a communication channel. In some embodiments, the method and system include at least one computing processor, at least one storage repository, a transmitter having a source for receiving source data to be transmitted, an encoder for encoding the source data, and a front-end interface for transmitting the encoded codeword as a modulated signal into the communication channel. In some embodiments, the method and system also include a communication channel, which includes a wired media channel, a wireless media channel, an optical fiber channel, a vacuum free space channel, a data storage medium, or a variant thereof. In some embodiments, the method and system also include a receiver having a front-end interface for receiving an output signal from the communication channel, a decoder for decoding the output signal, and a sink for providing a decoded codeword. In other embodiments, the method and system have a controller configured to specify (determine) parameters of a pre-shaping code, a post-shaping code, a shaping mapper, and a shaping demapper used in an encoder and a decoder based on knowledge (type) of a channel link, wherein the parameters also include codeword length, code rate, and overhead.

[0012] In this manner, the method and system of the present invention uses reverse operations at the receiver to recover the shaped bits and the original data through the FEC decoding and the shaping demapper. Specifically, a computer-implemented method for recovering a coded bit stream is performed by one or more computing processors at the receiver, resulting in the following steps: accessing input data representing a noisy codeword; demapping the input data to generate a soft decision bit stream given a noisy orthogonal amplitude modulation symbol; decoding the bit stream according to a post-shaping error correction code, mapping the decoded bit labels into amplitude modulation symbols; demapping the amplitude symbols according to the shaping demapper; and decoding the deshaped bit stream according to the pre-shaping error correction code.

[0013] According to some embodiments of the present invention, a system for data communication via a channel link is provided. The system is configured to include: a communication module configured to access the channel link according to a specification set for data communication; and a controller configured to include a physical information neural network (PINN), wherein the controller is configured to determine parameters represented by the specification set of the communication module according to a physical model of the channel link to compensate for signal waveform distortion in the data communication.

[0014] In addition, some embodiments may provide a method for communicating data via a channel link. In some cases, the method is referred to as a computer-implemented method. The method includes the following steps: accessing the channel link according to a communication method based on a set of specifications for data communication; and modifying the set of specifications for data communication according to a control method based on a physical information neural network (PINN) based on a physical model of the channel link. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] [ Figure 1 ]

[0016] Figure 1 is a functional diagram of a communication system and method for digital data transmission according to an embodiment of the present invention.

[0017] [ Figure 2 ]

[0018] Figure 2 The structure of a parallelizable LPR for real-time high-throughput DNN according to an embodiment of the present invention is shown.

[0019] [ Figure 3 ]

[0020] Figure 3 It shows how to improve the RP model with trainable phasor correction terms (complex-valued scalars) C = {C0, C1, ..., CN} at the end of each branch according to an embodiment of the present invention.

[0021] [ Figure 4 ]

[0022] Figure 4 An implementation using a cascaded LRP model controlled by multiple interleaved DNNs is shown.

[0023] [ Figure 5A ]

[0024] Figure 5A Another embodiment of residual model mismatch correction with additive aggregation using an external deep neural network (DNN) according to an embodiment of the present invention is shown.

[0025] [ Figure 5B ]

[0026] Figure 5B Another embodiment of residual model mismatch correction with multiplicative aggregation using an external deep neural network (DNN) according to an embodiment of the present invention is shown.

[0027] [ Figure 5C ]

[0028] Figure 5C Another embodiment of residual model mismatch correction with bilinear aggregation using an external deep neural network (DNN) according to an embodiment of the present invention is shown.

[0029] [ Figure 5D ]

[0030] Figure 5DAnother embodiment of residual model mismatch correction using a parallel LRP model aggregated with an external deep neural network (DNN) according to an embodiment of the present invention is shown.

[0031] [ Figure 5E ]

[0032] Figure 5E Another embodiment of residual model mismatch correction using a cascade stack of multiple LRP models and multiple deep neural network (DNN) blocks according to an embodiment of the present invention is shown.

[0033] [ Fig. 5F ]

[0034] Fig. 5F Another embodiment of residual model mismatch correction using a cascade stack of multiple LRP models with skip paths and multiple deep neural network (DNN) blocks according to an embodiment of the present invention is shown.

[0035] [ Figure 6 ]

[0036] Figure 6 An example performance gain of LRP-based PINN versus model-based SSFM digital backpropagation in a Fibre Channel facility is shown in accordance with an embodiment of the present invention.

[0037] [ Figure 7 ]

[0038] Figure 7 An exemplary block diagram of a system suitable for implementing different components of a transceiver for encoding, decoding, equalization, and de-shaping according to an embodiment of the present invention is shown. DETAILED DESCRIPTION

[0039] Various embodiments of the present invention are described below with reference to the accompanying drawings. It should be noted that the drawings are not drawn to scale, and in all drawings, elements of similar structure or function are represented by the same reference numerals. It should also be noted that the drawings are intended only to facilitate the description of specific embodiments of the present invention. They are not intended to serve as an exhaustive description of the present invention or as a limitation on the scope of the present invention. In addition, the aspects described in conjunction with a specific embodiment of the present invention are not necessarily limited to that embodiment, and may be practiced in any other embodiment of the present invention.

[0040] Some embodiments of the present invention are based on the recognition that signal equalization uses physical information neural networks (PINNs) that integrate physical models into neural networks to improve the quality of data communication and storage systems. For example, some embodiments enable improved machine learning methods and systems based on inverse normal perturbation (RP) models to represent the physical phenomena of light wave propagation through optical fiber communication. Specifically, photon physics in optical fibers is typically dominated by nonlinear Schrodinger equations (NLSE) and their variants (such as Manakov equations). RP models use finite difference approximations in parallel structures to numerically solve NLSE. Some embodiments use learning RP (LRP) models to jointly optimize trainable parameters (such as step size, gain, and phase rotation) to generalize parallel RP branches. LRP-based DNN models can outperform corresponding learning digital back propagation (DBP) methods based on split-step Fourier method (SSFM) in standard single-mode fiber links. In this way, LRP also allows segmented per-step score (SPS) modeling to reduce complexity while maintaining performance that is better than 1-SPS SSFM-DBP.

[0041] The physical models of the channel link to be embedded in PINN include finite difference method (such as, step-by-step Fourier method), finite element method (such as, conventional perturbation), collocation model (such as, Runge-Kutta integration), Volterra series expansion, Koopman operator, exponential integrator, ordinary differential equations, partial differential equations, nonlinear Schrodinger equations, finite impulse response, infinite impulse response, autoregressive model, diffusion process, space-time-frequency dispersion model, Maxwell equations, quantum dynamics, molecular dynamics, etc.

[0042] In the past few decades, the rapid development of digital signal processing (DSP) technology has led to a significant increase in the throughput and reliability of coherent fiber communication systems. For example, linear impairments such as chromatic dispersion (CD), polarization mode dispersion (PMD), and phase noise have been extensively studied and solved in the digital domain. As a result, Kerr fiber nonlinearity has become the main source that limits the maximum achievable information rate and effective signal-to-noise ratio (SNR) of optical communication systems.

[0043] The Manakov equation has been used to model the propagation of dual polarization (DP) signals through standard single mode fiber (SSMF). It can be numerically solved using split-step Fourier (SSFM), which sequentially operates nonlinear and linear operations with small finite difference steps. Reducing the step size makes the model more accurate. Alternatively, many models including regular perturbations (RP) have been studied. Digital back propagation (DBP) is a state-of-the-art method for nonlinear compensation (NLC) that reverses the propagation of light waves by reversing the SSFM calculation. Although it provides significantly improved performance over most other methods, this comes at the cost of higher computational complexity. In addition, it is highly sensitive to model parameters such as Kerr nonlinear factors and dispersion factors. Therefore, the main challenge in realizing practical NLC is to find the best balance between complexity and performance.

[0044] Recent advances in machine learning (ML) and deep neural networks (DNNs) have revolutionized various scientific fields including fiber-optic communications and networking. Several physically-informed DNNs have been proposed for DBPs in the context of NLC and equalization. Perturbation theory has also been used to enhance learning of DBPs, while ML techniques have been shown to be effective in improving nonlinear equalization based on symbolic triple interactions.

[0045] In some embodiments, the ML-assisted NLC method based on the inverted RP physical model uses a parallel branch structure with generalized phasor correction parameters adjusted with low-complexity ML techniques to significantly increase accuracy. In addition, LRP with fractional steps per span (SPS) case (where each RP branch models more than one span) can maintain high performance that is superior to 1-SPS SSFM-DBP while reducing computational complexity.

[0046] PINN-assisted fiber optic communications

[0047] Figure 1A communication system for transmitting digital data from a transmitter 110 to a receiver 130 via a channel link 120 is shown according to some embodiments. The channel link 120 is configured to provide data communication based on electromagnetic propagation, light wave propagation, acoustic propagation, molecular propagation, or a variant thereof. For example, the communication channel 120 includes, but is not limited to, an air medium for radio communication, a copper cable for wired communication, a solid-state drive for data storage read / write, a vacuum for free space satellite communication, and an optical fiber cable for optical fiber communication. During the communication of transferring digital data from the transmitter 110 to the receiver 130, the digital data may be corrupted by noise occurring across the channel and data processing path between the data source 111 and the data sink 135. For example, noise includes, but is not limited to, thermal noise, spontaneous emission amplifier noise, reflection / refraction of an inhomogeneous medium, interference noise, and pulse shot noise. The transmitter 110 uses a cascade of an encoder 112, a shaping mapper 113, and a PINN-based pre-equalizer 114 to achieve reliable data transmission. The receiver 130 uses a cascade of a post-equalizer 132 based on PINN, a shaping demapper 133, and a decoder 134 to recover the original data from the noisy message sent by the transmitter 110. The encoder and decoder are based on forward error correction (FEC) codes such as low-density parity check (LDPC), turbo, and polarization codes. Most communication systems use both the transmitter 110 and the receiver 130 as communication modules. Some communication systems use only the transmitter as a communication module, while some communication systems use only the receiver as a communication module.

[0048] At the transmitter 110, the data to be sent comes from a source 111 configured to accept raw data. The source may include, but is not limited to, a repository for reading data, an interface port for receiving data, and a device for generating data. For example, in some embodiments, the source includes a voice communication device that converts an input voice signal into digital data. The input data from the source 111 is encoded by the FEC encoder 112. In some cases, the encoded data may be referred to as a codeword. The pre-shaping FEC encoder appends a series of overhead parity bits to resist potential burst errors. The coded data is mapped to a series of amplitude symbols according to the shaping mapper 113, and the shaping mapper 113 further appends redundancy to match the probability mass function (PMF) of the amplitude occurrence to the target distribution. The shaping amplitude symbol is marked as a series of shaping bits and is further transformed by the PINN pre-equalizer 114. The PINN pre-equalizer modifies the shaping amplitude based on a physical model such as RP to pre-eliminate channel impairments. The pre-equalized symbols are fed into the channel medium via the front-end circuit 115, which uses various modulation formats, including but not limited to quadrature amplitude modulation (QAM) with or without linear transformation (such as, orthogonal frequency division multiplexing (OFDM)). The front-end circuit 115 may also include but is not limited to electro-optical circuits for optical communications and radio frequency circuits for radio communications. For example, the front-end circuit includes a digital-to-analog converter, a power amplifier, and signal preprocessing (such as, bandpass filters, pulse shaping, precoding, power loading, pilot insertion, and predistortion). For some embodiments, the transmitter uses wavelength division multiplexing (WDM) and spatial multiplexing for multi-mode / multi-core optical fibers.

[0049] The transmitted signal is distorted by the channel 120. For example, the channel adds additive white Gaussian noise (AWGN), co-channel interference, deep fading, impulse noise, inter-symbol interference, Kerr-induced nonlinear interference, polarization crosstalk and linear dispersion, as well as residual hardware imperfections such as quantization error, clock jitter, overflow, laser linewidth, and carrier phase noise.

[0050] The receiver 130 first converts the channel output into an electrical received signal via a front-end circuit 131, which is generally complementary to the front-end 115 at the transmitter. For example, the front-end circuit includes, but is not limited to, an analog-to-digital converter, linear equalization, nonlinear equalization, adaptive filtering, channel estimation, carrier phase recovery, synchronization, and polarization recovery. With the front-end circuit, the received signal is demodulated by a PINN-based post-equalizer 132 to produce an initial estimate of the transmitted codeword bits, thereby mitigating channel noise and waveform distortion. For example, the demodulated signal represents a log-likelihood ratio (LLR) value, which is input to the FEC decoder as a soft input message.

[0051] The decoded message is then demapped by a reshaping demapper 133 to convert the shaped non-uniform symbols into a uniform data sequence by removing the overhead introduced by the reshaping mapper 113. To correct residual errors, the deshaped bit sequence is further decoded by an FEC decoder 134 before being fed into a sink 135. The data sink 135 includes, but is not limited to, a storage repository for writing data, an output interface port for sending data, and a device for receiving data. For example, in some embodiments, the sink includes a voice communication device that converts the decoded data into a sound signal.

[0052] Some embodiments are based on the recognition that, based on the auxiliary information 140 of the communication channel 120, the controller 141 adaptively controls the FEC code and shaping specifications. For example, parameters such as code rate (or overhead), codeword length, shaping rate and shaping length are adaptively selected based on channel knowledge such as signal-to-noise ratio (SNR), power delay profile, channel transfer function and nonlinear statistics (including but not limited to mean, variance, kurtoris and higher moments). The controller 141 is configured to use a lookup table or another PINN model to determine the specifications of the transmitter and / or receiver, such as the best FEC code and modulation selection given the channel knowledge for some embodiments. Based on the knowledge (type) of the channel link, the specifications indicate the parameters of the pre-shaping code, post-shaping code, shaping mapper and shaping demapper used in the encoder and decoder, wherein the parameters include codeword length, code rate and overhead, the best FEC code and modulation selection method for the channel link used in the data communication of some embodiments. The specification set for the communication module also includes parameter sets for channel encoders, data compressors, constellation shapers, modulators, pulse shaping filters, multiplexers, pre-equalizers, amplifiers, digital-to-analog converters, oscillators, antennas, mixers, analog-to-digital converters, equalizers, demultiplexers, demodulators, constellation deshapers, data decompressors, channel decoders, etc. Therefore, the parameter set specified by the controller includes a generation matrix for channel coding, a shaping rate, a shaping method, a modulation format, a pulse shaping filter length, a pre-equalization method, an amplifier gain, a sampling rate and quantization bits of a digital-to-analog converter, an oscillator frequency of an analog-to-digital converter, an antenna size, a sampling rate and quantization bits, an equalization method, a demodulation method, a constellation deshaping method, a channel decoder method, etc. When the controller 141 determines or modifies the specification, the parameters are adaptively selected to best match the type of channel link used in the data communication system.

[0053] The transmitter 110 and / or the receiver 130 may be implemented using a hardware processor operably connected to a memory. Each of the transmitter 110 and the receiver 130 may include one or more processors. For example, the memory of the receiver 130 may store some information related to one or a combination of the following: a shaping mapper and a demapper; soft inputs and soft outputs of the decoder 133; parameters of encoding and decoding and results of intermediate calculations; and an adaptive encoding strategy. All components in the transmitter 110 and the receiver 130 may be implemented by hardware, one or more hardware processors, computer software (programs or program modules), or a combination of hardware and computer software.

[0054] Physical Information Model Based on PR

[0055] Signal propagation in optical fibers is based on the basic physical theory of NLSE variants including the Manakov equation. Specifically, the signal propagation of the DP complex field u(z, t) with lumped optical amplification (OA) is represented by the partial differential equation (PDE):

[0056]

[0057] Where β2 is the dispersion coefficient, γ is the Kerr nonlinear factor, and n is the noise vector due to amplified spontaneous emission (ASE). Function f(z) = exp(-alpha z + alpha L sp floor(z / L sp )) represents the amplification and attenuation in the optical fiber, where alpha is the fiber loss factor and L sp is the span length.

[0058] This physical information PDE model based on Manakov NLSE is usually difficult to derive the actual solution under arbitrary position z and arbitrary initial conditions analytically. In order to solve the physical equations, finite difference or finite element method is usually used to numerically identify waveform propagation. For some embodiments, SSFM uses finite difference steps and solves linear and nonlinear effects subsequently. The linear step considers CD, fiber attenuation and PMD based on Fourier domain, and operates waveform transformation in an effective manner. The nonlinear step uses time domain to modify its amplitude and phase according to instantaneous optical wave power. ASE noise is also added at the amplifier.

[0059] For some embodiments, the RP model is used to numerically solve the Manakov NLSE by using finite difference steps to form parallel branches with linear and nonlinear operations. Based on the recognition that the propagation of optical signals through SSMF can be approximated by the RP model, which solves the Manakov equations in the linear domain and bundles the nonlinear components into small additional terms. Similar to SSFM-DBP, the direction of the RP model can be reversed by flipping the direction of f(z) (i.e., switching attenuation to amplification) and changing the signs of β2 and γ parameters. Therefore, the inverted RP uses the received signal u(L, t) to reconstruct u(0, t) for NLC (i.e., the reverse propagation signal). For some embodiments, in order to achieve better results, the γ parameter is adjusted through a machine learning framework based on the gradient method.

[0060] Figure 2 The structure of LPR with parallelizable branches suitable for real-time high-throughput DNN is shown. The first-order RP model is expressed as

[0061]

[0062] Among them, O(γ 2 ) represents the high-order residual of the Manakov model, L is the total link length, and the first term

[0063]

[0064] is a linear branch, which contains a dispersion block, given by

[0065]

[0066] Where F represents discrete Fourier transform (DFT), F -1 represents the inverse DFT, Ω represents the angular frequency. The second term u NL It is the aggregation of N nonlinear branches, as follows:

[0067]

[0068] Here, the nonlinear block K is given by:

[0069]

[0070] where ||.|| represents the 2-norm. Assign a step size to each branch to form an (N+1) element vector z={z0, z1, ..., z N}. The last element of z is the step size of the linear branch. The corresponding effective step size is calculated as:

[0071]

[0072] Similar to the SPS in SSFM-DBP, the accuracy of RP increases with the number of branches and decreases with the optical launch power (i.e., more fiber nonlinearity). Note that the model allows z n = {0, L}, so that the front / back linear blocks cover the entire link length. It is found that this can improve the performance for the case with a small number of branches.

[0073] Although the RP model can provide a reasonably accurate approximation with a large number of branches, it has significant problems when the number of branches is small. Figure 3 As shown in FIG, a single branch conventional RP model takes a linear signal 31 and adds a 90 degree shifted amplitude dependent signal 32 due to the K nonlinear operation to provide a nonlinear phase rotation. Adding these two vectors can result in a phasor towards the desired rotation 33. However, as the nonlinearity increases, gain expansion outside the unit power circle 34 is inevitably caused. Therefore, the model accuracy is significantly reduced at higher power states.

[0074] The present invention provides a method for improving the RP model, wherein at the end of each branch there is a trainable phasor correction term (complex valued scalar) C = {C0, C1, ..., C N},like Figure 3 The nonlinear term becomes

[0075]

[0076] And the linear branch u L (0, t) is modified to

[0077]

[0078] By this simple modification, the gain and rotation of each branch 35 can be uniformly adjusted, and a better phasor close to unit power 36 can be found. Therefore, the LRP model in the present invention can more accurately approximate the nonlinear effect and effectively mitigate the unwanted gain expansion.

[0079] As an example implementation of the system, a single-carrier DP64-ary quadrature amplitude modulation (QAM) signal with a symbol rate of 64 Gbaud is generated at the transmitter. The generated electrical signal is pulse shaped by a root raised cosine (RRC) filter with a roll-off factor of 0.1. It is modulated into an optical carrier with an in-phase / quadrature modulator. The carrier is provided by a laser with a center frequency of 1550 nm and zero frequency offset. The analog optical signal is upsampled to 8sa / sym and propagated through 10 span 80km SSMF links. Each span link is followed by an erbium-doped OA with 16dB gain and 4dB noise figure. Nonlinear inter-channel interference may occur in a 5-channel, 50GHz spacing wavelength division multiplexing (WDM) system. The Kerr coefficient of the SSMF is γ=1.2W / km, the loss factor is alpha=0.2dB / km, and the dispersion factor is beta=17ps / nm / km. The received optical signal is downsampled to 2sa / sym and passed through a PINN-based equalizer including linear CD compensation, SSFM-DBP or LRP-DBP model to mitigate channel impairments. The output is then shaped with a matched RRC filter. Subsequently, the received signal is normalized and derotated with a 1st-order equalizer and downsampled to 1sa / sym.

[0080] For some embodiments, the LRP-based PINN equalizer is trained by an adaptive momentum (Adam) optimizer with a learning rate of 0.001 to find the optimal values ​​of the phase correction factor C and the step size z. 200 randomly generated data frames are used, respectively, for training and testing at a ratio of 80% and 20%. A single frame contains a snapshot of a coherently detected digital reverse propagation signal as a target. Each snapshot has 8192 samples per polarization under an oversampling of 2sa / sym. The frames used for training are simulated (forward and reverse propagation) with 100-SPS Manakov SSFM. The forward propagation signal is downsampled to 2sa / sym. The original nonlinear phase rotation is not compensated before training and is included in the optimization, and a 1st order equalization is used after NLC. Subsequently, the signal is passed to 100-SPSDBP, and the corresponding nonlinear compensation output is saved as the second element of the snapshot. Although the detected signal is at 2sa / sym, the forward propagation in the analog domain is at 8sa / sym. For some embodiments, a logarithmic step profile and asymmetric SSFM are used on each fiber span, ie, the nonlinear steps are located at the segment boundaries.

[0081] Each transmit power is optimized individually or jointly. The mini-batch size is set to 40 frames; there are B = 160 batches (i.e., 160 frames) per epoch for training (B = 40 for validation); and the number of epochs is set to 6500. For Ns = 4096 symbols / P = 2 polarizations, the mean square error (MSE) loss between the predicted transmission signal s and the original transmission signal s is calculated:

[0082]

[0083] The complex value C is adjusted by the gradient of the MSE loss function.

[0084] Proper initialization of trainable parameters is a key aspect to achieve higher performance and faster convergence. Some embodiments initialize z to a logarithmic step size distribution on each span, while the phase correction C is initialized to a vector of all ones on the real axis and all zeros on the imaginary axis. For some embodiments, the model provides better convergence when Δ is decoupled from the initial value of f(z) and z.

[0085] For some embodiments, ML-based adjustment of trainable parameters in the physical model is implemented in an adaptive manner by a deep neural network. Specifically, methods and systems using DNNs use additional trainable factors on top of the RP model to correct the phasers. The DNN acquires auxiliary information such as power of the signal kurtoris and instantaneous waveform at different locations z. Specifically, such a system uses different auxiliary information including fiber facility information to control parameters of the LRP model via the DNN. For some embodiments, PINN-based parallel equalizers are cascaded in a pipeline sequence to adjust the parallel factor and the pipeline factor.

[0086] Figure 6 The exemplary performance of LRP-based PINN for standard single-mode fiber facilities is shown. PINN-based nonlinear compensation is superior to the learned SSFM-based method. Compared with 1-sps SSFM digital back propagation, 10-branch LRP achieves a gain of 0.8dB, while the computational complexity is comparable. More importantly, even with lower computational complexity, 5-branch LRP is still 0.25dB higher than 1-sps SSFM. This is the benefit of trainable phase correction. Compared with 3-sps SSFM, 30-branch LRP still shows a gain of 0.6dB.

[0087] Another embodiment is based on the cascaded use of physical models such as LRP controlled by additional DNNs. Figure 4 A cascade model controlled by an interleaved DNN is shown. Here, the DNN uses an intermediate signal to modify the parameters of the LRP, such as the step size and nonlinear constant. By using the intermediate signal, the potential error caused by model mismatch can be reduced. In addition, the cascaded use of LRPs can further reduce the model mismatch of each LRP.

[0088] Yet another embodiment uses additional DNN modules to mitigate model mismatch error. Figure 5A Such an embodiment is shown to compensate the residual error of LRP in an additional manner using an external DNN such as a convolutional neural network (CNN) and a multi-layer perceptron (MLP). Figure 5B An implementation using additional DNN modules in a multiplicative manner is shown. Figure 5C Embodiments using additional DNN modules and trainable physical models such as LRP in a bilinear weighted manner are shown. Here, CNNs are interpreted as cascaded finite impulse response (FIR) filters, which generalize the good linear operation of SSFM. For some embodiments, recursive neural networks (RNNs) are used to represent infinite impulse response filters (IIR). In certain embodiments, bilinear aggregation is further generalized by additional DNN blocks. The RP model has different variants, including log-domain RP and high-order RP. Certain embodiments use learnable parameterizations based on variants of the RP model.

[0089] Figure 5D Another embodiment is shown in which parallel physics models are aggregated by DNN blocks. Figure 5E Another embodiment is shown in which multiple LRPs and DNNs are stacked in a cascaded manner. Fig. 5F Another embodiment is shown where a skip path using an intermediate signal is fed into a DNN block at a later stage. Figure 4 as well as FIG. 5A to FIG. 5F The implementation methods in are only examples of potentially integrating physical models into DNN architectures through a combination of cascade stacking, parallel aggregation, jump aggregation, interleaved control, etc.

[0090] Some embodiments use SSFM instead of RP as the underlying physical model to generalize the adjustable model with additional phasor correction and low-pass filter. For the SSFM model, there are four different variants: i) simple SSFM; ii) full SSFM; iii) reduced SSFM; iv) Agrawal SSFM, as follows.

[0091]

[0092] Some embodiments use different parameterizations according to those different types of SSFM physical models. Agrawal SSFM requires an iterative loop to propagate the waveform. Some embodiments use implicit neural networks to solve the iterative process. For example, the Neural Ordinary Differential Equation (NODE), Deep Equilibrium (DEQ), and the Neural Diffusion Model are used to implement a PINN-based equalizer. Although linear operations are usually implemented in the frequency domain, some embodiments may also use time domain convolution or filtering. In addition, both time domain and frequency domain operations are mixed in the PINN architecture. For WDM and spatial multiplexing systems, for some embodiments, spatial domain processing is also incorporated into the PINN. The equalizer is also used as a pre-equalizer or pre-distortion method at the transmitter, which reverses the signal distortion in a similar manner before transmission through the channel for post-equalization at the receiver. Some embodiments use both pre-equalizers and post-equalizers.

[0093] In addition to RP and SSFM, there are different methods to solve NLSE. For example, the Runge-Kutta (RK) method, which is one of the point matching methods, can numerically solve PDE with higher accuracy. Some embodiments use the RK model integrated in the DNN architecture to solve the inverse NLSE. Another embodiment of the numerical method is the exponential integrator (EI), in which the matrix exponential operator uses the Krylov subspace approximation. For example, the Marcus method and the Blow-Wood method are used as the EI framework. Some embodiments use the EI method as a PINN-based equalization.

[0094] Nonlinear Fourier Transform (NFT)

[0095] There is another physical modeling framework called nonlinear Fourier transform (NFT) to solve NLSE. NFT transforms the waveform to the eigendomain where the NLSE dynamic table behaves linearly. For example, the Koopman operator implements NFT. To implement the Koopman-based NFT, the example PINN uses an autoencoder (AE) that can be used to find a coordinate transformation that transforms a nonlinear PDE into a linear PDE. Some embodiments of the present invention use the Koopman-AE DNN to model the behavior of the Manakov equation applied to nonlinear optical fibers. For long sequence transformations with high oversampling rates, some embodiments split the symbol sequence into smaller blocks and splice them together at the end. In order to deal with the channel memory effects caused by dispersion, block overlap and edge discarding are used during DNN recovery. Specifically, a sliding window is applied to the DNN input tensor and the edge samples of each processing block are discarded. PINN is trained to minimize the minimum square error function (MSE) between time-domain SSFM data and generated predictions. In this case, the task of the KoopmanDNN is to predict each step of a 100-step SSFM Manakov simulation over several fiber spans. For some embodiments, other cost functions such as cross entropy loss are used instead.Some embodiments use a reversible residual network to facilitate the optimization of forward NFT and inverse NFT.

[0096] End-to-end design based on digital twins

[0097] PINN-based equalization can provide additional benefits to optimize other system parameters such as pulse shaping filters, modulation schemes, constellation shaping, and FEC parameters through gradient propagation on the system graph. For example, once the LRP-based PINN model is trained to model the channel for communication, the trained PINN model can be used to predict forward behavior and backward behavior as a digital twin model. In this way, PINN implements end-to-end design of transmitter parameters and receiver parameters. For some embodiments, those parameters are also trained by reinforcement learning for gradient-free optimization. For some embodiments, the end-to-end design is extended to design intermediate subsystem components such as parametric amplifiers, repeaters, relays, switches, and routers. For example, routing optimization and gain control at the amplifier are implemented by a digital twin PINN model.

[0098] Other features

[0099] Other embodiments include quantum communication, where quantum physics is modeled in a PINN-based equilibrium. Yet another embodiment includes molecular communication, where molecular dynamics and chemical reaction physics are integrated into a PINN-based equilibrium. Some other embodiments use neuronal communication, where neuronal physics is modeled in a PINN-based equilibrium.

[0100] Figure 7 An exemplary block diagram of a system suitable for implementing different components of a receiver for decoding, equalization, and deshaping according to some embodiments and / or a transmitter for encoding, pre-equalization, and forward codewords according to some embodiments is shown. System 1700 may include one or a combination of sensor 1710, inertial measurement unit (IMU) 1730, processor 1750, memory 1760, transceiver 1770, and display / screen 1780, which may be operably coupled to other components via connection 1720. Connection 1720 may include a bus, wire, fiber, link, or a combination thereof.

[0101] The transceiver 1770 may, for example, include a transmitter capable of transmitting one or more signals through one or more types of communication networks and a receiver capable of receiving one or more signals transmitted through one or more types of communication networks. The transceiver 1770 may allow communication with a wired or wireless network based on various technologies, such as but not limited to a femtocell, a Wi-Fi network or a wireless local area network (WLAN) (which may be based on the IEEE 802.11 family of standards), a wireless personal area network (WPAN) (such as Bluetooth), a near field communication (NFC), a network based on the IEEE 802.11 family of standards, and / or a wireless wide area network (WWAN) (such as LTE, WiMAX, etc.). The system may also include one or more ports for communicating through a wired network such as fiber optic communications.

[0102] In some embodiments, the processor 1750 may also receive input from the IMU 1730. In other embodiments, the IMU 1730 may include a 3-axis accelerometer, a 3-axis gyroscope, and / or a magnetometer. The IMU 1730 may provide speed, orientation, and / or other position-related information to the processor 1750. In some embodiments, the IMU 1730 may output measured information in synchronization with each image frame captured by the sensor 1710. In some embodiments, the processor 1750 uses, in part, the output of the IMU 1730 to fuse sensor measurements and / or further process the fused measurements.

[0103] The system 1700 may also include a screen or display and a speaker 1780 that presents images (such as color and / or depth images). In some embodiments, the display and speaker 1780 may be used to display real-time images, fused images, augmented reality images, graphical user interfaces (GUIs), and other program outputs captured by the sensor 1710. In some embodiments, the display 1780 may include a touch screen and / or be housed with a touch screen to allow a user to input data via a virtual keyboard, icons, menus, or other GUIs, user gestures, and / or input devices (such as styluses and other writing tools). In some embodiments, the display 1780 may be implemented using a liquid crystal display or a light emitting diode (LED) display (such as an organic LED display). In other embodiments, the display 1780 may be a wearable display.

[0104] The exemplary system 1700 may also be modified in various ways consistent with the present disclosure, such as by adding, combining, or omitting one or more functional blocks shown. For example, in some configurations, the system 1700 does not include an IMU 1730 or a sensor 1770. In some implementations, portions of the system 1700 take the form of one or more chipsets, etc.

[0105] The processor 1750 may be implemented using a combination of hardware, firmware, and software. The processor 1750 may represent one or more circuits that may be configured to perform at least a portion of an operational program or process associated with sensor fusion and / or a method for further processing fused measurements. The processor 1750 retrieves instructions and / or data from the memory 1760. The processor 1750 may be implemented using one or more application specific integrated circuits (ASICs), central processing units (CPUs), graphics processing units (GPUs), digital signal processors (DSPs), DSP devices, programmable logic devices (PLDs), field programmable gate arrays (FPGAs), controllers, microcontrollers, microprocessors, embedded processor cores, quantum computing processors, electronic devices, quantum processors, molecular processors, other electronic units designed to perform the functions described herein, or a combination thereof.

[0106] Memory 1760 may be implemented within processor 1750 and / or external to processor 1750. As used herein, the term "memory" refers to any type of long-term, short-term, volatile, non-volatile, or other memory, and is not limited to any particular type of memory or amount of memory, or type of physical medium on which the memory is stored. In some embodiments, memory 1760 stores program code that facilitates equalization, pre-equalization, decoding, shaping, de-shaping, and encoding.

[0107] In some embodiments, additionally or alternatively, the processor 1750 can perform one or a combination of encoding, decoding, and shaping / deshaping applications 1755. For example, the output of the decoding can be used to decode a cascaded ECC formed by combining multiple component ECCs into a higher performance code. Another embodiment is a system that uses iterative equalization and decoding, where the soft decision output from the decoder is fed back to the demodulator to iteratively refine the decoder input. Yet another embodiment acts on the decoded output, for example, displaying the output on a display and speaker 1780, storing the output in a memory 1760, transmitting the output using a transceiver 1770, and / or taking action based on the measurement of the sensor 1710 output and.

[0108] In addition, another embodiment of the present invention can provide an encoder circuit for generating encoded digital data from input digital data. The encoder / shaping circuit is configured to generate encoded / shaped digital data from a source bit stream as input digital data. The encoder / shaping circuit is configured to receive a source bit stream 111, at least one storage repository configured to store a computer executable coding method (program / computer executable instructions / or equivalent circuit) and one or more computing processors, and the one or more computing processors are configured to generate code words from input digital data as encoded digital data by performing the steps of the computer executable coding method. In this case, the computer executable coding method is configured to cause the processor to perform steps based on code specifications. In some embodiments, the generated digital data is modulated to be fed into the communication channel 120 via the front-end circuit 115.

[0109] All of the above embodiments of the present invention may be implemented in any of a variety of ways. For example, the embodiments may be implemented using hardware, firmware, software, or a combination thereof. When implemented in software, the software code may be executed on any suitable processor or set of processors (whether provided in a single computer or distributed in multiple computers). Such processors may be implemented as integrated circuits, wherein one or more processors are in an integrated circuit component. However, the processor may be implemented using circuits of any suitable format.

[0110] Moreover, embodiments of the present invention may be embodied as a method, an example of which has been provided. The actions performed as part of the method may be ordered in any suitable manner. Thus, embodiments may be constructed in which the actions are performed in a different order than shown, which may include performing some actions simultaneously (even if shown as sequential actions in illustrative embodiments).

[0111] The use of ordinal terms such as "first", "second" and the like in the claims to modify claim elements does not in itself imply any priority, precedence or order of one claim element relative to another claim element or a temporal order of the actions of a method of performing the method, but merely serves as a label to distinguish one claim element with a particular name from another element with the same name (but for the use of ordinal terms to distinguish claim elements).

[0112] Although the invention has been described by way of examples of preferred embodiments, it is to be understood that various other adaptations and modifications may be made within the spirit and scope of the invention.

[0113] Therefore, it is the object of the appended claims to cover all such variations and modifications as fall within the true spirit and scope of the invention.

Claims

1. A system for communicating data via a channel link, the system comprising: a communication module, the communication module being configured to access the channel link according to the specification set of the data communication; as well as A controller is configured to include a physical information neural network PINN, wherein the controller is configured to determine the parameters represented by the specification set of the communication module according to the physical model of the channel link to compensate for the signal waveform distortion in the data communication.

2. The system according to claim 1, wherein: The channel link is based on electromagnetic propagation, light wave propagation, acoustic propagation, molecular propagation or variations thereof for the data communication.

3. The system according to claim 1, wherein: The set of specifications for the communication module includes parameter sets for a channel encoder, a data compressor, a constellation shaper, a modulator, a pulse shaping filter, a multiplexer, a pre-equalizer, an amplifier, a digital-to-analog converter, an oscillator, an antenna, a mixer, an analog-to-digital converter, an equalizer, a demultiplexer, a demodulator, a constellation deshaper, a data decompressor, a channel decoder and variations thereof.

4. The system according to claim 3, wherein: The parameter set includes a channel coding generation matrix, a shaping rate, a shaping method, a modulation format, a pulse shaping filter length, a pre-equalization method, an amplifier gain, a sampling rate and quantization bits of a digital-to-analog converter, an oscillator frequency of an analog-to-digital converter, an antenna size, a sampling rate and quantization bits, an equalization method, a demodulation method, a constellation deshaping method, a channel decoder method and variants thereof.

5. The system according to claim 1, wherein: The physical model of the channel link is based on finite difference methods such as the split-step Fourier method, finite element methods such as conventional perturbations, collocation models such as Runge-Kutta integration, Volterra series expansion, Koopman operator, exponential integrator, ordinary differential equations, partial differential equations, nonlinear Schrodinger equations, finite impulse response, infinite impulse response, autoregressive model, diffusion process, space-time-frequency dispersion model, Maxwell equations, quantum dynamics, molecular dynamics and their variants.

6. The system according to claim 1, wherein: The PINN is configured to integrate the physical model of the channel link into a deep neural network (DNN) with an additional set of trainable parameters to adjust residual errors caused by model mismatch.

7. The system according to claim 6, wherein: The DNN integrated with the PINN is based on a combination of parallel aggregation, cascade stacking, interleaved control, skip aggregation and their variants.

8. The system according to claim 1, wherein: The PINN is based on the cascaded use of conventional perturbation models with phase corrections trained by a deep neural network DNN, which uses statistical information of the channel link to adaptively modify the set of specifications of the communication module.

9. The system according to claim 1, wherein: The communication module uses another PINN modified by the controller to further modify the set of specifications of the communication module, such as a pre-equalizer and an equalizer.

10. The system according to claim 1, wherein: The communication module comprises: An encoder configured to encode data into codewords based on a channel code; a reshaping mapper, the reshaping mapper being used to map the codeword to an amplitude symbol; A pre-equalizer, the pre-equalizer being used to modify the mapped amplitude symbols into pre-equalization symbols based on the physical model using a trained physical information neural network PINN; A digital-to-analog converter, the digital-to-analog converter being used to transmit the digital data of the pre-equalized symbols as channel data through the channel link; an analog-to-digital converter, the analog-to-digital converter being configured to receive the channel data from the channel link to generate a received symbol; a demodulator for modifying the received symbols into intermediate estimates of the digital data; a PINN-based post-equalizer for mitigating channel noise and waveform distortion caused by the channel link based on the intermediate estimate of the digital data to produce equalized data; a reshaping demapper, the reshaping demapper being used to modify the equalized data into a deshaping bit sequence as deshaping data; a decoder that decodes the deshaped data to correct a residual error by using channel decoding; and Its variants.

11. A method for communicating data via a channel link, the method comprising the steps of: accessing the channel link according to a communication method based on a set of specifications for the data communication; as well as According to the physical model of the channel link, the specification set of the data communication is modified according to the control method based on the physical information neural network PINN.

12. The method according to claim 11, wherein: The channel link is based on electromagnetic propagation, light wave propagation, acoustic propagation, molecular propagation or variations thereof for the data communication.

13. The method according to claim 11, wherein: The set of specifications for the data communication includes a set of parameters for channel coding, data compression, constellation shaping, modulation, pulse shaping filtering, multiplexing, pre-equalization, amplification, digital-to-analog conversion, oscillation, analog-to-digital conversion, equalization, demultiplexing, demodulation, constellation deshaping, data decompression, channel decoding and their variations.

14. The method according to claim 13, wherein: The parameter set includes a generation matrix of channel coding, a shaping rate, a shaping method, a modulation format, a pulse shaping filter length, a pre-equalization method, an amplification gain, a sampling rate and a quantization bit of digital-to-analog conversion, an oscillation frequency, a sampling rate and a quantization bit of analog-to-digital conversion, an equalization method, a demodulation method, a constellation deshaping method, a channel decoding method and variants thereof.

15. The method according to claim 11, wherein: The physical model of the channel link is based on finite difference methods such as the split-step Fourier method, finite element methods such as conventional perturbations, collocation models such as Runge-Kutta integration, Volterra series expansion, Koopman operator, exponential integrator, ordinary differential equations, partial differential equations, nonlinear Schrodinger equations, finite impulse response, infinite impulse response, autoregressive model, diffusion process, space-time-frequency dispersion model, Maxwell equations, quantum dynamics, molecular dynamics and their variants.

16. The method according to claim 11, wherein: The PINN is configured to integrate the physical model of the channel link into a deep neural network (DNN) with an additional set of trainable parameters to adjust residual errors caused by model mismatch.

17. The method according to claim 16, wherein: The DNN integrated with the PINN is based on a combination of parallel aggregation, cascade stacking, interleaved control, skip aggregation and their variants.

18. The method according to claim 11, wherein: The PINN is based on the cascaded use of conventional perturbation models with phase corrections trained by a deep neural network DNN, which uses statistical information of the channel link to adaptively modify the set of specifications of the communication module.

19. The method according to claim 11, wherein: The communication method uses another PINN modified by the control method to further modify the set of specifications of the communication method, such as pre-equalization and equalization.

20. The method according to claim 11, wherein: The communication method comprises a combination of the following steps: Acquiring source data to be transmitted via the data interface port of the data communication; Encoding the source data into codewords based on channel coding; Mapping the codeword to an amplitude symbol; Using pre-equalization based on a trained physical information neural network PINN, the mapped amplitude symbols are modified into pre-equalization symbols based on the physical model; transmitting the digital data of the pre-equalized symbols as channel data via the channel link; receiving the channel data from the channel link to generate receive symbols; demodulating the received symbols to produce an intermediate estimate of the digital data; mitigating channel noise and waveform distortion caused by the channel link based on the intermediate estimate of the digital data using PINN-based post-equalization to produce equalized data; converting the equalized data into a deshaped bit sequence as deshaped data by using a shaping demapping; decoding the deshaped data using channel decoding to correct residual errors; storing the corrected channel data to a data sink; and Its variants.

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