A deep expansion channel decoding method and device based on penalty dual decomposition method

Abstract

The present application proposes a deep unfolding channel decoding method and device based on the penalty dual decomposition method, which relates to the field of wireless communication technology. The method comprises the following steps: constructing a maximum likelihood decoding problem based on the channel decoding problem; obtaining an equivalent cascade form of the maximum likelihood decoding problem according to the cascade decomposition method; converting discrete constraints into continuous constraints, and obtaining a relaxed decoding optimization problem with a penalty term by introducing a first auxiliary variable and a penalty term; solving the relaxed decoding optimization problem according to the penalty dual decomposition method to obtain a double-layer cyclic penalty dual decomposition decoder; performing deep unfolding based on the structure of the penalty dual decomposition decoder to obtain a learnable penalty dual decomposition decoding network; training the learnable penalty dual decomposition decoding network by generating training data, so as to use a penalty dual decomposition decoder with optimal parameters for decoding. The present invention applies linear programming and deep learning methods to channel decoding to improve decoding performance and reduce decoding complexity.

Description

Technical Field

[0001] The present application relates to the field of wireless communication technology, and in particular to a deep expansion channel decoding method and device based on a penalty dual decomposition method. Background Art

[0002] Channel decoding is a key link to ensure the reliable transmission of information. It ensures that the receiver can recover the information transmitted by the sender by adding redundant information to the information bits. The Linear Programming (LP) decoding algorithm is a maximum likelihood (ML) decoding algorithm based on LP relaxation. It has recently been applied to linear codes, such as the decoding of low-density parity check (LDPC) codes, and has received widespread attention from academia and industry. Compared with the classic Belief Propagation (BP) decoding algorithm, the LP decoding algorithm has a lower bit error rate in high signal-to-noise ratio areas and no error flattening, so it is more suitable for application scenarios with ultra-high reliability requirements such as magnetic recording and optical fiber transmission networks. However, the LP decoding algorithm also has the disadvantages of worse decoding performance in low signal-to-noise ratio areas and higher computational complexity.

[0003] In order to overcome the shortcomings of the LP decoding algorithm, efficient distributed LP decoding algorithms such as the alternating direction method of multipliers (ADMM) and the penalized dual decomposition (PDD) have been proposed in recent years.

[0004] At the same time, deep learning has also been widely used in the field of communications in recent years and can be used to solve some signal processing problems. Deep unfolding is a model-driven deep learning method that can unfold an iterative algorithm into a learnable neural network, retaining the inherent structure of the iterative algorithm, with high interpretability, and after training, it can achieve better performance than the original algorithm. Summary of the invention

[0005] The purpose of the present invention is to propose a deep unfolding decoding method and device based on the penalty dual decomposition method for channel coding. The iterative process of the penalty dual decomposition decoder is unfolded into a model-driven neural network with a fixed number of network layers, and the adjustable decoding parameters are converted into trainable network parameters. The gradient descent method in deep learning is used to find the optimal parameters. After training, the network parameters are fixed to obtain an optimized decoder for online channel decoding. This optimized decoding network has better decoding performance and lower decoding complexity.

[0006] In a first aspect, the present application proposes a deep unfolding channel decoding method based on a penalty dual decomposition method, comprising:

[0007] Constructing a maximum likelihood decoding problem based on the channel decoding problem, wherein the maximum likelihood decoding problem includes an objective function and a first discrete parity check constraint;

[0008] Decomposing the first discrete parity check constraint into a second discrete parity check constraint according to a cascade decomposition method, and converting the maximum likelihood decoding problem into an equivalent cascade form;

[0009] Converting the second discrete parity check constraint into a continuous constraint, and obtaining a relaxed decoding optimization problem with a penalty term by introducing a penalty term and a first auxiliary variable;

[0010] Solving the relaxed decoding optimization problem according to the penalty dual decomposition method to obtain a double-layer cyclic penalty dual decomposition decoder;

[0011] Converting adjustable decoding parameters of the penalty dual decomposition decoder into trainable parameters, and constructing a learnable penalty dual decomposition decoding network according to the trainable parameters;

[0012] Generate training data, and train the learnable penalty dual decomposition decoding network according to the training data to perform decoding using a penalty dual decomposition decoder with optimal parameters.

[0013] Optionally, constructing a maximum likelihood decoding problem based on a channel decoding problem includes:

[0014] For a binary linear code of length N Each codeword is specified by an M×N parity check matrix H, x∈{0,1} N×1 is a transmission codeword of length N, is the log-likelihood ratio of the received codeword, and the maximum likelihood decoding problem is expressed as:

[0015]

[0016] Where [·]2 represents modulo 2 operation, H represents the check matrix, Represents the index sets of variable nodes and check nodes respectively.

[0017] Optionally, decomposing the first discrete parity check constraint into a second discrete parity check constraint according to a cascade decomposition method, and converting the maximum likelihood decoding problem into an equivalent cascade form, comprises:

[0018] The first discrete constraint parity check constraint is converted into a second discrete parity check constraint, wherein the second discrete parity check constraint is a finite number of three-variable parity check constraints, and Tx≤t, x∈{0,1} is defined. 3×1 ,in

[0019]

[0020] For a degree d j The discrete parity check constraint of The second auxiliary variable is There are three-variable parity check constraints, so the maximum likelihood decoding problem is converted into an equivalent cascade form, including:

[0021]

[0022] in, is the second auxiliary variable introduced, represents the Kronecker product, Q γ Used to select the variables in u corresponding to the γth three-variable equation.

[0023] Optionally, converting the second discrete parity check constraint into a continuous constraint, and obtaining a relaxed decoding optimization problem with a penalty term by introducing a penalty term and a first auxiliary variable, comprises:

[0024] The first auxiliary variable z is introduced to convert the inequality constraint in formula (3) into an equality constraint, and the variable u is relaxed to a continuous variable. At the same time, a penalty function is introduced into the objective function to obtain the relaxed decoding optimization problem with a penalty term, including:

[0025]

[0026] The penalty function g is: Specifically Where α is the penalty coefficient.

[0027] Optionally, solving the relaxed decoding optimization problem according to the penalty dual decomposition method to obtain a double-layer cyclic penalty dual decomposition decoder includes:

[0028] Introducing the penalty parameter μ and the dual variable y, the augmented Lagrangian term is obtained by the equality constraint Taking the complete augmented Lagrangian function as the objective function, we get:

[0029]

[0030] The penalty dual decomposition method is used to solve the augmented Lagrangian problem in formula (5) to obtain the penalty dual decomposition decoder, which specifically includes the update of u, z in the inner loop and the update of the dual variable y and penalty parameter μ in the outer loop.

[0031] Optionally, converting the adjustable decoding parameters of the penalty dual decomposition decoder into trainable parameters, and constructing a learnable penalty dual decomposition decoding network according to the trainable parameters includes:

[0032] The adjustable parameters μ, α and β in the penalty dual decomposition decoder are converted into independent trainable parameters μ = [μ1, ..., μ L ]、α=[α1,...α L ] and β=[β1,...β L ];

[0033] Since each inner layer of the penalty dual decomposition decoding network contains two types of nodes: u nodes and z nodes, and each outer layer contains K inner layers and one y node, (u k,l ,z k,l ) indicates that the u node and the z node are the kth inner layer outputs in the lth outer layer, y l represents the output of the y node in the lth outer layer. The node update is as follows:

[0034]

[0035]

[0036] y l =y l-1 +μ l (Au K,l +z K,l -b) (8)

[0037] where θ = 1 / (α l -μ l diag(A T A)), 1 means the length is N+Γ a The symbol ⊙ represents the Hadamard product, and the ReLU (·) activation function is equivalent to ∏ [0,∞) (·). For the final layer output u K,L Make a hard decision, specifically: u i <0.5 then x i = 0, otherwise x i =1, thus obtaining the network’s decoded output x.

[0038] Optionally, generating training data, and training the learnable penalty dual decomposition decoding network according to the training data to use a penalty dual decomposition decoder with optimal parameters for decoding, comprises:

[0039] The sigmoid function is selected as the activation function of the output layer, the cross entropy is used as the loss function, and the output of each outer layer is introduced into the loss function, which is specifically expressed as:

[0040]

[0041] where c i =1-2u i will output u K,l Converted into bipolar form, σ(·) represents the sigmoid function.

[0042] The penalty dual decomposition decoding network is trained according to the gradient descent method to obtain the learned training parameters {α, β, μ}.

[0043] The second aspect of the present application proposes a deep expansion channel decoding device based on a penalty dual decomposition method, comprising:

[0044] An initialization module, configured to construct a maximum likelihood decoding problem based on the channel decoding problem, wherein the maximum likelihood decoding problem includes an objective function and a first discrete parity check constraint;

[0045] A first building module is used to decompose the first discrete parity check constraint into a second discrete parity check constraint according to a cascade decomposition method, and convert the maximum likelihood decoding problem into an equivalent cascade form;

[0046] A second building module is used to convert the second discrete parity check constraint into a continuous constraint, and obtain a relaxed decoding optimization problem with a penalty term by introducing a penalty term and a first auxiliary variable;

[0047] A penalty dual decomposition decoder construction module is used to solve the relaxed decoding optimization problem according to the penalty dual decomposition method to obtain a double-layer cyclic penalty dual decomposition decoder;

[0048] A penalty dual decomposition decoder training module converts the adjustable decoding parameters of the penalty dual decomposition decoder into trainable parameters, and constructs a learnable penalty dual decomposition decoding network according to the trainable parameters;

[0049] A decoding module generates training data, and trains the learnable penalty dual decomposition decoding network according to the training data, so as to use a penalty dual decomposition decoder with optimal parameters for decoding.

[0050] In a third aspect of the present application, a computer device is proposed, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the method described in any one of the first aspects above is implemented.

[0051] In a fourth aspect of the present application, a non-temporary computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the method described in any one of the first aspects above is implemented.

[0052] The technical solution provided by the embodiments of the present disclosure brings at least the following beneficial effects:

[0053] The advantages of LP decoding are fully utilized to improve the decoding performance. At the same time, the advantages of deep learning methods are fully utilized to expand the decoder based on the penalty dual decomposition method into a model-driven neural network. After training through deep learning methods, the optimal training parameters can be obtained. The decoder loaded with the optimal parameters can further improve the decoding performance and greatly reduce the decoding complexity.

[0054] Additional aspects and advantages of the present application will be given in part in the description below, and in part will become apparent from the description below, or will be learned through the practice of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] The above and / or additional aspects and advantages of the present application will become apparent and easily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:

[0056] Figure 1 It is a flowchart of a deep expansion channel decoding method based on a penalty dual decomposition method according to an exemplary embodiment of the present application;

[0057] Figure 2 is a network structure diagram of LPDN according to an exemplary embodiment of the present application;

[0058] Figure 3 is a frame error rate curve diagram of a BP decoder, a penalty dual decomposition decoder and a LPDN decoder in an additive Gaussian noise channel according to an exemplary embodiment of the present application;

[0059] Figure 4 is a line graph showing a comparison of average inner iteration times of a penalty dual decomposition decoder and a LPDN decoder according to an exemplary embodiment of the present application;

[0060] Figure 5 A block diagram of a deep expansion channel decoding device based on a penalty dual decomposition method according to an exemplary embodiment of the present application;

[0061] Figure 6 is a schematic block diagram of an electronic device. DETAILED DESCRIPTION

[0062] The embodiments of the present application are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present application, and should not be construed as limiting the present application.

[0063] Consider the transmission of signals in an additive Gaussian noise channel, the modulation method is binary phase shift keying (BPSK), and the code type is [128,64] CCSDS LDPC code

[0064] Figure 1 is a flowchart of a deep expansion channel decoding method based on a penalty dual decomposition method according to an exemplary embodiment of the present application, such as Figure 1 As shown, the method comprises the following steps:

[0065] Step 101: construct a maximum likelihood decoding problem based on a channel decoding problem, wherein the maximum likelihood decoding problem includes an objective function and a first discrete parity check constraint.

[0066] For a binary linear code of length N Each codeword is specified by an M×N parity check matrix H, x∈{0,1} N×1 is a transmission codeword of length N, is the log-likelihood ratio of the received codeword, and the maximum likelihood decoding problem is expressed as:

[0067]

[0068] Where [·]2 represents modulo 2 operation, H represents the check matrix, Represents the index sets of variable nodes and check nodes respectively.

[0069] Step 102: Decompose the first discrete parity check constraint into a second discrete parity check constraint according to a cascade decomposition method, and convert the maximum likelihood decoding problem into an equivalent cascade form.

[0070] The first discrete parity check constraint is transformed into a second discrete parity check constraint, wherein the degree of the first discrete parity check constraint is higher than that of the second discrete parity check constraint, and the second discrete parity check constraint is a finite number of three-variable parity check constraints, and Tx≤t, x∈{0,1} is defined. 3×1 ,in

[0071]

[0072] For a degree d j The first discrete parity check constraint is introduced The second auxiliary variable is There are three-variable parity check constraints, so the maximum likelihood decoding problem is transformed into an equivalent cascade form, including:

[0073]

[0074] in, is the second auxiliary variable introduced, represents the Kronecker product, Q γ Used to select the variables in u corresponding to the γth three-variable equation.

[0075] Step 103: convert the second discrete parity check constraint into a continuous constraint, and obtain a relaxed decoding optimization problem with a penalty term by introducing a penalty term and a first auxiliary variable.

[0076] The first auxiliary variable z is introduced to convert the inequality constraint in formula (3) into an equality constraint, and the variable u is relaxed to a continuous variable. At the same time, a penalty function is introduced into the objective function to obtain a relaxed decoding optimization problem with a penalty term, including:

[0077]

[0078] The penalty function g is: Specifically Where α is the penalty coefficient.

[0079] Step 104, solving the relaxed decoding optimization problem according to the penalty dual decomposition method, and obtaining a double-layer loop penalty dual decomposition decoder.

[0080] Introducing the penalty parameter μ and the dual variable y, the augmented Lagrangian term is obtained by the equality constraint Taking the complete augmented Lagrangian function as the objective function, we get:

[0081]

[0082] The augmented Lagrangian problem in formula (5) is solved according to the penalty dual decomposition method, and a penalty dual decomposition decoder is obtained, which specifically includes the update of u, z in the inner loop and the update of the dual variable y and penalty parameter μ in the outer loop.

[0083] The update of the variable u in the inner loop can be regarded as a quadratic optimization problem, which can be decomposed into N+Γa Each sub-problem is as follows:

[0084]

[0085] st0≤u i ≤1

[0086] in e i Indicates A T The i-th diagonal element of A, a i represents the i-th column of A. The optimal solution of the subproblem is:

[0087]

[0088] The update of variable z can be specifically as follows:

[0089]

[0090] Let β represent the super-relaxation parameter. The update of the variable z using the super-relaxation mechanism can be specifically as follows:

[0091]

[0092] The update of the dual variables in the outer loop is as follows:

[0093] y l+1 =y l +μ l (Au+zb)

[0094] At the same time, update the penalty parameter μ l+1 =cμ l , where c>1 is a control parameter.

[0095] Step 105, converting the adjustable decoding parameters of the penalty dual decomposition decoder into trainable parameters, and constructing a learnable penalty dual decomposition decoding network according to the trainable parameters.

[0096] Based on the penalty dual decomposition decoder, the inner and outer iterative loops are expanded into a network with a fixed number of layers, and a learnable penalty dual decomposition decoding network LPDN is obtained. Figure 2 As shown in Figure 2, LPDN consists of L outer layers, each of which includes K inner layers. L = 20, K = 5. The updating process of the network corresponds to the iterative process of the penalty dual decomposition decoder. The adjustable parameters μ, α and β in the penalty dual decomposition decoder are converted into independent trainable parameters μ = [μ1, ..., μ L ]、α=[α1,...α L ] and β=[β1,...βL ];

[0097] Since each inner layer of the penalty dual decomposition decoding network contains two types of nodes: u nodes and z nodes, and each outer layer contains K inner layers and one y node, (u k,l ,z k,l ) indicates that the u node and the z node are the kth inner layer outputs in the lth outer layer, y l represents the output of the y node in the lth outer layer. The node update is as follows:

[0098]

[0099]

[0100] y l =y l-1 +μ l (Au K,l +z K,l -b) (8)

[0101] where θ = 1 / (α l -μ l diag(A T A)), 1 means the length is N+Γ a The symbol ⊙ represents the Hadamard product, and the ReLU (·) activation function is equivalent to ∏ [0,∞) (·). For the final layer output u K,L Make a hard decision, specifically: u i <0.5 then x i = 0, otherwise x i =1, thus obtaining the network’s decoded output x.

[0102] Step 106 , generating training data, and training a learnable penalty dual decomposition decoding network according to the training data, so as to use a penalty dual decomposition decoder with optimal parameters for decoding.

[0103] The sigmoid function is selected as the activation function of the output layer, the cross entropy is used as the loss function, and the output of each outer layer is introduced into the loss function, which is specifically expressed as:

[0104]

[0105] where c i =1-2u i will output u K,l Converted into bipolar form, σ(·) represents the sigmoid function.

[0106] The penalty dual decomposition decoding network is trained according to the gradient descent method to obtain the learned training parameters {α, β, μ}.

[0107] According to the trained parameters {α, β, μ} loaded by LPDN, they are restored to the iterative form of the penalty dual decomposition decoder, and the LPDN decoder can be obtained for iterative decoding.

[0108] The embodiment of the present application fully utilizes the advantages of LP decoding to improve the decoding performance, and at the same time fully utilizes the advantages of deep learning methods to expand the decoder based on the penalty dual decomposition method into a model-driven neural network. After training through deep learning methods, the optimal training parameters can be obtained. The decoder loaded with the optimal parameters can further improve the decoding performance and greatly reduce the decoding complexity.

[0109] Figure 3 Figure 1 is a simulation image of the frame error rate (FER) of the BP decoder, the penalty dual decomposition (PDD) decoder and the LPDN decoder in an additive Gaussian noise channel according to an exemplary embodiment of the present application. It can be seen from the figure that the performance of the penalty dual decomposition decoder and the LPDN decoder is 10 -3 Compared with the BP decoder, the performance gain in this area is about 0.5dB.

[0110] Figure 4 This is a line graph comparing the average inner iteration times of the penalty dual decomposition decoder and the LPDN decoder according to an exemplary embodiment of the present application. As can be seen from the figure, the LPDN decoder reduces the iteration times by 50% in the high signal-to-noise ratio region compared to the penalty dual decomposition decoder, greatly reducing the decoding delay.

[0111] Figure 5 is a block diagram 500 of a deep expansion channel decoding device based on a penalty dual decomposition method according to an exemplary embodiment, referring to Figure 5 The device includes: an initialization module 510, a first construction module 520, a second construction module 530, a penalty dual decomposition decoder construction module 540, a penalty dual decomposition decoder training module 550 and a decoding module 560.

[0112] Initialization module 510, configured to construct a maximum likelihood decoding problem based on the channel decoding problem, wherein the maximum likelihood decoding problem includes an objective function and a first discrete parity check constraint;

[0113] A first construction module 520 is used to decompose the first discrete parity check constraint into a second discrete parity check constraint according to a cascade decomposition method, and convert the maximum likelihood decoding problem into an equivalent cascade form;

[0114] A second construction module 530 is used to convert the second discrete parity check constraint into a continuous constraint, and obtain a relaxed decoding optimization problem with a penalty term by introducing a penalty term and a first auxiliary variable;

[0115] A penalty dual decomposition decoder construction module 540 is used to solve the relaxed decoding optimization problem according to the penalty dual decomposition method to obtain a double-layer cyclic penalty dual decomposition decoder;

[0116] A penalty dual decomposition decoder training module 550, used to convert the adjustable decoding parameters of the penalty dual decomposition decoder into trainable parameters, and construct a learnable penalty dual decomposition decoding network according to the trainable parameters;

[0117] The decoding module 560 generates training data for training a learnable penalty dual decomposition decoding network according to the training data, so as to use a penalty dual decomposition decoder with optimal parameters for decoding.

[0118] Regarding the device in the above embodiment, the specific manner in which each module performs operations has been described in detail in the embodiment of the method, and will not be elaborated here.

[0119] Figure 6 A schematic block diagram of an example electronic device 600 that can be used to implement an embodiment of the present disclosure is shown. The electronic device is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device can also represent various forms of mobile devices, such as personal digital processing, cellular phones, smart phones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the present disclosure described and / or required herein.

[0120] like Figure 6 As shown, the device 600 includes a computing unit 601, which can perform various appropriate actions and processes according to a computer program stored in a read-only memory (ROM) 602 or a computer program loaded from a storage unit 608 into a random access memory (RAM) 603. In the RAM 603, various programs and data required for the operation of the device 600 can also be stored. The computing unit 601, the ROM 602, and the RAM 603 are connected to each other via a bus 604. An input / output (I / O) interface 605 is also connected to the bus 604.

[0121] A number of components in the device 600 are connected to the I / O interface 605, including: an input unit 606, such as a keyboard, a mouse, etc.; an output unit 607, such as various types of displays, speakers, etc.; a storage unit 608, such as a disk, an optical disk, etc.; and a communication unit 609, such as a network card, a modem, a wireless communication transceiver, etc. The communication unit 609 allows the device 600 to exchange information / data with other devices through a computer network such as the Internet and / or various telecommunication networks.

[0122] The computing unit 601 may be a variety of general and / or special processing components with processing and computing capabilities. Some examples of the computing unit 601 include, but are not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various dedicated artificial intelligence (AI) computing chips, various computing units running machine learning model algorithms, digital signal processors (DSPs), and any appropriate processors, controllers, microcontrollers, etc. The computing unit 601 performs the various methods and processes described above, such as the voice instruction response method. For example, in some embodiments, the voice instruction response method may be implemented as a computer software program, which is tangibly contained in a machine-readable medium, such as a storage unit 608. In some embodiments, part or all of the computer program may be loaded and / or installed on the device 600 via ROM 602 and / or communication unit 609. When the computer program is loaded into RAM 603 and executed by the computing unit 601, one or more steps of the voice instruction response method described above may be performed. Alternatively, in other embodiments, the computing unit 601 may be configured to perform the voice instruction response method in any other appropriate manner (e.g., by means of firmware).

[0123] Various implementations of the systems and techniques described above herein can be implemented in digital electronic circuit systems, integrated circuit systems, field programmable gate arrays (FPGAs), application specific integrated circuits (ASICs), application specific standard products (ASSPs), systems on chips (SOCs), load programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various implementations may include: being implemented in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which can be a special purpose or general purpose programmable processor that can receive data and instructions from a storage system, at least one input device, and at least one output device, and transmit data and instructions to the storage system, the at least one input device, and the at least one output device.

[0124] The program code for implementing the method of the present disclosure may be written in any combination of one or more programming languages. These program codes may be provided to a processor or controller of a general-purpose computer, a special-purpose computer, or other programmable data processing device, so that the program code, when executed by the processor or controller, enables the functions / operations specified in the flow chart and / or block diagram to be implemented. The program code may be executed entirely on the machine, partially on the machine, partially on the machine and partially on a remote machine as a stand-alone software package, or entirely on a remote machine or server.

[0125] In the context of the present disclosure, a machine-readable medium may be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, device, or equipment. A machine-readable medium may be a machine-readable signal medium or a machine-readable storage medium. A machine-readable medium may include, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, device, or equipment, or any suitable combination of the foregoing. A more specific example of a machine-readable storage medium may include an electrical connection based on one or more lines, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

[0126] To provide interaction with a user, the systems and techniques described herein can be implemented on a computer having: a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to the user; and a keyboard and pointing device (e.g., a mouse or trackball) through which the user can provide input to the computer. Other types of devices can also be used to provide interaction with the user; for example, the feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including acoustic input, voice input, or tactile input).

[0127] The systems and techniques described herein can be implemented in a computing system that includes backend components (e.g., as a data server), or a computing system that includes middleware components (e.g., an application server), or a computing system that includes frontend components (e.g., a user computer with a graphical user interface or a web browser through which a user can interact with implementations of the systems and techniques described herein), or a computing system that includes any combination of such backend components, middleware components, or frontend components. The components of the system can be interconnected by any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include: a local area network (LAN), a wide area network (WAN), the Internet, and a blockchain network.

[0128] A computer system may include a client and a server. The client and the server are generally remote from each other and usually interact through a communication network. The relationship between the client and the server is generated by computer programs running on the corresponding computers and having a client-server relationship with each other. The server may be a cloud server, also known as a cloud computing server or cloud host, which is a host product in the cloud computing service system to solve the defects of difficult management and weak business scalability in traditional physical hosts and VPS services ("Virtual Private Server", or "VPS" for short). The server may also be a server of a distributed system, or a server combined with a blockchain.

[0129] It should be understood that the various forms of processes shown above can be used to reorder, add or delete steps. For example, the steps recorded in this disclosure can be executed in parallel, sequentially or in different orders, as long as the desired results of the technical solutions disclosed in this disclosure can be achieved, and this document does not limit this.

[0130] The above specific implementations do not constitute a limitation on the protection scope of the present disclosure. It should be understood by those skilled in the art that various modifications, combinations, sub-combinations and substitutions can be made according to design requirements and other factors. Any modification, equivalent substitution and improvement made within the spirit and principle of the present disclosure shall be included in the protection scope of the present disclosure.

Claims

1. A deep unfolding channel decoding method based on penalty dual decomposition method, characterized in that: include: Constructing a maximum likelihood decoding problem based on the channel decoding problem, wherein the maximum likelihood decoding problem includes an objective function and a first discrete parity check constraint; Decomposing the first discrete parity check constraint into a second discrete parity check constraint according to a cascade decomposition method, and converting the maximum likelihood decoding problem into an equivalent cascade form; Converting the second discrete parity check constraint into a continuous constraint, and obtaining a relaxed decoding optimization problem with a penalty term by introducing a penalty term and a first auxiliary variable; Solving the relaxed decoding optimization problem according to the penalty dual decomposition method to obtain a double-layer cyclic penalty dual decomposition decoder; Converting adjustable decoding parameters of the penalty dual decomposition decoder into trainable parameters, and constructing a learnable penalty dual decomposition decoding network according to the trainable parameters; Generate training data, and train the learnable penalty dual decomposition decoding network according to the training data to perform decoding using a penalty dual decomposition decoder with optimal parameters; Decomposing the first discrete parity check constraint into a second discrete parity check constraint according to a cascade decomposition method, and converting the maximum likelihood decoding problem into an equivalent cascade form, comprises: The first discrete parity check constraint is transformed into a second discrete parity check constraint, wherein the second discrete parity check constraint is a finite number of three-variable parity check constraints, and defines , ,in （2） For a degree The discrete parity check constraint of The second auxiliary variable is There are three-variable parity check constraints, so the maximum likelihood decoding problem is converted into an equivalent cascade form, including: （3） in, , , is the second auxiliary variable introduced, , , represents the Kronecker product, Used to select The three-variable equation corresponds to Variables in The step of converting the adjustable decoding parameters of the penalty dual decomposition decoder into trainable parameters and constructing a learnable penalty dual decomposition decoding network according to the trainable parameters comprises: The penalty dual decomposition is used to decompose the adjustable parameters in the decoder , and Convert to independent trainable parameters between layers , and ; Because each inner layer of the penalty dual decomposition decoding network contains two types of nodes: Node and Nodes, each outer layer contains K inner layers and one Node, use express Node and The node is in the kth inner layer output in the lth outer layer, Indicates the first outer layer The output of the node, the update of the node is specifically: Among them, for a binary linear code of length N , each codeword consists of Parity Check Matrix Specify, is a transmission codeword of length N, is the log-likelihood ratio of the received codeword, , , is the second auxiliary variable introduced, , , represents the Kronecker product, Used to select The three-variable equation corresponds to The variables in and are penalty coefficients, , Indicates the length The all-one vector of represents the Hadamard product, The activation function is equivalent to , for the final layer output Make hard decisions, specifically: but ,otherwise , thus obtaining the network's decoded output ; The generating of training data and training the learnable penalty dual decomposition decoding network according to the training data to use the penalty dual decomposition decoder with optimal parameters for decoding include: The sigmoid function is selected as the activation function of the output layer, the cross entropy is used as the loss function, and the output of each outer layer is introduced into the loss function, which is specifically expressed as: (9) in Will output Converted to bipolar form, represents the sigmoid function, N is the length of the binary linear code; The penalty dual decomposition decoding network is trained according to the gradient descent method to obtain the learned training parameters. .

2. The method according to claim 1, characterized in that The constructing of the maximum likelihood decoding problem based on the channel decoding problem includes: For a binary linear code of length N , each codeword consists of Parity Check Matrix Specify, is a transmission codeword of length N, is the log-likelihood ratio of the received codeword, and the maximum likelihood decoding problem is expressed as: （1） in, represents modulo 2 operation, represents the check matrix, Represents the index sets of variable nodes and check nodes respectively.

3. The method according to claim 2, characterized in that The step of converting the second discrete parity check constraint into a continuous constraint and obtaining a relaxed decoding optimization problem with a penalty term by introducing a penalty term and a first auxiliary variable comprises: Introducing the first auxiliary variable Convert the inequality constraint in formula (3) into an equality constraint and change the variable Relaxation is a continuous variable, and a penalty function is introduced into the objective function to obtain the relaxation decoding optimization problem with penalty term, including: (4) The penalty function , specifically ,in is the penalty coefficient.

4. The method according to claim 3, characterized in that The method of solving the relaxed decoding optimization problem according to the penalty dual decomposition method to obtain a double-layer cyclic penalty dual decomposition decoder includes: Introducing penalty parameters and dual variables , the augmented Lagrangian term is obtained by the equality constraint , taking the complete augmented Lagrangian function as the objective function, we get: （5） The penalty dual decomposition method is used to solve the augmented Lagrangian problem in formula (5), and the penalty dual decomposition decoder is obtained, which specifically includes the inner loop , Update and outer loop dual variables and penalty parameters Updates.

5. A deep unfolding channel decoding device based on penalty dual decomposition method, characterized in that: include: An initialization module constructs a maximum likelihood decoding problem based on the channel decoding problem, wherein the maximum likelihood decoding problem includes an objective function and a first discrete parity check constraint; A first building module is configured to decompose the first discrete parity check constraint into a second discrete parity check constraint according to a cascade decomposition method, and convert the maximum likelihood decoding problem into an equivalent cascade form; A second construction module converts the second discrete parity check constraint into a continuous constraint, and obtains a relaxed decoding optimization problem with a penalty term by introducing a penalty term and a first auxiliary variable; A penalty dual decomposition decoder construction module is used to solve the relaxed decoding optimization problem according to the penalty dual decomposition method to obtain a double-layer loop penalty dual decomposition decoder; A penalty dual decomposition decoder training module converts the adjustable decoding parameters of the penalty dual decomposition decoder into trainable parameters, and constructs a learnable penalty dual decomposition decoding network according to the trainable parameters; A decoding module generates training data, and trains the learnable penalty dual decomposition decoding network according to the training data, so as to use a penalty dual decomposition decoder with optimal parameters for decoding; Decomposing the first discrete parity check constraint into a second discrete parity check constraint according to a cascade decomposition method, and converting the maximum likelihood decoding problem into an equivalent cascade form, comprises: The first discrete parity check constraint is transformed into a second discrete parity check constraint, wherein the second discrete parity check constraint is a finite number of three-variable parity check constraints, and defines , ,in （2） For a degree The discrete parity check constraint of The second auxiliary variable is There are three-variable parity check constraints, so the maximum likelihood decoding problem is converted into an equivalent cascade form, including: （3） Among them, for a binary linear code of length N , each codeword consists of Parity Check Matrix Specify, is a transmission codeword of length N, is the log-likelihood ratio of the received codeword, , , is the second auxiliary variable introduced, , , represents the Kronecker product, Used to select The three-variable equation corresponds to Variables in The step of converting the adjustable decoding parameters of the penalty dual decomposition decoder into trainable parameters and constructing a learnable penalty dual decomposition decoding network according to the trainable parameters comprises: The penalty dual decomposition is used to decompose the adjustable parameters in the decoder , and Convert to independent trainable parameters between layers , and ; Because each inner layer of the penalty dual decomposition decoding network contains two types of nodes: Node and Nodes, each outer layer contains K inner layers and one Node, use express Node and The node is in the kth inner layer output in the lth outer layer, Indicates the first outer layer The output of the node, the update of the node is specifically: in, , , is the second auxiliary variable introduced, , , represents the Kronecker product, Used to select The three-variable equation corresponds to The variables in and are penalty coefficients, , Indicates the length The all-one vector of represents the Hadamard product, The activation function is equivalent to , for the final layer output Make hard decisions, specifically: but ,otherwise , thus obtaining the network's decoded output ; The generating of training data and training the learnable penalty dual decomposition decoding network according to the training data to use the penalty dual decomposition decoder with optimal parameters for decoding include: The sigmoid function is selected as the activation function of the output layer, the cross entropy is used as the loss function, and the output of each outer layer is introduced into the loss function, which is specifically expressed as: (9) in Will output Converted to bipolar form, represents the sigmoid function, N is the length of the binary linear code; The penalty dual decomposition decoding network is trained according to the gradient descent method to obtain the learned training parameters. .

6. A computer device, characterized in that: The method comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the method according to any one of claims 1 to 4 is implemented.

7. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 4 is implemented.

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