Optical communication transmission quality cross-layer sensing method and system based on deep neural network

Abstract

The invention discloses an optical communication transmission quality cross-layer sensing method and system based on a deep neural network, and belongs to the field of data optical communication, and the method comprises the following steps: collecting optical path physical layer damage information through simulation optical communication network transmission, and generating a physical layer information data set; extracting physical damage characteristics related to transmission quality from the physical layer information data set, predicting optical communication transmission quality based on the physical damage characteristics by using a deep neural network model, and constructing a loss function based on a transmission quality predicted value and a transmission quality index to optimize model parameters; and predicting the cross-layer perception transmission quality of the new optical communication network by using the parameter-optimized deep neural network model, and optimizing the network configuration of the new optical communication network according to the cross-layer perception transmission quality to realize the network cross-layer design of physical layer perception.

Description

Technical Field

[0001] The present invention belongs to the technical field of optical communication, and particularly relates to a cross-layer perception method and system for the transmission quality of optical communication based on a deep neural network. Background Art

[0002] In recent years, with the emergence and wide application of optical communication technologies and devices such as coherent optical detection, dense wavelength division multiplexing, and reconfigurable optical add-drop multiplexers, the data rate and transmission distance of optical communication have been greatly improved, and high-speed, long-distance transmission and all-optical networks have become an inevitable trend for future optical communication. On the other hand, with the development of digital signal processing technology at the optical communication transceiver end, multi-carrier modulation methods with higher spectral efficiency and more flexible parameter configuration have been widely studied, providing an efficient signal transmission solution for optical communication systems and networks. However, the continuously increasing data rate and distance will bring serious physical layer impairments to optical communication (such as transceiver noise, fiber dispersion, noise caused by amplifier spontaneous emission, crosstalk, etc.), affecting the transmission quality (Quality of Transmission, QoT) of optical communication. In the past, the planning of optical networks was based on ideal physical layer transmission conditions. With the increase of physical layer impairments, it is necessary to conduct cross-layer design to configure and optimize optical networks based on physical layer impairments.

[0003] QoT estimation is an important part of optical communication. During network deployment, the link performance estimated by QoT can be used to improve the existing or candidate network configurations, monitor the health of existing optical paths, or check the feasibility of candidate optical paths by comparing the predicted QoT with a predefined threshold. Compared with traditional physical models (such as the distributed Fourier method, Gaussian noise model, etc.), the machine learning-based QoT estimation method can better model complex link components (such as optical amplifiers, etc.), with fast modeling speed and low computational complexity in practical applications, and has been widely studied in the QoT estimation of optical communication networks. Through literature retrieval, some research scholars based on the Artificial Neural Network (ANN), by simulating the optical network structure, using the vector composed of the optical path length, the number of optical amplifiers, the maximum link length, the destination node order, and the wavelength as input features, the ANN judges the Bit Error Rate (BER) and outputs 0 or 1 (0: this network configuration does not meet the transmission requirements; 1: this network configuration meets the transmission requirements), achieving a judgment accuracy rate of over 95%. Through literature retrieval again, some other research scholars based on the Deep Neural Network (DNN), on a 563.4 km field test bench from Bristol to London in the UK, using the transmit power, laser bias, input and output powers of optical amplifiers as input features, estimate the Q factor, achieving a Root Mean Square Error (RMSE) of less than 0.02 dB. The above methods directly and efficiently estimate the QoT of optical networks through machine learning methods, but do not consider the impact of physical layer impairments on QoT.

[0004] In summary, to ensure the efficient configuration of future optical communication and achieve high-speed long-distance communication, it is necessary to consider the impact of physical layer impairments on transmission quality when deploying the network structure. Optimizing the configuration of optical communication networks based on QoT will greatly improve the service quality and service flexibility of future optical communication. Therefore, it is necessary to provide a cross-layer perception scheme for transmission quality based on physical layer information applicable to optical communication networks. Summary of the Invention

[0005] In view of the above, the object of the present invention is to provide a cross-layer perception method and system for optical communication transmission quality based on a deep neural network, design a deep neural network model, estimate the transmission quality according to the physical layer impairments of optical communication, and the transmission quality perceived based on physical layer impairments helps to optimize the configuration of optical communication network parameters and realize the cross-layer design of the network with physical layer perception.

[0006] To achieve the above object of the invention, a cross-layer perception method for optical communication transmission quality based on a deep neural network provided by an embodiment includes the following steps: Collect the physical layer impairment information of the optical path through the simulation of the optical communication network and generate a physical layer information dataset; Extract the physical layer impairment information related to the transmission quality from the physical layer information dataset as physical impairment features, use a deep neural network model to predict the optical communication transmission quality based on the physical impairment features, and construct a loss function based on the transmission quality prediction value and the transmission quality index to optimize the model parameters; Use the deep neural network model with optimized parameters to predict the cross-layer perception transmission quality of the new optical communication network structure, and optimize the network configuration of the new optical communication network according to the cross-layer perception transmission quality.

[0007] As a further preferred technical solution of the above technical solution, collecting the physical layer impairment information of the optical path through the simulation of the optical communication network and generating a physical layer information dataset includes: Simulate different network topologies and transmission signals, adjust the configuration parameters of the optical communication network, and simulate the changes in the optical path transmission conditions; For all optical paths in the optical communication network, collect the inter-symbol interference, amplifier noise, nonlinear effects, and node crosstalk as the physical layer impairment information of the optical path and as physical impairment features, and use the optical signal-to-noise ratio as the transmission quality index for supervision to generate a physical layer information dataset.

[0008] As a further preferred technical solution of the above technical solution, the configuration parameters of the optical communication network include: the number of spans, span length, bit rate, signal peak power, fiber loss, dispersion coefficient, and nonlinear coefficient.

[0009] As a further preferred technical solution of the above technical solution, extract at least one of the inter-symbol interference, amplifier noise coefficient, nonlinear effect coefficient, and node crosstalk from the physical layer information dataset as the physical impairment feature related to the transmission quality.

[0010] As a further preferred technical solution of the above technical solution, the loss function constructed based on the transmission quality prediction value and the transmission quality index uses the MSE function.

[0011] As a further preferred technical solution of the above technical solution, the deep neural network model includes an input layer, multiple hidden layers, and an output layer, uses the Leaky ReLU function as the activation function of the hidden layer, and uses the linear function as the activation function of the output layer.

[0012] As a further preferred technical solution of the above technical solution, before the physical impairment features are input into the deep neural network model, they are also subjected to standardization or max-min normalization processing, and the processed physical impairment features are input into the deep neural network model.

[0013] As a further preferred technical solution of the above technical solution, the network configuration of the new optical communication network is optimized according to the cross-layer perceived transmission quality, including: Select a path with low physical damage according to the predicted transmission quality to achieve dynamic routing optimization, specifically increasing the number of spans, dynamically adjusting the span length, increasing the signal transmission rate, and reducing the bit error rate in the original link; Adopt elastic optical network technology, dynamically allocate wavelength intervals according to channel quality, and adjust the modulation formats of different links. Use narrow intervals and high-order modulation formats in high optical signal-to-noise ratio links, and switch to wide intervals and more robust modulation formats in low optical signal-to-noise ratio links.

[0014] To achieve the above invention purpose, the embodiment also provides an optical communication transmission quality cross-layer perception system based on a deep neural network, including: A physical layer information dataset construction module, which is used to collect optical path physical layer damage information through simulating optical communication network transmission and generate a physical layer information dataset; A deep neural network model construction and parameter optimization module, which is used to extract physical layer damage information related to transmission quality from the physical layer information dataset as physical damage features, use the deep neural network model to predict the optical communication transmission quality based on the physical damage features, and construct a loss function based on the transmission quality prediction value and the transmission quality index to optimize the model parameters; A transmission quality estimation and optimization module, which is used to predict the cross-layer perceived transmission quality of the new optical communication network structure by using the parameter-optimized deep neural network model, and optimize the network configuration of the new optical communication network according to the cross-layer perceived transmission quality.

[0015] To achieve the above invention purpose, the embodiment also provides a computing device, including a memory and one or more processors. An executable code is stored in the memory. When the one or more processors execute the executable code, it is used to implement the above-mentioned optical communication transmission quality cross-layer perception method based on a deep neural network.

[0016] To achieve the above invention purpose, the embodiment also provides a computer-readable storage medium, on which a program is stored. When the program is executed by a processor, it implements the above-mentioned optical communication transmission quality cross-layer perception method based on a deep neural network.

[0017] Compared with the prior art, the beneficial effects of the present invention at least include: The optical communication transmission quality cross-layer perception algorithm based on a deep neural network introduces physical layer damage into the QoT estimation algorithm, designs a deep neural network model, estimates the transmission quality according to the optical communication physical layer damage, and the transmission quality based on physical layer damage perception helps to optimize the optical communication network parameter configuration and realize the network cross-layer design with physical layer perception. Brief Description of the Drawings

[0018] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0019] Figure 1 is a flowchart of the cross-layer perception method for optical communication transmission quality based on a deep neural network provided by the embodiment; Figure 2 is a schematic diagram of the optical path structure applied to the acquisition of the physical layer damage data set provided by the embodiment; Figure 3 is a schematic diagram of the structure of the deep neural network model provided by the embodiment; Figure 4 is a training process diagram of the deep neural network model provided by the embodiment; Figure 5 is a schematic diagram of the structure of the cross-layer perception system for optical communication transmission quality based on a deep neural network provided by the embodiment. Detailed Embodiments

[0020] To make the objectives, technical solutions and advantages of the present invention clearer, the following further details the present invention with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not limit the protection scope of the present invention.

[0021] The inventive concept of the present invention is as follows: The embodiments of the present invention provide a cross-layer perception solution for optical communication transmission quality based on a deep neural network, which can estimate the transmission quality based on the physical layer damage of optical communication. The transmission quality perceived based on the physical layer damage helps to optimize the configuration of optical communication network parameters and realize the cross-layer design of the network with physical layer perception.

[0022] As Figure 1 shown, a cross-layer perception method for optical communication transmission quality based on a deep neural network provided by the embodiment includes the following steps: S1, construction of the physical layer information data set: Collect the optical path physical layer damage information through simulating the optical communication network transmission and generate the physical layer information data set.

[0023] In the embodiment, first, different network topologies and transmission signals are simulated, the configuration parameters of the optical communication network are adjusted, and the changes in the optical path transmission conditions are simulated. Specifically, optical network topologies such as NSFNET and CERNET are adopted, transmission signals such as QPSK signals are transmitted, and the configuration parameters include the number of spans, span length, bit rate, signal peak power, fiber loss, dispersion coefficient, nonlinear coefficient, etc.

[0024] Then, for all optical paths in the optical communication network, inter-symbol interference, amplifier noise, nonlinear effects, and node crosstalk are collected as optical path physical layer damage information. Among them, this optical path physical layer damage information serves as the physical damage characteristics of the deep neural network model, and the optical signal-to-noise ratio (Optical Signal-to-Noise Ratio, OSNR) is selected as the transmission quality index to generate a physical layer information data set for model training.

[0025] Figure 2 The figure shows a schematic diagram of an optical path structure for obtaining a simulation data set of optical network physical layer damage. The main parts include an optical switching module, an optical fiber link composed of optical fibers, and an optical amplifier. Among them, the optical switching module can be an optical cross-connect or a reconfigurable optical add-drop multiplexer, introducing single-node or multi-node crosstalk; the optical fiber can be a single-mode optical fiber, used to connect each optical device and introduce dispersion and nonlinear crosstalk; the optical amplifier can compensate for fiber loss and introduce amplified spontaneous emission-related noise. Inter-symbol interference is caused by fiber dispersion and self-phase modulation, and the amplified spontaneous emission-related noise can be directly obtained according to the network topology. By changing the above optical path structure, different main physical layer damage information and corresponding OSNR are obtained, and the OSNR is used as the transmission quality index. A physical layer information data set is generated based on the simulated physical layer damage information and OSNR for training the deep neural network model.

[0026] S2. Construction and parameter optimization of the deep neural network model: Extract the physical layer damage information related to the transmission quality from the physical layer information data set, use the deep neural network model to predict the optical communication transmission quality based on the physical damage characteristics, and construct a loss function based on the transmission quality prediction value and the transmission quality index to optimize the model parameters.

[0027] In the embodiment, the designed deep neural network model includes an input layer, a hidden layer, and an output layer. Among them, the neurons in each layer adopt a fully connected method. The number of neurons in the input layer is the number of physical damage features, and the number of neurons in the output layer is the number of transmission quality indicators. By optimizing the parameters of the neural network model, the relationship between the physical damage of the optical path and the transmission quality is modeled to perceive the transmission quality of the optical path. Specifically, the input layer is the physical loss feature, which extracts the physical layer damage information related to the transmission quality from the physical layer information dataset. Specifically, at least one of the inter-symbol interference, amplifier noise coefficient, non-linear effect coefficient, and node crosstalk in the physical layer information dataset is extracted as the physical damage feature related to the transmission quality. The output layer is the transmission quality indicator (such as OSNR). More specifically, as Figure 3 shown, the designed deep neural network model contains 6 hidden layers.

[0028] Using the above constructed deep neural network model to predict the optical communication transmission quality based on the physical damage features, and constructing a loss function based on the predicted transmission quality value and the transmission quality indicator to optimize the model parameters, as Figure 4 shown, the specific process is as follows: First, since the selected physical damage feature dimensions are not unified, before using the deep neural network model for gradient descent optimization, it is necessary to normalize the physical damage features first to enhance the learning ability of the network model. Specifically, the standardization or max-min normalization method is adopted.

[0029] Then, the physical layer information dataset is randomly divided into a training set and a validation set according to the ratio of 75% and 15%. For forward propagation, the Leaky ReLU function is used as the activation function of the hidden layer, and the linear function is used as the activation function of the output layer. The predicted transmission quality value is obtained through the activation function and compared with the transmission quality indicator as the label; Next, for gradient calculation, the MSE function is used as the loss function. The loss value calculated from the predicted transmission quality value and the transmission quality indicator reflects the forward propagation result. The derivative of the loss value with respect to the weight is calculated for each neuron in each layer of the model to obtain the gradient of each neuron, which is used for model parameter optimization; for backpropagation, the Adam optimizer is used to update the gradient, and the training starts with a learning rate of 0.001; during the training process, batch normalization and Dropout are performed before and after the activation function respectively to prevent gradient explosion and overfitting problems. After multiple rounds of training (for example, 200 rounds), the best deep neural network model parameters are obtained.

[0030] S3. Transmission quality estimation and optimization: Use the deep neural network model with optimized parameters to predict the cross-layer perception transmission quality of the new optical communication network structure, and optimize the network configuration of the new optical communication network according to the cross-layer perception transmission quality.

[0031] In the embodiment, a cross-layer perception calculation of an optical communication network is performed using a parameter-optimized deep neural network model. Specifically, for a new network topology structure in simulation or an actual optical communication network, which is a new optical communication network structure for the model, the physical layer damage information of the new optical communication network structure is collected, and the deep neural network model is used to predict the optical signal-to-noise ratio as the transmission quality based on the physical layer damage information to verify its ability to cross-layer perceive the transmission quality. Then, the communication network structure and parameters are improved and optimized based on the cross-layer perceived transmission quality. Specifically, a path with low physical damage is selected according to the predicted transmission quality (such as OSNR) to achieve dynamic routing optimization; the number of spans is increased in the original link, the span length is dynamically adjusted, the signal transmission rate is increased, and the bit error rate is reduced. Among them, the level of OSNR is determined according to user requirements. When the OSNR is higher, it indicates lower physical damage. For example, when the OSNR is higher than 20 dB, it is considered to correspond to low physical damage. In addition, the Elastic Optical Network (EON) technology can be adopted to dynamically allocate wavelength intervals according to the channel quality and adjust the modulation format of different links. A narrow interval and a high-order modulation format are used in high-OSNR links, and the link is switched to a wide interval and a more robust modulation format (such as QPSK) in low-OSNR links.

[0032] As Figure 5 shown, the embodiment also provides a cross-layer perception system for optical communication transmission quality based on a deep neural network, including: a physical layer information dataset construction module, a deep neural network model construction and parameter optimization module, and a transmission quality estimation and optimization module. Among them, the physical layer information dataset construction module is used to collect the optical path physical layer damage information through the simulation optical communication network transmission and generate a physical layer information dataset; the deep neural network model construction and parameter optimization module is used to extract the physical layer damage information related to the transmission quality from the physical layer information dataset as physical damage features, use the deep neural network model to predict the optical communication transmission quality based on the physical damage features, and construct a loss function based on the transmission quality prediction value and the transmission quality index to optimize the model parameters; the transmission quality estimation and optimization module is used to predict the cross-layer perception transmission quality of the new optical communication network structure using the parameter-optimized deep neural network model and optimize the network configuration of the new optical communication network according to the cross-layer perception transmission quality.

[0033] It should be noted that when the above-mentioned optical communication transmission quality cross-layer perception device based on a deep neural network performs optical communication transmission quality cross-layer perception, the above-mentioned division of each functional module should be used for illustration. The above functions can be assigned to different functional modules according to needs, that is, the internal structure of the terminal or server is divided into different functional modules to complete all or part of the functions described above. In addition, the above-mentioned optical communication transmission quality cross-layer perception device based on a deep neural network and the embodiment of the optical communication transmission quality cross-layer perception method based on a deep neural network belong to the same concept. For the specific implementation process, please refer to the embodiment of the optical communication transmission quality cross-layer perception method based on a deep neural network, which will not be elaborated here.

[0034] Based on the same inventive concept, the embodiment also provides a computing device, including a memory and one or more processors. The memory stores executable code. When the one or more processors execute the executable code, it is used to implement the above-mentioned optical communication transmission quality cross-layer perception method based on a deep neural network, specifically including the following steps: S1, Physical layer information dataset construction: Collect optical path physical layer damage information through simulating optical communication network transmission, and generate a physical layer information dataset; S2, Deep neural network model construction and parameter optimization: Extract physical layer damage information related to transmission quality from the physical layer information dataset, use the deep neural network model to predict the optical communication transmission quality based on physical damage characteristics, and construct a loss function based on the transmission quality prediction value and the transmission quality index to optimize the model parameters; S3, Transmission quality estimation and optimization: Use the deep neural network model with optimized parameters to predict the cross-layer perception transmission quality of the new optical communication network structure, and optimize the network configuration of the new optical communication network according to the cross-layer perception transmission quality.

[0035] For the computing device provided in the embodiment, at the hardware level, in addition to including a processor and a memory, it also includes other hardware required for other services such as an internal bus, a network interface, and a memory. The memory is a non-volatile memory. The processor reads the corresponding computer program from the non-volatile memory into the memory and then runs it to implement the above-mentioned optical communication transmission quality cross-layer perception method described in S1-S3. Of course, in addition to the software implementation method, the present invention does not exclude other implementation methods, such as logic devices or a combination of software and hardware, etc. That is to say, the execution subject of the following processing flow is not limited to each logic unit, and can also be hardware or a logic device.

[0036] Based on the same inventive concept, the embodiment also provides a computer-readable storage medium, on which a program is stored. When the program is executed by a processor, it implements the above-mentioned optical communication transmission quality cross-layer perception method, specifically including the following steps: S1, Physical layer information dataset construction: Collect optical path physical layer damage information through simulating optical communication network transmission, and generate a physical layer information dataset; S2, Deep neural network model construction and parameter optimization: Extract physical layer damage information related to transmission quality from the physical layer information dataset, use the deep neural network model to predict the optical communication transmission quality based on physical damage features, and construct a loss function based on the transmission quality prediction value and transmission quality indicators to optimize the model parameters; S3, Transmission quality estimation and optimization: Use the deep neural network model with optimized parameters to predict the cross-layer perception transmission quality of the new optical communication network structure, and optimize the network configuration of the new optical communication network according to the cross-layer perception transmission quality.

[0037] In the embodiment, the computer-readable medium includes permanent and non-permanent, removable and non-removable media, and information storage can be implemented by any method or technology. The information can be computer-readable instructions, data structures, program modules, or other data.

[0038] The above specific embodiments have detailed the technical solutions and beneficial effects of the present invention. It should be understood that the above is only the most preferred embodiment of the present invention and is not used to limit the present invention. Any modifications, supplements, equivalent replacements, etc. made within the scope of the principles of the present invention shall be included in the protection scope of the present invention.

Claims

1. A cross-layer perception method for optical communication transmission quality based on a deep neural network, characterized in that It includes the following steps: Transmit and collect optical path physical layer damage information through a simulated optical communication network, and generate a physical layer information dataset; Extract the physical layer damage information related to transmission quality from the physical layer information dataset as physical damage features, use a deep neural network model to predict the optical communication transmission quality based on the physical damage features, and construct a loss function based on the transmission quality prediction value and the transmission quality index to optimize the model parameters; Use the deep neural network model with optimized parameters to predict the cross-layer perception transmission quality of the new optical communication network structure, and optimize the network configuration of the new optical communication network according to the cross-layer perception transmission quality.

2. The cross-layer perception method for optical communication transmission quality based on a deep neural network according to claim 1, wherein Transmit and collect optical path physical layer damage information through a simulated optical communication network, and generate a physical layer information dataset, including: Simulate different network topologies and transmission signals, adjust the configuration parameters of the optical communication network, and simulate the changes in the optical path transmission conditions; For all optical paths in the optical communication network, collect inter-symbol interference, amplifier noise, non-linear effects, and node crosstalk as optical path physical layer damage information and use them as physical damage features, and use the optical signal-to-noise ratio as the transmission quality index for supervision to generate a physical layer information dataset.

3. The cross-layer perception method for optical communication transmission quality based on a deep neural network according to claim 2, characterized in that, The configuration parameters of the optical communication network include: the number of spans, span length, bit rate, signal peak power, fiber loss, dispersion coefficient, and non-linear coefficient.

4. The cross-layer perception method for optical communication transmission quality based on a deep neural network according to claim 2, characterized in that Extract at least one of inter-symbol interference, amplifier noise coefficient, non-linear effect coefficient, and node crosstalk from the physical layer information dataset as the physical damage feature related to transmission quality.

5. The cross-layer perception method for optical communication transmission quality based on a deep neural network according to claim 1, characterized in that The loss function constructed based on the transmission quality prediction value and the transmission quality index uses the MSE function; The deep neural network model includes an input layer, multiple hidden layers, and an output layer, uses the Leaky ReLU function as the activation function of the hidden layer, and uses the linear function as the activation function of the output layer.

6. The cross-layer perception method for optical communication transmission quality based on a deep neural network according to claim 1, characterized in that Before being input into the deep neural network model, the physical damage features are also processed by standardization or max-min normalization, and the processed physical damage features are input into the deep neural network model.

7. The cross-layer perception method for optical communication transmission quality based on a deep neural network according to claim 1, characterized in that Optimize the network configuration of the new optical communication network according to the cross-layer perception transmission quality, including: Select a path with low physical damage according to the predicted transmission quality to achieve dynamic routing optimization, specifically increase the number of spans in the original link, dynamically adjust the span length, increase the signal transmission rate, and reduce the bit error rate; Adopt elastic optical network technology, dynamically allocate wavelength intervals according to the channel quality, adjust the modulation format of different links, use narrow intervals and high-order modulation formats in high optical signal-to-noise ratio links, and switch to wide intervals and more robust modulation formats in low optical signal-to-noise ratio links.

8. An optical communication transmission quality cross-layer perception system based on a deep neural network, characterized in that, It includes: A physical layer information dataset construction module, which is used to transmit and collect optical path physical layer damage information through a simulated optical communication network, and generate a physical layer information dataset; A deep neural network model construction and parameter optimization module, which is used to extract the physical layer damage information related to transmission quality from the physical layer information dataset as physical damage features, use a deep neural network model to predict the optical communication transmission quality based on the physical damage features, and construct a loss function based on the transmission quality prediction value and the transmission quality index to optimize the model parameters; A transmission quality estimation and optimization module, which is used to predict the cross-layer perception transmission quality of a new optical communication network structure by using a parameter-optimized deep neural network model, and optimize the network configuration of the new optical communication network according to the cross-layer perception transmission quality.

9. A computing device, comprising a memory and one or more processors, wherein executable code is stored in the memory, characterized in that When the one or more processors execute the executable code, it is used to implement the cross-layer perception method for optical communication transmission quality based on a deep neural network according to any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, A program is stored thereon, and when the program is executed by a processor, it implements the cross-layer perception method for optical communication transmission quality based on a deep neural network according to any one of claims 1-7.

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