Decoding method in non-finite field and communication device

Abstract

The invention provides a decoding method in a non-finite field and a communication device, which can solve the problem of high decoding complexity caused by iterative decoding so as to improve the decoding efficiency and can be applied to a communication system. The method comprises the following steps: receiving end equipment acquires a first sequence; wherein the first sequence comprises values of transmission bits in the coded sequence, and the length of the first sequence is N1. The coded sequence is a sequence obtained by coding a sequence to be coded, the length of the sequence to be coded is N, N is equal to 2n, and n is a positive integer. N1 is a positive integer smaller than N. And then, the receiving end equipment determines a decoding result according to the signal probability distribution, the first set and the value of the transmission bit in the coded sequence. Wherein the signal probability distribution comprises the probability distribution of the sequence to be coded, and the first set indicates the position of each value in the first sequence in the coded sequence.

Description

Decoding method and communication device under non-finite field Technical Field

[0001] The present application relates to the field of wireless communication technology, and in particular to a decoding method and communication device under a non-finite field. Background Art

[0002] In compressed sensing (CS), the basis pursuit (BP) algorithm is often used to recover the true signal from the sampled data. Specifically, the BP algorithm uses a sampling matrix to reconstruct the signal through multiple iterations. The sampling matrix in the BP algorithm is randomly generated and not fixed. Furthermore, the BP algorithm suffers from the high number of iterations and computational complexity during signal reconstruction.

[0003] Summary of the Invention

[0004] This application provides a decoding method and communication device under a non-finite field, which can solve the problem of high decoding complexity caused by iterative decoding, thereby improving decoding efficiency. To achieve the above purpose, this application adopts the following technical solutions:

[0005] In a first aspect, a decoding method under a non-finite field is provided. The execution subject of the method can be a receiving device or a chip applied to the receiving device. The following description is based on the example of the execution subject being the receiving device. The method includes: the receiving device obtains a first sequence. The first sequence includes the value of the transmission bit in the encoded sequence, and the length of the first sequence is N1. The encoded sequence is the sequence after the sequence to be encoded is encoded, and the length of the sequence to be encoded is N, where N=2 n , n is a positive integer. N1 is a positive integer less than N. The receiving device then determines a decoding result based on the signal probability distribution, the first set, and the value of the transmitted bit in the encoded sequence. The signal probability distribution includes the probability distribution of the sequence to be encoded, and the first set indicates the position of each value in the first sequence in the encoded sequence.

[0006] In this embodiment of the present application, the encoded sequence includes the values ​​of the transmitted bits and the values ​​of the bits to be recovered. The reliability of the bits to be recovered is higher than that of the transmitted bits. Thus, after obtaining the first sequence, the receiving device, combining the signal probability distribution with the first set, can determine the values ​​of the bits to be recovered through recursive calculations, rather than iterative calculations. Knowing the values ​​of each transmitted bit and the values ​​of the bits to be recovered, the receiving device can determine the decoding result. In other words, in the decoding process described above, the receiving device performs a single calculation for each position, eliminating the need for iterative calculations and reducing decoding complexity.

[0007] In one possible design, the first sequence is a real number sequence, and the decoding result is a real number sequence.

[0008] In a possible design, the first sequence is a real number sequence, and the decoding result is a complex number sequence.

[0009] In one possible design, a receiving device determines a decoding result based on the signal probability distribution, the first set, and the values ​​of the transmitted bits in the encoded sequence, including determining a decoding path based on the signal probability distribution, the first set, and the values ​​of the transmitted bits in the encoded sequence, and then determining the decoding result based on the decoding path. The decoding path indicates the value of each position in the encoded sequence, so that the receiving device determines the decoding result based on the decoding path.

[0010] In one possible design, the value of the i-th transmission bit in the decoding path is the same as the value of the i-th transmission bit in the first sequence, where i is a positive integer less than or equal to N1.

[0011] That is, the receiving device uses the value of the i-th transmission bit in the first sequence as the value of the i-th transmission bit in the decoding path.

[0012] In one possible design, the number of bits to be recovered in the encoded sequence is N², where N² is a positive integer less than N. The value of the jth bit to be recovered in the decoding path corresponds to the maximum decoding metric among multiple decoding metrics, thereby improving decoding accuracy. Each of the multiple decoding metrics is determined based on the following two items: a signal probability distribution and the value of each position before the jth bit to be recovered in the decoding path. j is a positive integer less than or equal to N².

[0013] In one possible design, each decoding metric in the plurality of decoding metrics is determined through an f operation and a g operation.

[0014] The input to the f operation includes the probability distribution of the first variable and the probability distribution of the second variable. The output of the f operation includes the probability distribution of the third variable, which is the convolution of the probability distribution of the first variable and the probability distribution of the second variable. The input to the g operation includes the probability distribution of the first variable, the probability distribution of the second variable, and the probability distribution of the third variable, as well as the first value. The output of the g operation includes the conditional probability distribution of the fourth variable at the first value. The first value is the decoded value of the third variable.

[0015] The first variable is the value of the t-th position in the s-th layer of the encoding network, and the second variable is the value of the t+2-th position in the s-th layer. n-s The third variable is the value of the tth position in the s+1th layer of the encoding network, and the fourth variable is the value of the tth position in the s+1th layer. n-sThe encoding network includes n+1 layers. The first layer of the encoding network is used to input the sequence to be encoded. The second to nth layers of the encoding network are used to encode the sequence to be encoded to obtain the encoded sequence. The n+1th layer of the encoding network is used to output the encoded sequence. s is a positive integer less than or equal to n. t is a positive integer, and t traverses each parameter in the sth parameter set. Each parameter in the sth parameter set indicates a position in the sth layer. The number of positions indicated by the sth parameter set is N / 2.

[0016] That is, the decoding metric is determined by the receiving device using the f operation and the g operation, and the f operation can be used to perform a convolution operation, and the g operation can be used to perform a conditional probability operation.

[0017] In one possible design, the inputs to the f operation include the following two items:

[0018] The first item, A~P,P(a i )=p i ,i=1,...,I. A represents the set of the first variable, P represents the probability distribution of the first variable, a i represents the first variable i in A, p i Indicates that the first variable of the i-th is a i The probability of , I represents the number of the first variable.

[0019] The second item, B~Q,P(b j )=q j ,j=1,...,J. B represents the set of the second variable, Q represents the probability distribution of the second variable, b j represents the j-th second variable in B, q j Indicates that the jth second variable is b j The probability of , J represents the number of second variables.

[0020] The output of the f operation includes: C~F,F(c k )=f k ,k=1,...,K. C represents the set of the third variable, F represents the probability distribution of the third variable, c k represents the kth third variable in C, f k Indicates that the kth third variable is c k , K represents the number of third variables, and the values ​​of K third variables are different from each other.

[0021] Among them, c k is one of the IxJ values, where IxJ values ​​are obtained when i=1,...,I ​​and j=1,...,J are traversed. i,j The value of f i,j =pi q j , f i,j Indicates c i,j The probability of occurrence. k When L values ​​are the same as L values ​​in IxJ values, f k = is equal to the sum of the probabilities of occurrence of L values, where L is a positive integer less than or equal to 1 x J. In other words, the 1 x J values ​​can be different from each other; alternatively, the 1 x J values ​​can all be the same; alternatively, some of the 1 x J values ​​can be the same, while the rest can be the same or different.

[0022] That is to say, when the first variable and the second variable are discrete values, the f operation can determine the convolution operation result of the probability distribution of the two variables.

[0023] In one possible design, the inputs to the g operation include the following four items:

[0024] The first item, A~P,P(a i )=p i ,i=1,...,I. A represents the set of the first variable, P represents the probability distribution of the first variable, a i represents the first variable i in A, p i Indicates that the first variable of the i-th is a i The probability of , I represents the number of the first variable.

[0025] The second item, B~Q,P(b j )=q j ,j=1,...,J. B represents the set of the second variable, Q represents the probability distribution of the second variable, b j represents the j-th second variable in B, q j Indicates that the jth second variable is b j The probability of , J represents the number of second variables.

[0026] The third item, C represents a set of third variables, and μ represents a first value of the third variable.

[0027] The fourth term, P(μ)=f, represents the value of the probability distribution of the third variable at μ.

[0028] The outputs of the g operation include: exist The conditional probability distribution G,G(d m )=g m ,g m = p i q j / f,m=1,...,M, D represents the set of the fourth variable, G represents the probability distribution of the fourth variable, dm represents the mth fourth variable in D, g m Indicates that the mth fourth variable is d m The probability of , M represents the number of the fourth variable.

[0029] That is to say, when the first variable, the second variable and the third variable are discrete values, the g operation can determine the conditional probability distribution of the fourth variable at the first value based on the above four information.

[0030] In one possible design, the inputs to the f operation include the following two items:

[0031] The first item, A represents the first variable, η P Indicates that the first variable is taken from The probability of Indicates that the first variable is taken from In the case of i The probability is p i , P represents the Gaussian parameter matrix of the first variable.

[0032] The second item, B represents the second variable, η Q Indicates that the second variable is taken from The probability of Indicates that the second variable is taken from In the case of j The probability is q j , Q represents the Gaussian parameter matrix of the second variable.

[0033] The outputs of the f operation include: The probability distribution of .

[0034] Where C represents the third variable, and the probability distribution of C satisfies:

[0035] Among them, η U =η P η Q , η U Indicates that the third variable is taken from probability. Indicates that the third variable is taken from In the case of m The probability is f m . U represents the Gaussian parameter matrix of the third variable. and U are determined based on A and B.

[0036] That is to say, when the first variable and the second variable are continuous values, the f operation can determine the convolution operation result of the probability distribution of the two variables.

[0037] In one possible design, the values ​​of the M third variables are different from each other. m is one of the IxJ values, where IxJ values ​​are obtained when i=1,...,I ​​and j=1,...,J are traversed. i,j The value of . f i,j =p i q j , f i,j Indicates c i,j The probability of occurrence. m When L values ​​are the same as L values ​​in IxJ values, f m = is equal to the sum of the probabilities of occurrence of L values, where L is a positive integer less than or equal to 1 x J. In other words, the 1 x J values ​​can be different from each other; alternatively, the 1 x J values ​​can all be the same; alternatively, some of the 1 x J values ​​can be the same, while the rest can be the same or different.

[0038] That is, in the convolution operation result of the f operation, the values ​​of the third variable in the discrete parts are different from each other.

[0039] In one possible design, the Gaussian parameter matrix U satisfies:

[0040] Wherein, K represents the number of the first combination. The first combination is IxG Q +G P xJ+G P xG Q The Gaussian components of the K first combinations are different from each other, and IxG Q +G P xJ+G P xG Q The Gaussian component combination includes the following three items:

[0041] At t=1, and traverse i=1,…,I,j=1,…,G Q Combination of cases

[0042] At t=2, and traversing i=1,…,G P ,j=1,…,J

[0043] At t=3, and traversing i=1,…,G P ,j=1,…,G Q Combination of cases

[0044] Indicates the kth combination in the K first combinations sum.

[0045] When traversing i=1,…,I,j=1,…,G Q In the case of

[0046] When traversing i=1,…,G P ,j=1,…,J,

[0047] When traversing i=1,…,G P ,j=1,…,G Q In the case of

[0048] G P The number of columns of the Gaussian parameter matrix representing the first variable, P 1,i The element in the first row and column i of the Gaussian parameter matrix of the first variable, P 2,i The element in the second row and column i of the Gaussian parameter matrix of the first variable, P 3,i Represents the element in the third row and i column of the Gaussian parameter matrix of the first variable.

[0049] G Q The number of columns in the Gaussian parameter matrix representing the second variable, Q 1,j The element in the first row and j column of the Gaussian parameter matrix representing the second variable, Q 2,j The element in the second row and j column of the Gaussian parameter matrix of the second variable, Q 3,j The element in the third row and j column of the Gaussian parameter matrix representing the second variable.

[0050] In this way, the receiving device can determine the continuous part of the f operation.

[0051] In one possible design, the inputs to the g operation include the following four items:

[0052] The first item, A represents the first variable, η P Indicates that the first variable is taken from The probability of Indicates that the first variable is taken from In the case of i The probability is p i , P represents the Gaussian parameter matrix of the first variable.

[0053] The second item, B represents the second variable, η Q Indicates that the second variable is taken from The probability of Indicates that the second variable is taken from In the case of j The probability is q j , Q represents the Gaussian parameter matrix of the second variable.

[0054] The third item, Wherein, C represents the third variable.

[0055] The fourth term is the support of the discrete part of C {c1,c2,...,c M}. Among them, the support set {c1,c2,...,c M} means that when traversing i=1,...,I,j=1,...,J, c i,j M of them, Support {c1,c2,...,c M The elements in} are different from each other.

[0056] The outputs of the g operation include: exist The conditional probability distribution of . D represents the fourth variable. The conditional probability distribution of the output of the g operation is based on μ and the support {c1, c2, ..., c M}OK.

[0057] That is to say, when the first variable, the second variable, and the third variable are continuous values, the g operation can determine the conditional probability distribution of the fourth variable at the first value based on the above four pieces of information.

[0058] In one possible design, in μ, there is a support set {c1,c2,...,c M}, the conditional probability distribution satisfies: in, When traversing i=1,...,I,j=1,...,J, if Then order

[0059] That is, when μ is a support set {c1,c2,...,c M}, the conditional probability distribution of the g operation includes a discrete part.

[0060] In one possible design, in μ, in the support set {c1,c2,...,c M}, the conditional probability distribution satisfies:

[0061] in, When traversing i=1,...,I,j=1,...,J, if Then order

[0062] in,

[0063]

[0064]

[0065]

[0066] G P The number of columns of the Gaussian parameter matrix representing the first variable, P 1,i The element in the first row and column i of the Gaussian parameter matrix of the first variable, P 2,i The element in the second row and column i of the Gaussian parameter matrix of the first variable, P 3,i Represents the element in the third row and i column of the Gaussian parameter matrix of the first variable.

[0067] G Q The number of columns in the Gaussian parameter matrix representing the second variable, Q 1,j The element in the first row and j column of the Gaussian parameter matrix representing the second variable, Q 2,j The element in the second row and j column of the Gaussian parameter matrix of the second variable, Q 3,j The element in the third row and j column of the Gaussian parameter matrix representing the second variable.

[0068] That is, in μ, in the support set {c1,c2,...,c M}, the conditional probability distribution of the g operation includes both discrete and continuous parts.

[0069] In one possible design, each decoding metric in the plurality of decoding metrics is determined through an f operation and a g operation.

[0070] The input to the f operation includes the probability distribution of the first variable and the probability distribution of the second variable. The output of the f operation includes the probability distribution of the third variable, which is the convolution of the probability distribution of the first variable and the probability distribution of the second variable. The input to the g operation includes the probability distribution of the first variable, the probability distribution of the second variable, and the first value. The output of the g operation includes the conditional probability distribution of the fourth variable at the first value. The first value is the decoded value of the third variable.

[0071] The first variable is the value of the t-th position in the s-th layer of the encoding network, and the second variable is the value of the t+2-th position in the s-th layer. n-s The third variable is the value of the tth position in the s+1th layer of the encoding network, and the fourth variable is the value of the tth position in the s+1th layer. n-s The value of the position.

[0072] The encoding network includes n+1 layers. The first layer of the encoding network is used to input the sequence to be encoded. The second through n layers of the encoding network are used to encode the sequence to be encoded to obtain an encoded sequence. The n+1 layer of the encoding network is used to output the encoded sequence. s is a positive integer less than or equal to n. t is a positive integer, and t traverses each parameter in the sth parameter set. Each parameter in the sth parameter set indicates a position in the sth layer, and the number of positions indicated by the sth parameter set is N / 2.

[0073] That is, the decoding metric is determined by the receiving device using the f operation and the g operation, and the f operation can be used to perform a convolution operation, and the g operation can be used to perform a conditional probability operation.

[0074] In one possible design, the inputs to the f operation include the following two items:

[0075] The first item, A~f P .

[0076] Among them, A represents the first variable, f P represents the density function of the first variable, and P represents the sampling matrix of the first variable.

[0077] The second item, B~f Q .

[0078] Among them, B represents the second variable, f Q represents the density function of the second variable, and Q represents the sampling matrix of the second variable.

[0079] The outputs of the f operation include: The sampling matrix U of .

[0080] Where C represents the third variable,

[0081] in, P 1,1 Represents the element in the first row and first column of the sampling matrix P, Q 1,1 Represents the element in the first row and first column of the sampling matrix Q.

[0082] P 1,n+2 Represents the element in the first row and n+2 column of the sampling matrix P, Q 1,n+2 Represents the element in the first row and n+2 column of the sampling matrix Q.

[0083] u i is the i-th point among n points, and n points are [U min ,U max ] are points equally spaced between them, i = 1, 2, ..., n.

[0084] d(t,P) represents the discretization function of the first variable, Represents the discretized function of the second variable.

[0085] That is to say, when the first variable and the second variable are continuous values, the f operation can determine the convolution operation result of the probability distribution of the two variables.

[0086] In one possible design, the inputs to the g operation include the following three items:

[0087] The first item, A~f P .

[0088] Among them, A represents the first variable, f P represents the density function of the first variable, and P represents the sampling matrix of the first variable.

[0089] The second item, B~f Q .

[0090] Among them, B represents the second variable, f Q represents the density function of the second variable, and Q represents the sampling matrix of the second variable.

[0091] The third item, C represents a third variable, and μ represents a first value of the third variable.

[0092] The outputs of the g operation include: exist The conditional probability distribution V at ; D represents the fourth variable,

[0093]

[0094] in, P 1,1 Represents the element in the first row and first column of the sampling matrix P, Q 1,n+2 Represents the element in the first row and n+2 column of the sampling matrix Q.

[0095] Q 1,1 Represents the element in the first row and first column of the sampling matrix Q. P 1,n+2 Represents the element in the first row and n+2 column of the sampling matrix P.

[0096] v iis the i-th point among n points, and n points are [V min ,V max ] are points equally spaced between them, i = 1, 2, ..., n.

[0097] in, represents the discretized function of the first variable, Represents the discretized function of the second variable.

[0098] That is to say, when the first variable, the second variable, and the third variable are continuous values, the g operation can determine the conditional probability distribution of the fourth variable at the first value based on the above four pieces of information.

[0099] In a second aspect, a communication device is provided. The communication device may be a receiving device in the first aspect or any possible design of the first aspect, or a chip that implements the functions of the receiving device. The communication device includes modules, units, or means corresponding to the above-mentioned method. The modules, units, or means may be implemented in hardware, software, or hardware executing corresponding software implementations. The hardware or software includes one or more modules or units corresponding to the above-mentioned functions.

[0100] In a third aspect, a communication device is provided, comprising: a processor; the processor being coupled to a memory and configured to read instructions from the memory and then execute the method described in any of the above aspects in accordance with the instructions. The communication device may be the receiving device described in the first aspect, or a chip implementing the functions of the receiving device described above.

[0101] In one possible design, the communication device described in the third aspect may further include a transceiver. The transceiver may be a transceiver circuit or an interface circuit. The transceiver may be used for the communication device described in the third aspect to communicate with other communication devices.

[0102] In the present application, the communication device described in the third aspect may be the receiving device described in the first aspect, or may be a chip (system) or other parts or components that can be set in the receiving device.

[0103] In a fourth aspect, a chip is provided. The chip includes a processing circuit and an input / output interface. The input / output interface is used to communicate with modules outside the chip. For example, the chip may implement the functions of a receiving device in the first aspect or any possible design of the first aspect. The processing circuit is used to execute a computer program or instructions to implement the method in the first aspect or any possible design of the first aspect.

[0104] In a fifth aspect, a communication system is provided. The communication system includes a transmitting device and a receiving device. The transmitting device is used to perform a Hadamard transform on a sequence to be coded to obtain a coded sequence. The length of the sequence to be coded is N, where N=2 n , n is a positive integer. The transmitting device is further configured to transmit the coded sequence. The receiving device is configured to receive the coded sequence and determine a first sequence based on the received coded sequence. The first sequence includes the values ​​of the transmission bits in the coded sequence, and the length of the first sequence is N1, where N1 is a positive integer less than N. The receiving device is further configured to determine a decoding result based on the signal probability distribution, the first set, and the values ​​of the transmission bits in the coded sequence. The signal probability distribution includes the probability distribution of the sequence to be coded, and the first set indicates the position of each value in the first sequence in the coded sequence.

[0105] In one possible design, the receiving device is also used to execute the method in any possible design of the first aspect above.

[0106] In a sixth aspect, a computer-readable storage medium is provided, comprising: a computer program or instructions; when the computer program or instructions are run on a computer, the computer is caused to execute any one of the methods in any one of the above aspects.

[0107] In a seventh aspect, a computer program product is provided, comprising a computer program or instructions, which, when executed on a computer, causes the computer to execute any one of the methods in any one of the above aspects.

[0108] In an eighth aspect, a circuit system is provided, wherein the circuit system includes a processing circuit configured to execute any of the methods in any of the above aspects.

[0109] Among them, the technical effects brought about by any design in the second to eighth aspects can refer to the beneficial effects of the corresponding methods provided above, and will not be repeated here. BRIEF DESCRIPTION OF THE DRAWINGS

[0110] FIG1 is a schematic diagram of the architecture of a communication system provided in an embodiment of the present application;

[0111] FIG2 is a schematic diagram of a basic flow of wireless communication provided by an embodiment of the present application;

[0112] FIG3 is a schematic diagram of an encoding process provided in an embodiment of the present application;

[0113] FIG4 is a schematic diagram of a decoding process provided in an embodiment of the present application;

[0114] FIG5 is a flowchart of a decoding method under a non-finite field provided by an embodiment of the present application;

[0115] FIG6 is a schematic diagram of another decoding process provided in an embodiment of the present application;

[0116] FIG7 is a schematic diagram of another decoding process provided in an embodiment of the present application;

[0117] FIG8 is a flowchart of a decoding method under a non-finite field provided by an embodiment of the present application;

[0118] FIG9a is a flowchart of another decoding method under a non-finite field provided by an embodiment of the present application;

[0119] FIG9 b is a schematic diagram of a function gradient provided in an embodiment of the present application;

[0120] FIG10 is a flowchart of another decoding method under a non-finite field provided in an embodiment of the present application;

[0121] FIG11 is a simulation result provided by an embodiment of the present application;

[0122] FIG12 is another simulation result provided by an embodiment of the present application;

[0123] FIG13 is a first structural diagram of a communication device provided in an embodiment of the present application;

[0124] FIG14 is a second structural diagram of the communication device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0125] FIG1 is a schematic diagram of the architecture of a communication system 1000 used in an embodiment of the present application. As shown in FIG1 , the communication system 1000 includes at least one network device (such as 110a and 110b in FIG1 ) and at least one terminal device (such as 120a-120j in FIG1 ). The terminal device is connected to the network device wirelessly. FIG1 is only a schematic diagram, and the communication system may also include other network devices, such as wireless relay devices and wireless backhaul devices, which are not shown in FIG1 .

[0126] A network device may be a base station, an evolved NodeB (eNodeB), a transmission reception point (TRP), a next-generation NodeB (gNB) in a fifth-generation (5G) mobile communication system, a next-generation base station in a sixth-generation (6G) mobile communication system, a base station in a future mobile communication system, or an access node in a wireless fidelity (WiFi) system. It may also be a module or unit that performs some of the functions of a base station, for example, a centralized unit (CU) or a distributed unit (DU). The CU here completes the functions of the radio resource control (RRC) protocol and the packet data convergence protocol (PDCP) of the base station, and can also complete the function of the service data adaptation protocol (SDAP); the DU completes the functions of the radio link control (RLC) layer and the medium access control (MAC) layer of the base station, and can also complete the functions of part of the physical layer or all of the physical layer. For the specific description of the above-mentioned various protocol layers, please refer to the relevant technical specifications of the 3rd Generation Partnership Project (3GPP). The network device can be a macro base station (such as 110a in Figure 1), a micro base station or an indoor station (such as 110b in Figure 1), or a relay node or a donor node, etc. The embodiments of the present application do not limit the specific technology and specific device form adopted by the network device. For the convenience of description, the following description is taken as an example.

[0127] Terminal devices may also be referred to as terminals, user equipment (UE), mobile stations, mobile terminals, etc. Terminal devices can be widely used in various scenarios, for example, device-to-device (D2D), vehicle-to-everything (V2X) communication, machine-type communication (MTC), Internet of Things (IOT), virtual reality, augmented reality, industrial control, autonomous driving, telemedicine, smart grid, smart furniture, smart office, smart wearable, smart transportation, smart city, etc. Terminal devices may be mobile phones, tablet computers, computers with wireless transceiver functions, wearable devices, vehicles, drones, helicopters, airplanes, ships, robots, robotic arms, smart home devices, etc. The embodiments of the present application do not limit the specific technology and specific device form adopted by the terminal devices.

[0128] Network devices and terminal devices can be fixed or mobile. They can be deployed on land, including indoors or outdoors, handheld or vehicle-mounted; on water; and in the air on aircraft, balloons, and satellites. The embodiments of this application do not limit the application scenarios of network devices and terminal devices.

[0129] The roles of network devices and terminal devices can be relative. For example, the helicopter or drone 120i in Figure 1 can be configured as a mobile base station. To terminal devices 120j accessing the wireless access network via 120i, terminal device 120i is a network device. However, to network device 110a, 120i is a terminal device, meaning that communication between 110a and 120i occurs via a wireless air interface protocol. Of course, communication between 110a and 120i can also occur via a base station-to-base station interface protocol. In this case, 120i is also a network device relative to 110a. Therefore, both network devices and terminal devices can be collectively referred to as communication devices. 110a and 110b in Figure 1 can be referred to as communication devices with network device functionality, while 120a-120j in Figure 1 can be referred to as communication devices with terminal device functionality.

[0130] Network devices and terminal devices, network devices and network devices, and terminal devices and terminal devices can communicate through authorized spectrum, unauthorized spectrum, or both; can communicate through spectrum below 6 gigahertz (GHz), spectrum above 6 GHz, or spectrum below 6 GHz and spectrum above 6 GHz simultaneously. The embodiments of the present application do not limit the spectrum resources used for wireless communications.

[0131] In the embodiments of the present application, the functions of the network device may also be performed by a module (such as a chip) in the network device, or by a control subsystem that includes the network device functions. The control subsystem that includes the network device functions here may be a control center in the above-mentioned application scenarios such as smart grid, industrial control, smart transportation, and smart city. The functions of the terminal device may also be performed by a module (such as a chip or a modem) in the terminal device, or by a device that includes the terminal device functions.

[0132] Next, the basic process of wireless communication is introduced.

[0133] Figure 2 illustrates a basic wireless communication process. At the transmitting device, a signal undergoes source coding, channel coding, and modulation before being transmitted over a channel to the receiving device. At the receiving device, the signal is then demodulated, channel decoded, and finally decoded. In uplink transmission, the transmitting device is the terminal device in Figure 1, and the receiving device is the network device in Figure 1. In downlink transmission, the transmitting device is the network device in Figure 1, and the receiving device is the terminal device in Figure 1.

[0134] It should be understood that the basic process of wireless communication also includes additional processes, such as precoding and interleaving. Since these additional processes are common knowledge to those skilled in the art, they are not listed one by one.

[0135] It should be understood that the message names between the devices or the names of the parameters in the messages in the embodiment of the present application are only examples, and other names may be used in specific implementations. The embodiment of the present application does not specifically limit this.

[0136] To facilitate understanding of the embodiments of the present application, the following briefly describes the technologies involved in the embodiments of the present application. It should be understood that these descriptions are only for facilitating understanding of the embodiments of the present application and should not constitute any limitation on the present application.

[0137] 1. Non-finite domain polarization

[0138] Non-finite field polarization is a technique that generalizes polarization phenomena from the binary field to non-finite fields (such as the real or complex fields) to achieve better encoding and decoding. Furthermore, the use of successive cancellation (SC) decoding can achieve excellent decoding performance.

[0139] 2. Polar codes in binary domain

[0140] Polar code is a channel coding scheme that can be rigorously proven to asymptotically reach the Shannon capacity of a binary input channel. It has the characteristics of good performance and low complexity.

[0141] Referring to FIG. 3 , FIG. 3 is a schematic diagram of a typical 8×8 polar code source compression. The compressed sequence on the left is divided into received values ​​and values ​​to be recovered according to their respective reliabilities.

[0142] Source sequence After encoding, the encoded sequence is obtained Generally, the bits with higher reliability are set to the value to be recovered, and the bits with lower reliability are set to the received value, which need to be transmitted from the transmitting device to the receiving device. As shown in Figure 3, the four bits with higher reliability include: u3, u5, u6, and u7, which are set to the value to be recovered. The four bits with lower reliability include: u0, u1, u2, and u4, which are set to the received value. In other words, the source sequence It is compressed into u0, u1, u2, u4, and the 8-long sequence is compressed into a 4-long sequence, thus achieving the source compression requirement.

[0143] In order to restore the original source sequence from the compressed result (u0,u1,u2,u4) Polar code decoding requires using the compression result (i.e. the received value) and the distribution of the original source sequence to sequentially recover the value to be recovered (u3, u5, u6, u7), and then convert the coded sequence into Re-encoding to restore the original source sequence

[0144] 3. Compressed sensing (CS)

[0145] Compressed sensing is a technique for finding sparse solutions in underdetermined linear systems and has widespread applications in signal and image processing. In many practical problems in science and technology, it is often necessary to recover the true signal from sampled data. When the sampling system is linear, this problem can be viewed as solving a system of linear equations:

[0146] y=Ah formula (1-1)

[0147] Where y∈RM Represents the sampled data, which is a matrix of M rows and 1 column, \(A\in R\). M×N Represents the sampling matrix, which is a matrix of M rows and N columns, \(h\in R\). N Represents the true signal, which is a matrix of N rows and 1 column.

[0148] When \(M < N\), this is an underdetermined linear system, so the signal \(h\) cannot be accurately recovered from \(y\). However, if it is assumed that the signal \(h\) has a sparse structure, that is, most of the elements of \(h\) are 0, then the sampled data \(y\) can be used to efficiently and accurately recover the signal \(h\). Compressed sensing is a technique for solving sparse signals in such underdetermined linear systems.

[0149] Exemplarily, referring to Fig. 4, Fig. 4 shows a model framework of compressed sensing. In Fig. 4, each square represents an element.

[0150] Since sparse signals are very common in practical engineering problems, the application of compressed sensing technology is very extensive. For example, single-pixel imaging technology, nuclear magnetic resonance imaging technology, radar detection technology, etc. By using the sparse structure in these engineering problems and the theoretical analysis of compressed sensing, more accurate signal reconstruction can be completed with less sampled data, thus greatly reducing the cost and effectively improving the accuracy of the reconstructed image.

[0151] In compressed sensing, the most common and widely studied signal reconstruction algorithm is the Basis Pursuit (BP) algorithm. The BP algorithm transforms the problem of solving the sparse solution in a linear system into the problem of minimizing the L1 norm under linear constraints. Specifically, taking the model in Fig. 4 as an example, solving the sparse signal \(h\) that satisfies \(y = Ah\) can be transformed into the following optimization problem:

[0152] \(\min||z||_0\) subject to \(Ah = y\) Formula (1-2)

[0153] Among them, \(||z||_0\) (L0 norm) represents the number of non-zero elements in the sparse signal \(h\), \(y\) represents the sampled data, \(A\) represents the sampling matrix, and \(h\) represents the true signal. Since the above L0 optimization problem is a non-convex optimization, it is difficult to find an efficient solution algorithm. To overcome this difficulty, this optimization problem can be relaxed, and the L1 norm is used to approximate the L0 norm, transforming the problem into:

[0154] \(\min||z||_1\) subject to \(Ah = y\) Formula (1-3)

[0155] Among them, \(z\) irepresents the non-zero elements in the sparse signal h. The L1 optimization problem is a convex optimization problem. By using the properties of the L1 norm, a low-complexity iterative algorithm can be designed to solve the L1 optimization problem. Once the solution of the L1 optimization problem is obtained, the reconstructed signal is obtained. This process of recovering the sparse signal h is called the BP algorithm. According to compressed sensing theory, under certain regularization conditions, it can be proven that the BP algorithm can accurately recover any sparse signal h. This provides theoretical support for the reliability of the BP algorithm, and it is also the most common signal reconstruction method in practical applications.

[0156] In the process of obtaining the reconstructed signal using the BP algorithm, multiple iterative decoding is required, and the decoding complexity is high.

[0157] In view of this, the embodiment of the present application provides a decoding method under a non-finite field, which can be applied to the communication system of Figure 1. In the embodiment of the present application, the receiving device obtains a first sequence. The first sequence includes the value of the transmission bit in the encoded sequence, and the length of the first sequence is N1. The encoded sequence is the sequence after the sequence to be encoded is encoded, and the length of the sequence to be encoded is N, where N=2 n , n is a positive integer. N1 is a positive integer less than N. Then, the receiving device determines the decoding result based on the signal probability distribution, the first set, and the value of the transmission bit in the encoded sequence. The signal probability distribution includes the probability distribution of the sequence to be encoded, and the first set indicates the position of each value in the first sequence in the encoded sequence. In other words, the encoded sequence includes the value of the transmission bit and the value of the bit to be recovered. The reliability of the bit to be recovered is higher than the reliability of the transmission bit. In this way, after obtaining the first sequence, the receiving device can combine the signal probability distribution and the first set to determine the value of the bit to be recovered through recursive operation. When the value of each transmission bit and the value of the bit to be recovered are known, the receiving device can determine the decoding result. In the above decoding process, the receiving device performs one operation for the value of each position, and there is no iterative operation process, and the decoding complexity is low.

[0158] In the embodiments of the present application, the sequence to be encoded refers to the sequence before encoding by the transmitting device. The encoded sequence refers to the sequence after the transmitting device encodes the sequence to be encoded. The values ​​of the transmission bits in the encoded sequence constitute the first sequence.

[0159] 5 to 12 , a decoding method 500 under a non-finite field according to an embodiment of the present application is described in detail. The decoding method 500 under a non-finite field according to an embodiment of the present application includes the following steps:

[0160] S501: The transmitting device encodes the sequence to be encoded to obtain an encoded sequence.

[0161] In the uplink transmission, the originating device is the terminal device in Figure 1. In the downlink transmission, the originating device is the network device in Figure 1.

[0162] Among them, the length of the sequence to be encoded is N, N=2 n , n is a positive integer. For example, N = 2, 4, 8, or 16. Taking Figure 8 as an example, the sequence to be encoded includes

[0163] The coded sequence includes at least one bit to be restored and at least one transmission bit. Exemplarily, the coded sequence includes N1 transmission bits and N2 bits to be restored. N=N1+N2, where N1 and N2 are positive integers.

[0164] It is easy to understand that in the embodiment of the present application, in the encoded sequence, the reliability of the transmission bit is lower than the reliability of the bit to be restored, and the position before the first bit to be restored in the encoded sequence is the transmission bit.

[0165] Taking Figure 8 as an example, the encoded sequence includes That is, the encoded sequence in Figure 8 has four positions, numbered 0 through 3. The value at position 0 is z0, the value at position 1 is z1, and the values ​​for the other positions can be deduced similarly and are not further described. In the encoded sequence in Figure 8, there are two transmitted bits, namely positions 0 and 2. In the encoded sequence in Figure 8, there are two bits to be recovered, namely positions 1 and 3.

[0166] S502a: The transmitting device sends the coded sequence to the receiving device. Correspondingly, the receiving device receives the coded sequence from the transmitting device.

[0167] For example, the coded sequence is sent by the transmitting device after coding and modulation, and is transmitted to the receiving device through a channel. Correspondingly, the receiving device obtains the coded sequence through demodulation.

[0168] It is easy to understand that the processing that the coded sequence undergoes before transmission over the channel, such as rate matching, precoding, interleaving, modulation, etc., is common knowledge to those skilled in the art and will not be listed one by one. In the embodiments of this application, the transmission of the coded sequence is used as an example for description, which should not be construed as limiting the embodiments of this application.

[0169] Illustratively, in uplink transmission, the transmitting device is the terminal device in Figure 1 and the receiving device is the network device in Figure 1. In downlink transmission, the transmitting device is the network device in Figure 1 and the receiving device is the terminal device in Figure 1.

[0170] S502b: The receiving device determines a first sequence according to the received encoded sequence.

[0171] The first sequence includes the value of each transmission bit in the coded sequence. The coded sequence includes N1 transmission bits, and accordingly, the length of the first sequence is N1.

[0172] Taking FIG8 as an example, the first sequence includes [z0, z2]. In other words, the first sequence includes the values ​​of the two transmission bits in the encoded sequence.

[0173] Exemplarily, the first sequence is a real number sequence. For example, each value in the first sequence is a discrete value, such as the first sequence includes [0, 2]. For another example, each value in the first sequence is a continuous value, such as the first sequence includes [0.5, -0.67].

[0174] For the receiving device, after the receiving device obtains the first sequence, the receiving device executes S503:

[0175] S503: The receiving device determines a decoding result according to the signal probability distribution, the first set, and the value of the transmission bit in the encoded sequence.

[0176] The signal probability distribution includes the probability distribution of the sequence to be encoded.

[0177] For example, the signal probability distribution includes: X ~ [-1 + 1; 0.5 0.5], that is, in FIG8 Among the 4 positions, the probability of each position being -1 is 0.5, and the probability of each position being +1 is 0.5.

[0178] For example, the signal probability distribution may be preconfigured.

[0179] The first set indicates the position of each value in the first sequence in the encoded sequence.

[0180] Taking Figure 8 as an example, the first set includes {0, 2}. The first set {0, 2} can be understood as meaning that positions 0 and 2 in the encoded sequence are transmission bits. Furthermore, when the first sequence includes [z0, z2], the first value z0 in the first sequence is at position 0, and the second value z2 is at position 2.

[0181] Exemplarily, the first set may be preconfigured.

[0182] In some embodiments, the first sequence is a real number sequence, and the decoding result is a real number sequence, as described in the following examples 1 and 3. Alternatively, the first sequence is a real number sequence, and the decoding result is a complex number sequence, as described in the following example 2.

[0183] Exemplarily, as shown in FIG6 , S503 includes S5031 and S5032:

[0184] S5031. The receiving device determines a decoding path according to the signal probability distribution, the first set, and the value of the transmission bit in the encoded sequence.

[0185] Among them, the decoding path indicates the value of each position in the encoded sequence. Taking Figure 8 as an example, the decoding path indicates the value of each position in the encoded sequence, that is,

[0186] Exemplarily, the various positions in the decoding path and the values ​​at each position are described as follows:

[0187] For the kth transmission bit in the decoding path, the value of the transmission bit is the same as the value of the kth transmission bit in the first sequence. Here, k is a positive integer less than or equal to N1. In other words, the receiving device uses the value of the kth transmission bit in the first sequence as the value of the kth transmission bit in the decoding path.

[0188] Taking Figure 8 as an example, k=1, the first transmitted bit is the position of sequence 0, in, It represents the value of the first transmission bit indicated by the decoding path (i.e., the position of sequence 0), and u0 represents the value of the first transmission bit indicated by the first sequence.

[0189] For the jth bit to be restored in the decoding path, the value of the bit to be restored corresponds to the maximum decoding metric among multiple decoding metrics, where j is a positive integer less than or equal to N2.

[0190] Taking Figure 8 as an example, j = 1, and the first bit to be restored is the position of sequence number 1. The conditional probability distribution of the position of sequence number 1 includes: P(-1) = 1 / 2, P(0) = 1 / 4, P(+1) = 1 / 4. When the conditional probability distribution is used as the decoding metric, the value of the position of sequence number 1 is -1, that is, in, Indicates the value of the first bit to be restored (i.e., the position of sequence 1) indicated by the decoding path.

[0191] Each of the multiple decoding metrics is determined based on the following two items:

[0192] The first item is the signal probability distribution.

[0193] The second item is the value of each position before the jth bit to be restored in the decoding path.

[0194] It will be readily understood that in some embodiments, the positions preceding the jth bit to be restored in the decoding path are all transmission bits. In this case, each position preceding the jth bit to be restored includes each transmission bit preceding the jth bit to be restored. In other embodiments, the positions preceding the jth bit to be restored in the decoding path include both transmission bits and bits to be restored. Accordingly, each position preceding the jth bit to be restored includes both the transmission bits preceding the jth bit to be restored and the bits to be restored.

[0195] For example, FIG7 illustrates a decoding process. In FIG7, the coded sequence includes N positions, and the sequence of positions is 1 to N. The decoding path indicates the value of N positions, which is recorded as

[0196] Taking FIG. 7 as an example, S5031 includes the following steps:

[0197] For the first position in the encoded sequence (i.e., position number 1, or described as the first transmitted bit), the receiving device performs step 2:

[0198] Step 2: The receiving device processes the signal probability distribution through the f operation to obtain the probability distribution of the value z1 at the first position of the encoded sequence. The receiving device determines

[0199] in, It represents the value of the first transmission bit (i.e. the position of sequence number 1) indicated by the decoding path, and z1 represents the value of the first transmission bit indicated by the first sequence.

[0200] For the positions after the first position, such as the i-th position (i.e., the position with sequence number i), if i is an odd number, the receiving device executes step 3a; if i is an even number, the receiving device executes step 3b:

[0201] Step 3a: The receiving device processes the signal probability distribution and the values ​​of the first i-1 positions through the g operation to obtain the g operation result, and then processes the signal probability distribution and the g operation result through the f operation to obtain the conditional probability distribution at the i-th position.

[0202] Step 3b: The receiving device processes the signal probability distribution and the values ​​of the first i-1 positions through the g operation to obtain the conditional probability distribution at the i-th position.

[0203] Among them, the value of the first i-1 position can be recorded as The conditional probability distribution at the i-th position can be recorded as

[0204] Then, the receiving device determines whether the i-th position belongs to the first set. If so, the receiving device executes step 5. If not, the receiving device executes step 4. Steps 4 and 5 are described as follows:

[0205] Step 4: The receiving device determines the value of the i-th position

[0206] in, satisfy:

[0207]

[0208] in, Indicates the value of the i-th position indicated by the decoding path, Indicates that the value at the first i-1 position is In the case of , the value of the i-th position is z i The probability of express Maximize the conditional probability distribution of the i-th position.

[0209] It is easy to understand that, when the conditional probability distribution is used as the decoding metric, the value of the i-th position in the decoding path corresponds to the largest decoding metric among multiple decoding metrics.

[0210] Step 5: Determine the receiving device

[0211] in, Indicates the value of the i-th position indicated by the decoding path, z i Represents the value of the i-th position (the i-th position is the transmission bit) indicated by the first sequence.

[0212] For the receiving device, after executing step 4 or step 5, if i is less than N, the receiving device replaces i with i+1 and executes step 3 again. If i is equal to N, the receiving device executes step 6:

[0213] Step 6: Output from receiving device

[0214] That is to say, the receiving device can obtain the decoding path through steps 1 to 6.

[0215] It should be understood that in S5031, the f operation and the g operation are described as follows:

[0216] The input to the f operation includes the probability distribution of the first variable and the probability distribution of the second variable. The output of the f operation includes the probability distribution of the third variable, which is the convolution of the probability distribution of the first variable and the probability distribution of the second variable. See the description of Example 1 (or Example 2, or Example 3) below for details.

[0217] The input to the g operation includes the probability distribution of the first variable, the probability distribution of the second variable, and the probability distribution of the third variable, as well as the first value of the third variable. The output of the g operation includes the conditional probability distribution of the fourth variable at the first value of the third variable, as described in Example 1 (or Example 3) below. Alternatively, the input to the g operation includes the probability distribution of the first variable, the probability distribution of the second variable, and the first value of the third variable. The output of the g operation includes the conditional probability distribution of the fourth variable at the first value of the third variable, as described in Example 2 below. The first value is the decoded value of the third variable.

[0218] The first variable is the value of the t-th position in the s-th layer of the encoding network, and the second variable is the value of the t+2-th position in the s-th layer. n-s The third variable is the value of the tth position in the s+1th layer of the encoding network, and the fourth variable is the value of the tth position in the s+1th layer. n-s The encoding network includes n+1 layers, the first layer of the encoding network is used to input the sequence to be encoded, the second to nth layers of the encoding network are used to encode the sequence to be encoded to obtain the encoded sequence, and the n+1th layer of the encoding network is used to output the encoded sequence. s is a positive integer less than or equal to n. t is a positive integer, and t traverses each parameter in the sth parameter set, each parameter in the sth parameter set indicates a position in the sth layer, and the number of positions indicated by the sth parameter set is N / 2.

[0219] It is easy to understand that during the decoding process, the receiving device performs N*n / 2 f operations and N*n / 2 g operations. The specific process is as follows:

[0220] u s,t is the value of the t-th position in the s-th layer of the encoding network. 1,1 ,…,u 1,N is the sequence to be encoded, u n+1,1 ,…,u n+1,N is the encoded sequence. The parameter t is a positive integer greater than or equal to 1 and less than or equal to N. is 0 or 1, which can be understood as is the binary representation of t-1. When t is greater than 1, Right now The position of the first 1 in .

[0221] The receiving device sequentially decodes un+1,1 ,…,u n+1,N The receiving device decodes u n+1,1 When N-1 f operations are performed, the decoding u n+1,t When t is greater than 1 and t is an even number, perform 1 g operation; when decoding u n+1,t When t is greater than 1 and t is an odd number, execute g operations, f operations, specifically:

[0222] In decoding u n+1,1 When j traverses from 1 to n, i traverses from 1 to 2 n-s , the input of operation f includes the first variable u j,i The probability distribution of the second variable The output of the f operation includes the third variable u j+1,i The probability distribution of .

[0223] In decoding u n+1,t When t is greater than 1 and t is an even number, the input of the g operation includes the first variable u n,t-1 The probability distribution of the second variable u n,t The probability distribution of the third variable, the probability distribution of the third variable, and the decoded value of the third variable The output of the g operation includes the third variable u n+1,t The probability distribution of , and then the decoded value is obtained.

[0224] In decoding u n+1,t , when t is greater than 1 and t is an odd number, the receiving device first g operations, i traverses from t to The input to the g operation includes the first variable The probability distribution of the second variable The probability distribution of the third variable The probability distribution of , and the decoded value of the third variable The output of the g operation includes the third variable Then, the receiving device performs f operations, j from no t +2 traverses to n, i traverses from t to t+2 n-j -1, the input of the f operation includes the first variable u j,i The probability distribution of the second variable The probability distribution of the f operation includes the third variable u j+1,i The probability distribution of , and then the decoded value is obtained.

[0225] For example, the encoding network can be a butterfly structure. The number of layers in the encoding network = log2N+1. Where N represents the length of the sequence to be encoded. When the length of the sequence to be encoded N = 4, the number of layers in the encoding network is 3. See the following examples 1 to 3 for details.

[0226] S5032. The receiving device determines the decoding result according to the decoding path.

[0227] Taking Figure 7 as an example, the value of the decoding path indication is recorded as Receiving device pair Perform inverse Hadamard transform to obtain the decoding result.

[0228] Next, the decoding process of the embodiment of the present application is introduced through three examples (Example 1 to Example 3 below):

[0229] Example 1

[0230] In Example 1, both the first sequence and the decoding result are real number sequences. The decoding process is described below using discrete values ​​as an example:

[0231] Figure 8 illustrates a decoding process for a non-finite field. In Figure 8, the code length of the sequence to be encoded is N = 4. x0, x1, x2, and x3 are the sequence to be encoded and are also the values ​​at positions 1, 2, 3, and 4 in the first layer of the encoding network. y0, y1, y2, and y3 are the values ​​at positions 1, 2, 3, and 4 in the second layer of the encoding network. z0 and z2 are the values ​​of the transmitted bits, and z1 and z3 are the values ​​of the bits to be recovered. z0, z1, z2, and z3 are also the values ​​at positions 1, 2, 3, and 4 in the third layer of the encoding network.

[0232] The input of the receiving device includes the following three items:

[0233] The first item is the first sequence [z0, z2]. In Figure 8, z0=0, z2=2.

[0234] The second item is the signal probability distribution. In Figure 8, the signal probability distribution of x0, x1, x2, and x3 is P(-1) = 1 / 4, P(1) = 3 / 4).

[0235] The third item is the position number of the transmission bit {0,2}.

[0236] The output of the receiving device includes:

[0237] First, we introduce the f operation and g operation applicable to discrete values. Among them, the f operation is used to perform convolution operations, and the g operation is used to perform conditional probability operations. The introduction of the f operation and g operation is as follows:

[0238] 1. f operation

[0239] The inputs to the f operation include the following two items:

[0240] The first item, A~P,P(a i )=p i ,i=1,...,I; A represents the set of the first variable, P represents the probability distribution of the first variable, a i represents the first variable i in A, p i Indicates that the first variable of the i-th is a i The probability of , I represents the number of the first variable.

[0241] The second item, B~Q,P(b j )=q j ,j=1,...,J; B represents the set of the second variable, Q represents the probability distribution of the second variable, b j represents the j-th second variable in B, q j Indicates that the jth second variable is b j The probability of , J represents the number of second variables.

[0242] The outputs of the f operation include:

[0243] C~F,F(c k )=f k ,k=1,...,K; C represents the set of the third variable, F represents the probability distribution of the third variable, c k represents the kth third variable in C, f k Indicates that the kth third variable is c k , K represents the number of third variables, and the values ​​of K third variables are different from each other.

[0244] Among them, c k is one of the IxJ values, where IxJ values ​​are obtained when i=1,...,I ​​and j=1,...,J are traversed. i,j The value of f i,j =p i q j , f i,j Indicates c i,j The probability of occurrence. k When L values ​​are the same as L values ​​in IxJ values, f k It is equal to the sum of the occurrence probabilities of L values, where L is a positive integer less than or equal to IxJ.

[0245] In other words, the operation f includes steps a1 and b1:

[0246] Step a1: traverse i=1,...,I,j=1,...,J and calculate the following two items: f i,j =p i q j .

[0247] Step a2, for different i,j, calculate c i,j May be the same, will take the same value c i,j Merge. Merge can be understood as combining c with the same value i,j The corresponding f i,j Add up.

[0248] 2. g operation

[0249] The input to the g operation includes the following four items:

[0250] The first item, A~P,P(a i )=p i ,i=1,...,I; A represents the set of the first variable, P represents the probability distribution of the first variable, a i represents the first variable i in A, p i Indicates that the first variable of the i-th is a i The probability of , I represents the number of the first variable.

[0251] The second item, B~Q,P(b j )=q j ,j=1,...,J; B represents the set of the second variable, Q represents the probability distribution of the second variable, b j represents the j-th second variable in B, q j Indicates that the jth second variable is b j The probability of , J represents the number of second variables.

[0252] The third item, C represents a set of third variables, and μ represents a first value of the third variable.

[0253] The fourth term, P(μ)=f; P(μ) represents the value of the probability distribution of the third variable at μ.

[0254] The outputs of the g operation include:

[0255] exist The conditional probability distribution G,G(d m )=g m ,g m =p i q j / f,m=1,...,M, D represents the set of the fourth variable, G represents the probability distribution of the fourth variable, d m represents the mth fourth variable in D, g mIndicates that the mth fourth variable is d m The probability of , M represents the number of the fourth variable.

[0256] In other words, the operation g includes: in the process of traversing i=1,...,I,j=1,...,J, if Then calculate the following two items: g m =p i q j / f.

[0257] Among them, the introduction of the above-mentioned first variable to the fourth variable can be found in the description of S5031, and will not be repeated here.

[0258] Next, the steps in Example 1 (hereinafter referred to as S11 to S18) are described:

[0259] S11, the receiving device performs f operation.

[0260] Exemplarily, the receiving device performs an f operation, where the input of the f operation includes the probability distribution of a first variable (the value x0 at the first position in the first layer of the encoding network) and the probability distribution of a second variable (the value x2 at the third position in the first layer). The output of the f operation includes the probability distribution of a third variable (the value y0 at the first position in the second layer).

[0261] In S11, the inputs to the f operation include the following two items:

[0262] The first term, x0~P,P(a i )=p i ,i=1...I.

[0263] Specifically, the probability that x0 is -1 is 1 / 4, and the probability that x0 is 1 is 3 / 4.

[0264] For example, it can be expressed as: a1 = -1, a2 = 1.

[0265] p1=1 / 4,p2=3 / 4.

[0266] The second term, x2~Q,P(b j )=q j ,j=1...J.

[0267] Specifically, the probability that x2 is -1 is 1 / 4, and the probability that x2 is 1 is 3 / 4.

[0268] For example, it can be written as: b1 = -1, b2 = 1.

[0269] q1=1 / 4,q2=3 / 4.

[0270] In S11, the output of the f operation includes: The conditional probability distribution F.

[0271] Specifically, in the process of traversing i=1...I=2, j=1...J=2, the following two items are calculated: f ij =p i q j .

[0272] For example, it can be written as: c 12 =0,c 21 =0,

[0273]

[0274] After merging, it can be recorded as: c2=0,

[0275]

[0276] In S11, the output of the f operation can be recorded as: y0~F,P(c k )=f k ,k=1,...,K,K=3.

[0277] S12, the receiving device performs f operation.

[0278] Exemplarily, the receiving device performs an f operation, where the input of the f operation includes the probability distribution of a first variable (the value x1 at the second position in the first layer of the encoding network) and the probability distribution of a second variable (the value x3 at the fourth position in the first layer). The output of the f operation includes the probability distribution of a third variable (the value y1 at the second position in the second layer).

[0279] In S12, the inputs to the f operation include the following two items:

[0280] The first term, x1~P,P(a i )=p i ,i=1...I.

[0281] Specifically, the probability that x1 is -1 is 1 / 4, and the probability that x1 is 1 is 3 / 4.

[0282] For example, it can be expressed as: a1 = -1, a2 = 1.

[0283] p1=1 / 4,p2=3 / 4.

[0284] The second term, x3~Q,P(b j )=q j,j=1...J.

[0285] Specifically, the probability that x3 is -1 is 1 / 4, and the probability that x3 is 1 is 3 / 4.

[0286] For example, it can be written as: b1 = -1, b2 = 1.

[0287] q1=1 / 4,q2=3 / 4.

[0288] In S12, the output of the f operation includes: The conditional probability distribution F.

[0289] Specifically, in the process of traversing i=1...I=2, j=1...J=2, the following two items are calculated: f ij =p i q j .

[0290] For example, it can be written as: c 12 =0,c 21 =0,

[0291]

[0292] After merging, it can be recorded as: c2=0,

[0293]

[0294] In S12, the output of the f operation can be recorded as: y1~F,P(c k )=f k ,k=1,...,K,K=3.

[0295] S13, the receiving device performs f operation.

[0296] Exemplarily, the receiving device performs an f operation, where the input of the f operation includes the probability distribution of a first variable (the value y0 at the first position in the second layer of the encoding network) and the probability distribution of a second variable (the value y1 at the second position in the second layer). The output of the f operation includes the probability distribution of a third variable (the value z0 at the first position in the third layer).

[0297] In S13, the inputs to the operation f include the following two items:

[0298] The first term, y0~P,P(a i )=p i ,i=1...I.

[0299] Specifically, y0 is The probability of y0 being 0 is 1 / 16, the probability of y0 being 0 is 6 / 16, and y0 is The probability is 9 / 16.

[0300] For example, it can be written as: a2=0,

[0301]

[0302] The second term, y1~Q,P(b j )=q j ,j=1...J.

[0303] Specifically, y1 is The probability of y1 being 0 is 1 / 16, the probability of y1 being 0 is 6 / 16, and y1 is The probability is 9 / 16.

[0304] For example, it can be written as: b2=0,

[0305]

[0306] In S13, the output of the f operation includes: The conditional probability distribution F.

[0307] Specifically, in the process of traversing i=1...I=3, j=1...J=3, the following two items are calculated: f ij =p i q j .

[0308] For example, it can be written as:

[0309] c 11 =-2,c 12 =-1,c 13 =0,c 21 =-1,c 22 =0,c 23 =1,c 31 =0,c 32 =1,c 33 =2.

[0310]

[0311] After merging, it can be recorded as: c1 = -2, c2 = -1, c3 = 0, c4 = 1, c5 = 2.

[0312]

[0313] In S13, the output of the f operation can be recorded as: z0~F,P(c k )=f k ,k=1,...,K,K=5.

[0314] Since z0=0 is known,

[0315] S14: The receiving device performs g operation.

[0316] Exemplarily, the receiving device performs a g operation, the input of which includes the probability distribution of the first variable (the value y0 of the first position in the second layer of the coding network), the probability distribution of the second variable (the value y1 of the second position in the second layer), the probability distribution of the third variable (the value z0 of the first position in the third layer), and the decoded value of z0. The output of the g operation includes the fourth variable (the value z1 at the second position in the third layer) in The conditional probability distribution at .

[0317] In S14, the input of the g operation includes the following four items:

[0318] The first term, y0~P,P(a i )=p i ,i=1...I.

[0319] Specifically, y0 is The probability of y0 being 0 is 1 / 16, the probability of y0 being 0 is 6 / 16, and y0 is The probability is 9 / 16.

[0320] For example, it can be written as: a2=0,

[0321]

[0322] The second term, y1~Q,P(b j )=q j ,j=1...J.

[0323] Specifically, y1 is The probability of y2 being 0 is 6 / 16, and the probability of y1 being The probability is 9 / 16.

[0324] For example, it can be written as: b2=0,

[0325]

[0326] The third and fourth items,

[0327] In S14, the output of the g operation includes: Given the conditional probability distribution G where z0=0.

[0328] Specifically, in the process of traversing i=1...I=3,j=1...J=3, if Then calculate the following two items: g m =p i q j / f.

[0329] For example, it can be recorded as: d1 = -2, d2 = 0, d3 = 2.

[0330]

[0331] In S14, the output of the g operation can be recorded as: z1~G,P(d m )=g m ,m=1,...,M,M=3.

[0332] Since z1 is to be restored, That is to say, is the maximum g m The corresponding value d m .

[0333] because so,

[0334] S15, the receiving device performs g calculation.

[0335] Exemplarily, the receiving device performs a g operation, the input of which includes the probability distribution of the first variable (the value x0 of the first position in the first layer of the coding network), the probability distribution of the second variable (the value x2 of the third position in the first layer), the probability distribution of the third variable (the value y0 of the first position in the second layer), and the decoded value of y0. The output of the g operation includes the fourth variable (the value y2 at the third position in the second layer) in The conditional probability distribution at .

[0336] In S15, the input of the g operation includes the following four items:

[0337] The first term, x0~P,P(a i )=p i,i=1...I.

[0338] Specifically, the probability that x0 is -1 is 1 / 4, and the probability that x0 is 1 is 3 / 4.

[0339] For example, it can be expressed as: a1 = -1, a2 = 1.

[0340] p1=1 / 4,p2=3 / 4.

[0341] The second term, x2~Q,P(b j )=q j ,j=1...J.

[0342] Specifically, the probability that x2 is -1 is 1 / 4, and the probability that x2 is 1 is 3 / 4.

[0343] For example, it can be written as: b1 = -1, b2 = 1.

[0344] q1=1 / 4,q2=3 / 4.

[0345] The third and fourth items,

[0346] In S15, the output of the g operation includes: In the known The conditional probability distribution G.

[0347] Specifically, in the process of traversing i=1...I=2,j=1...J=2, if Then calculate the following two items: g m =p i q j / f.

[0348] For example, it can be written as:

[0349]

[0350] In S15, the output of the g operation can be recorded as: y2~G,P(d m )=g m ,m=1,...,M,M=2.

[0351] S16: The receiving device performs g operation.

[0352] Exemplarily, the receiving device performs a g operation, the input of which includes the probability distribution of the first variable (the value x1 at the second position in the first layer of the coding network), the probability distribution of the second variable (the value x3 at the fourth position in the first layer), the probability distribution of the third variable (the value y1 at the second position in the second layer), and the decoded value of y1. The output of the g operation includes the fourth variable (the value y3 at the fourth position in the second layer) in The conditional probability distribution at .

[0353] In S16, the inputs to the g operation include the following four items:

[0354] The first term, x1~P,P(a i )=p i ,i=1...I.

[0355] Specifically, the probability that x1 is -1 is 1 / 4, and the probability that x1 is 1 is 3 / 4.

[0356] For example, it can be expressed as: a1 = -1, a2 = 1.

[0357] p1=1 / 4,p2=3 / 4.

[0358] The second term, x3~Q,P(b j )=q j ,j=1...J.

[0359] Specifically, the probability that x3 is -1 is 1 / 4, and the probability that x3 is 1 is 3 / 4.

[0360] For example, it can be written as: b1 = -1, b2 = 1.

[0361] q1=1 / 4,q2=3 / 4.

[0362] The third and fourth items,

[0363] In S16, the output of the g operation includes: In the known The conditional probability distribution G.

[0364] Specifically, in the process of traversing i=1...I=2,j=1...J=2, if Then calculate the following two items: g m =p i q j / f.

[0365] For example, it can be written as:

[0366]

[0367] In S16, the output of the g operation can be recorded as: y3~G,P(d m )=g m ,m=1,...,M,M=2.

[0368] S17, the receiving device performs f operation.

[0369] Exemplarily, the receiving device performs the f operation, the input of the f operation includes the probability distribution of the first variable (the value y2 of the third position in the second layer of the coding network), the probability distribution of the second variable (the value y3 of the fourth position in the second layer), and the output of the f operation includes the probability distribution of the third variable (the value z2 of the third position in the third layer).

[0370] In S17, the inputs to the f operation include the following two items:

[0371] The first term, y2~P,P(a i )=p i ,i=1...I.

[0372] Specifically, y2 is The probability of y2 is 1 / 2, The probability is 1 / 2.

[0373] For example, it can be written as:

[0374] p1=1 / 2,p2=1 / 2.

[0375] The second term, y3~Q,P(b j )=q j ,j=1...J.

[0376] Specifically, y3 is The probability of y1 is 1 / 2, The probability is 1 / 2.

[0377] For example, it can be written as:

[0378] q1=1 / 2,q2=1 / 2.

[0379] In S17, the output of the f operation includes: The conditional probability distribution F.

[0380] Specifically, in the process of traversing i=1...I=2, j=1...J=2, the following two items are calculated: f ij =p i qj .

[0381] For example, it can be written as: c 12 =0,c 21 =0,

[0382]

[0383] After merging, it can be recorded as: c2=0,

[0384]

[0385] In S17, the output of the f operation can be recorded as: z2~F,P(c k )=f k ,k=1,...,K,K=3.

[0386] Since z2=2,

[0387] S18: The receiving device performs g operation.

[0388] Exemplarily, the receiving device performs a g operation, the input of which includes the probability distribution of the first variable (the value y2 of the third position in the second layer of the coding network), the probability distribution of the second variable (the value y3 of the fourth position in the second layer), the probability distribution of the third variable (the value z2 of the third position in the third layer), and the decoded value of z2. The output of the g operation includes the fourth variable (the value z3 at the fourth position in the third layer) in The conditional probability distribution at .

[0389] In S18, the input of the g operation includes the following four items:

[0390] The first term, y2~P,P(a i )=p i ,i=1...I.

[0391] Specifically, y2 is The probability of y2 is 1 / 2, The probability is 1 / 2.

[0392] For example, it can be written as:

[0393] p1=1 / 2,p2=1 / 2.

[0394] The second term, y3~Q,P(b j )=qj ,j=1...J.

[0395] Specifically, y3 is The probability of y2 is 1 / 2, The probability is 1 / 2.

[0396] The third and fourth items,

[0397] In S18, the output of the g operation includes: In the known The conditional probability distribution G.

[0398] Specifically, in the process of traversing i=1...I=2,j=1...J=2, if Then calculate the following two items: g m =p i q j / f.

[0399] For example, it can be recorded as: d1 = 0.

[0400] g1=1.

[0401] In S18, the output of the g operation can be recorded as: z3~G,P(d m )=g m ,m=1,...,M,M=1.

[0402] Since z3 is to be restored, That is to say, is the maximum g m The corresponding value d m .

[0403] After the above S11 to S18, Calculate:

[0404] Depend on Calculate:

[0405] Depend on Calculate:

[0406] In this way, the receiving device obtains the decoding result

[0407] Example 2

[0408] In Example 2, the first sequence is a real number sequence, and the decoding result is a complex number sequence. The following describes the decoding process using continuous values ​​as an example:

[0409] Figure 9a shows a decoding process in a non - finite field. In Figure 9a, the code length N of the sequence to be encoded is 4. x0, x1, x2, x3 are the sequence to be encoded and also the values at the 1st, 2nd, 3rd, and 4th positions in the first layer of the encoding network. y0, y1, y2, y3 are the values at the 1st, 2nd, 3rd, and 4th positions in the second layer of the encoding network. z0, z2 are the values of the transmitted bits, z1, z3 are the values of the bits to be recovered, and z0, z1, z2, z3 are also the values at the 1st, 2nd, 3rd, and 4th positions in the third layer of the encoding network.

[0410] The input of the receiving - end device includes the following three items:

[0411] The first item is the first sequence [z0, z2]. In Figure 9a, z0 = 0.50 and z2 = - 0.67.

[0412] The second item is the signal probability distribution. In Figure 9a, taking the complex signals c0 = x0 + x1i and c1 = x2 + x3i as an example, the signal probability distribution includes: x0, x1, x2, x3 are independently and identically distributed, following a double - peak Gaussian distribution with a variance of 0.1 where, φ(x; μ, σ) represents the Gaussian distribution density function with a mean of μ and a variance of σ.

[0413] The third item is the position sequence numbers {0, 2} of the transmitted bits.

[0414] The output of the receiving - end device includes:

[0415] Estimated values of the complex signals c0 and c1

[0416] First, define the sampling matrix and the discretization function:

[0417] Definition 1: Sampling matrix

[0418] Given a sampling interval [a, b] and n sampling points a < c1 < c2 <... < c n < b, the sampling matrix P of the density function f X (x) is a 2×(n + 2) matrix, which stores the sampling interval and the values of the density function f X (x) at the sampling points, that is:

[0419]

[0420] where, in the first column of the sampling matrix P, a represents an end - point value of the sampling interval, and the value of the density function f X (x) at the end - point a is 0. In the (i + 1) - th column of the sampling matrix P, the value of the density function f X (x) at the sampling point c iThe value of p i . Among them, the density function f X (x) can be expressed as: f X (c i )=p i ,i=1,2,…,n. In the i+2th column of the sampling matrix P, b represents the other endpoint value of the sampling interval, and the density function f X The value of (x) at endpoint b is 0.

[0421] Definition 2, Discretization Function

[0422] Given a sampling matrix P and a real number x, define the discretization function d(x,P) as:

[0423]

[0424] In the discretization function d(x,P), P 1,1 Represents the element in the first row and first column of the sampling matrix P, that is, the endpoint value a. 1,n+2 Represents the element in the 1st row and n+2th column of the sampling matrix P, that is, the endpoint value b. 1,i Represents the element of the 1st row and the ith column of the sampling matrix P, that is, the sampling point c i-1 .P 2,j Represents the element of the 2nd row and jth column of the sampling matrix P, that is, the sampling point p i-1 .

[0425] In the discretization function d(x,P), if x≤P 1,1 Or x ≥ P 1,n+2 , then d(x,P)=0. If P 1,1 <x<P 1,n+2 , then d(x,P)=P 2,j . It can be understood that the sampling point P of the sampling matrix P 1,j The distance to x is the smallest.

[0426] It is easy to understand that the discretization function d(x,P) is the density function f X The step function approximation of (x) is shown in Figure 9b.

[0427] Then, define the f operation and the g operation:

[0428] 1. f operation:

[0429] The input to the f operation includes the following three items:

[0430] The first item, A~f P .

[0431] Among them, A represents the first variable, f Prepresents the density function of the first variable, and P represents the sampling matrix of the first variable.

[0432] The second item, B~f Q .

[0433] Among them, B represents the second variable, f Q represents the density function of the second variable, and Q represents the sampling matrix of the second variable.

[0434] The third item is the number of sampling points n.

[0435] The outputs of the f operation include:

[0436] The sampling matrix U of .

[0437] The process of determining the sampling matrix U through the f operation includes:

[0438] Step 1: Determine the sampling points:

[0439] make In the interval [U min ,U max ] Select n points with equal spacing, denoted as u1,u2,u3,…,u n .

[0440] Step 2: For the i-th sampling point, calculate the sampling value near the i-th sampling point

[0441] The sample values ​​near the i-th sampling point satisfy:

[0442] d(·,·) is a discretization function. Please refer to the introduction of formula (3-2) and will not be repeated here.

[0443] Step 3, Do normalization calculations

[0444] make

[0445] Then, according to the normalized f i , and get the sampling matrix U:

[0446]

[0447] 2. g operation:

[0448] The input to the g operation includes the following four items:

[0449] The first item, A~f P .

[0450] Among them, A represents the first variable, f P represents the density function of the first variable, and P represents the sampling matrix of the first variable.

[0451] The second item, B~f Q .

[0452] Among them, B represents the second variable, f Q represents the density function of the second variable, and Q represents the sampling matrix of the second variable.

[0453] The third item, Here, C represents the third variable, and μ represents the first value of the third variable.

[0454] The fourth item is the number of sampling points n.

[0455] The outputs of the g operation include:

[0456] exist The conditional probability distribution V at .

[0457] Where D represents the set of the fourth variable, and V satisfies:

[0458]

[0459] in, P 1,1 Represents the element in the first row and first column of the sampling matrix P, Q 1,n+2 Represents the element in the first row and n+2 column of the sampling matrix Q.

[0460] Q 1,1 Represents the element in the first row and first column of the sampling matrix Q; P 1,n+2 Represents the element in the first row and n+2 column of the sampling matrix P.

[0461] v i is the i-th point among n points, and n points are [V min ,V max ] are points equally spaced between them, i = 1, 2, ..., n.

[0462] represents the discretized function of the first variable, Represents the discretized function of the second variable.

[0463] In other words, the g operation involves:

[0464] Step b1, determine the sampling point

[0465] make In the interval [V min ,V max ] Take n points with medium spacing, record them as v1,v2,v3,…,v n .

[0466] Step b2, let

[0467] Step b3, Do normalization

[0468] calculate make

[0469] Output

[0470] Among them, the above-mentioned first to fourth variables can be found in the introduction of S5031 and will not be repeated here.

[0471] Next, the steps in Example 2 (the following preprocessing steps, S21 to S28) are introduced:

[0472] Preprocessing: Sample the signal probability distribution to obtain the sampling matrix P.

[0473] Let the sampling interval be [-2, 2], and the number of sampling points n = 4, so the sampling matrix P is obtained:

[0474]

[0475] S21, the receiving device performs f operation.

[0476] In S21, the input of operation f includes the following three items:

[0477] The first item,

[0478] The second item,

[0479] The third item is the number of sampling points n=4.

[0480] In S21, the output of the f operation includes: The sampling matrix U.

[0481] Specifically, first, the receiving device calculates Then determine the sampling points, that is, u1 = -1.6971, u2 = -0.5657, u3 = 0.5657, u4 = 1.6971.

[0482] Then, the receiving device traverses i=1,2,3,4 and calculates the density function near each sampling point: To get:

[0483] Then normalize and calculate make To get:

[0484] f1=0.1636, f2=0.1966, f3=0.1966, f4=0.1636.

[0485] In S21, the output of the f operation can be expressed as:

[0486]

[0487] S22: The receiving device performs operation f.

[0488] In S22, the input of operation f includes the following three items:

[0489] The first item,

[0490] The second item,

[0491] The third item is the number of sampling points n=4.

[0492] In S22, the output of the f operation includes: The sampling matrix U.

[0493] Specifically, first, the receiving device calculates Then determine the sampling points, that is, u1 = -1.6971, u2 = -0.5657, u3 = 0.5657, u4 = 1.6971.

[0494] Then, the receiving device traverses i=1,2,3,4 and calculates the density function near each sampling point: Accordingly,

[0495] Then normalize and calculate make To get:

[0496] f1=0.1636, f2=0.1966, f3=0.1966, f4=0.1636.

[0497] In S22, the output of the f operation can be expressed as:

[0498]

[0499] S23, the receiving device performs f operation.

[0500] In S23, the input of operation f includes the following three items:

[0501] The first item,

[0502] The second item,

[0503] The third item is the number of sampling points n = 4.

[0504] In S23, the output of the f operation includes: The sampling matrix U.

[0505] Specifically, first, the receiving device calculates Then determine the sampling points, that is, u1 = -2.4, u2 = -0.8, u3 = 0.8, u4 = 2.4.

[0506] Then, the receiving device traverses i=1,2,3,4 and calculates the density function near each sampling point: To get:

[0507] Then normalize and calculate make To get:

[0508] f1=0.0844, f2=0.1859, f3=0.1859, f4=0.0844.

[0509] In S23, the output of the f operation can be expressed as:

[0510]

[0511] Since z0=0.5 is known,

[0512] S24, the receiving device performs g operation.

[0513] In S24, the input of the g operation includes the following four items:

[0514] The first item,

[0515] The second item,

[0516] The third item,

[0517] The fourth item is the number of sampling points n = 4.

[0518] In S24, the output of the g operation includes: The conditional distribution sampling matrix V is known to be z0=0.5.

[0519] Specifically, first, the receiving device calculates Then determine the sampling points, that is, v1 = -2.1, v2 = -0.7, v3 = 0.7, v4 = 2.1.

[0520] Then, the receiving device traverses i=1,2,3,4 and calculates the density function near each sampling point: To get:

[0521] Then normalize and calculate make To get:

[0522] g1=0.1213, g2=0.1752, g3=0.1752, g4=0.1213

[0523] In S24, the output of the g operation can be expressed as:

[0524]

[0525] Since z1 is to be restored,

[0526] because so,

[0527] S25, the receiving device performs g operation.

[0528] In S25, the input of the g operation includes the following four items:

[0529] The first item,

[0530] The second item,

[0531] The third item,

[0532] The fourth item is the number of sampling points n=4.

[0533] In S25, the output of the f operation includes: The conditional distribution sampling matrix V is known to be y0 = -0.1414.

[0534] Specifically, first, the receiving device calculates Then determine the sampling points, that is, v1 = -1.6122, v2 = -0.5374, v3 = 0.5374, v4 = 1.6122.

[0535] Then, the receiving device traverses i=1,2,3,4 and calculates the density function near each sampling point: To obtain: g1 = 0.2667, g2 = 0.0109, g3 = 0.0109, g4 = 0.2667.

[0536] Then normalize and calculate make To get:

[0537] g1=0.3019, g2=0.0123, g3=0.0123, g4=0.3019

[0538] In S25, the output of the g operation can be expressed as:

[0539]

[0540] S26: The receiving device performs g operation.

[0541] In S26, the input of the g operation includes the following four items:

[0542] The first item,

[0543] The second item,

[0544] The third item,

[0545] The fourth item is the number of sampling points n = 4.

[0546] In S26, the output of the g operation includes:

[0547] The conditional distribution sampling matrix V is known to be y1 = 0.8485.

[0548] Specifically, first, the receiving device calculates Then determine the sampling points, that is, v1 = -1.1879, v2 = -0.3960, v3 = 0.3960, v4 = 1.1879.

[0549] Then, the receiving device traverses i=1,2,3,4 and calculates the density function near each sampling point: To obtain: g1 = 0.0539, g2 = 0.0539, g3 = 0.0539, g4 = 0.0539.

[0550] Then normalize and calculate make To get:

[0551] g1=0.2525, g2=0.2525, g3=02525, g4=0.2525

[0552] In S26, the output of the g operation can be expressed as:

[0553]

[0554] S27, the receiving device performs f operation.

[0555] In S27, the input of operation f includes the following three items:

[0556] The first item,

[0557] The second item,

[0558] The third item is the number of sampling points n = 4.

[0559] In S27, the output of the f operation includes: Sampling matrix U.

[0560] Specifically, first, the receiving device calculates Then determine the sampling points, that is, u1 = -1.98, u2 = -0.66, u3 = 0.66, u4 = 1.98.

[0561] Then, the receiving device traverses i=1,2,3,4 and calculates the density function near each sampling point: To get:

[0562] Then normalize and calculate make To get:

[0563] f1=0.1487, f2=0.1557, f3=0.1557, f4=0.1487.

[0564] In S27, the output of the f operation can be expressed as:

[0565]

[0566] Since z2=-0.67, we know that

[0567] S28, the receiving device performs g operation.

[0568] In S28, the input of the g operation includes the following four items:

[0569] The first item,

[0570] The second item,

[0571] The third item,

[0572] The fourth item is the number of sampling points n = 4.

[0573] In S28, the output of the g operation includes:

[0574] The conditional distribution sampling matrix V is known to be z2 = -0.67.

[0575] Specifically, first, the receiving device calculates Then determine the sampling points, that is, v1 = -2.078, v2 = -1.026, v3 = 0.026, v4 = 1.078.

[0576] Then, the receiving device traverses i=1,2,3,4 and calculates the density function near each sampling point: To obtain: g1 = 0.0762, g2 = 0.0762, g3 = 0.0031, g4 = 0.0031.

[0577] Then normalize and calculate make To get:

[0578] g1=0.3653, g2=0.3653, g3=0.0149, g4=0.0149

[0579] In S28, the output of the g operation can be expressed as:

[0580]

[0581] Since z3 is to be restored,

[0582] Depend on Calculate:

[0583] Depend on Calculate:

[0584] Depend on Calculate:

[0585] In this way, the receiving device is estimated

[0586] Example 3

[0587] In Example 3, both the first sequence and the decoding result are real number sequences. The decoding process is described below using continuous values ​​as an example:

[0588] Figure 10 illustrates a decoding process for a non-finite field. In Figure 10, the code length of the sequence to be encoded is N = 4. x0, x1, x2, and x3 are the sequence to be encoded and are also the values ​​at positions 1, 2, 3, and 4 in the first layer of the encoding network. y0, y1, y2, and y3 are the values ​​at positions 1, 2, 3, and 4 in the second layer of the encoding network. z0 and z2 are the values ​​of the transmitted bits, and z1 and z3 are the values ​​of the bits to be recovered. z0, z1, z2, and z3 are also the values ​​at positions 1, 2, 3, and 4 in the third layer of the encoding network.

[0589] The input of the receiving device includes the following three items:

[0590] The first item, the first sequence [z0, z2]. In Figure 10, z0 = 0.60, z2 = -0.60.

[0591] The second term is the signal probability distribution. In Figure 10, the signal probability distribution P is 0.5δ0+0.5φ(x;0,1), that is, P is drawn from 0 with a probability of 0.5 and from the Gaussian distribution with a probability of 0.5, and the signal sparsity is 0.5.

[0592] The third item is the position number of the transmission bit {0,2}.

[0593] The output of the receiving device includes:

[0594] Considering the continuous part of the signal to be a mixed Gaussian distribution,

[0595] In the embodiment of this application, Represents the Gaussian distribution density function with mean μ and variance σ.

[0596] For a mixed Gaussian distribution Expressed as a 3×G matrix P:

[0597]

[0598] Each column of the matrix P represents a Gaussian component, the first row represents the mean, the second row represents the variance, and the third row represents the scaling factor. It is easy to understand that after the f and g operations, the mixed Gaussian distribution remains a mixed Gaussian distribution; only the mean and variance change.

[0599] First, we introduce the f operation and g operation applicable to sparse signals. Among them, the f operation is used to perform convolution operations, and the g operation is used to perform conditional probability operations. The introduction of the f operation and g operation is as follows:

[0600] 1. f operation

[0601] The inputs to the f operation include the following two items:

[0602] The first item,

[0603] Where A represents the first variable, η P Indicates that the first variable is taken from The probability of Indicates that the first variable is taken from In the case of i The probability is p i , P represents the Gaussian parameter matrix of the first variable.

[0604] The second item,

[0605] Where B represents the second variable, η Q Indicates that the second variable is taken from The probability of Indicates that the second variable is taken from In the case of j The probability is q j , Q represents the Gaussian parameter matrix of the second variable.

[0606] The outputs of the f operation include: The probability distribution of .

[0607] Where C represents the third variable. The probability distribution of C satisfies:

[0608] The f operation includes the following steps:

[0609] Step 1: Determine the proportion of the discrete part and let η U =η P η Q .

[0610] Step 2, determine the discrete part:

[0611] When traversing i=1,…,I,j=1,…,J, calculate f ij =p i q j . For different i,j, calculate c ij May be the same, merge the same c ij .Remember the combined values ​​are c1,…,c M ;f1,…,f M .

[0612] Step 3, determine the continuous part:

[0613] When traversing i=1,…,I,j=1,…,G Q In the case of

[0614] When traversing i=1,…,G P ,j=1,…,J, calculate

[0615] When traversing i=1,…,G P ,j=1,…,G Q In the case of

[0616] Step 4, merge consecutive parts:

[0617] For different i, j, t, Gaussian components May be the same, merge the same Assume that there are K Gaussian components (μ1,σ1,λ1),…,(μ K ,σ K ,λ K ),make make

[0618]

[0619] 2. g operation

[0620] The input to the g operation includes the following four items:

[0621] The first item,

[0622] Where A represents the first variable, η P Indicates that the first variable is taken from The probability of Indicates that the first variable is taken from In the case of iThe probability is p i , P represents the Gaussian parameter matrix of the first variable.

[0623] The second item,

[0624] Where B represents the second variable, η Q Indicates that the second variable is taken from The probability of Indicates that the second variable is taken from In the case of j The probability is q j , Q represents the Gaussian parameter matrix of the second variable.

[0625] The third item,

[0626] The fourth term is the support of the discrete part of C {c1,c2,...,c M}.

[0627] Among them, the support set {c1,c2,...,c M} means that when traversing i=1,...,I,j=1,...,J, c i,j M of them, Support {c1,c2,...,c M The elements in} are different from each other.

[0628] The outputs of the g operation include: exist The conditional probability distribution of . Where D represents the fourth variable.

[0629] The processing steps of the g operation include:

[0630] If u∈{c1,c2,…,c M}, that is, u is in the discrete support of operation f, then the processing steps of operation g include:

[0631] In the case of traversing i=1,…,I,j=1,…,J, if Then order g m =p i q j .make Accordingly,

[0632] if That is, u is outside the discrete support of the f operation, then the processing steps of the g operation include:

[0633] Step 1, determine the proportion of discrete parts:

[0634] calculate

[0635]

[0636]

[0637] F(u)=F1(u)+F2(u)+F3(u). Let

[0638] Step 2, determine the discrete part:

[0639] calculate

[0640] make

[0641] Step 3, determine the continuous part:

[0642] When traversing i=1,…,G P ,j=1,…,G Q In this case, calculate the following three items:

[0643]

[0644]

[0645]

[0646] Step 4, merge consecutive parts:

[0647] For different i,j, the Gaussian component (μ ij ,σ ij ) may be the same, merge the same (μ ij ,σ ij ).

[0648] make

[0649] Accordingly,

[0650] Among them, the above-mentioned first to fourth variables can be found in the introduction of S5031 and will not be repeated here.

[0651] Next, the steps in Example 3 (hereinafter referred to as S31 to S38) are described:

[0652] S31, the receiving device performs f operation.

[0653] In S31, the inputs to the f operation include the following two items:

[0654] The first item,

[0655] The second item,

[0656] In S31, the output of the f operation includes: The distribution of .

[0657] Specifically, calculate η U =η P η Q =0.5*0.5=0.25. f1=p1q1=1.

[0658] calculate

[0659]

[0660]

[0661] Merge the same Gaussian components and normalize to get

[0662] In S31, the output of the f operation can be recorded as: y0~0.25δ0+0.75U.

[0663] S32: The receiving device performs operation f.

[0664] In S32, the input of the f operation includes the following two items:

[0665] The first item,

[0666] The second item,

[0667] In S32, the outputs of the f operation include: The distribution of .

[0668] Specifically, calculate η U =η P η Q =0.5*0.5=0.25. f1=p1q1=1.

[0669] calculate

[0670]

[0671]

[0672] Merge the same Gaussian components and normalize to get

[0673] In S32, the output of the f operation can be recorded as: y1~0.25δ0+0.75U.

[0674] S33: The receiving device performs operation f.

[0675] In S33, the inputs to the f operation include the following two items:

[0676] The first item,

[0677] The second item,

[0678] In S33, the output of the f operation includes: The distribution of .

[0679] Specifically, calculate η U =η P η Q =0.25*0.25=0.0625. f1=p1q1=1.

[0680] Traverse i=1,j=1,2, calculate

[0681]

[0682] Traverse i=1,2,j=1, calculate

[0683]

[0684] Traverse i=1,2,j=1,2, calculate

[0685]

[0686]

[0687] Merge the same Gaussian components and normalize to get

[0688] In S33, the output of the f operation can be recorded as: z0~0.0625δ0+0.9375U.

[0689] Since z0=0.6 is known,

[0690] S34, the receiving device performs g operation.

[0691] In S34, the inputs to the g operation include the following four items:

[0692] The first item,

[0693] The second item,

[0694] The third term, z0 = 0.6.

[0695] The fourth term is the support {0} of the discrete part of z0.

[0696] In S34, the output of the g operation includes: Conditional distribution at z0=0.6.

[0697] because Therefore, the receiving device determines:

[0698]

[0699]

[0700]

[0701] F(z0)=F1(z0)+F2(z0)+F3(z0)=0.3561, let

[0702] calculate

[0703]

[0704] For g i After normalization, we get g1 = g2 = 0.5.

[0705] Traverse i=1,2,j=1,2, calculate

[0706] μ 11 =0,σ 11 =0.5,λ 11 =0.4690;μ 12 =-0.2, λ 12 =0.2159;

[0707] μ 21 =0.2, λ 21 =0.2159;μ 22 =0,σ 22 =1,λ22 =0.0993.

[0708] Merge the same Gaussian components to get

[0709] Output

[0710] Since z1 needs to be restored, if z1 takes a discrete distribution, the most likely value is -0.6 = {d m :max g m}, with probability p d =η V *max g m =0.4108*0.5=0.2054.

[0711] If z1 takes continuous distribution, the most likely mean is 0 = {V 1,m :max V 3,m} is a Gaussian distribution with probability p c =(1-η V )*max V 3,m =0.5892*0.4690=0.2763.

[0712] Because p c >p d ,get

[0713] Depend on Calculate

[0714] S35, the receiving device performs g operation.

[0715] In S35, the input of the g operation includes the following four items:

[0716] The first item,

[0717] The second item,

[0718] The third term, y0 = 0.4243.

[0719] The fourth term is the support {0} of the discrete part of y0.

[0720] In S35, the output of the g operation includes: Conditional distribution with y0=0.4243.

[0721] because Therefore, the receiving device determines:

[0722]

[0723]

[0724]

[0725] F(y0)=F1(y0)+F2(y0)+F3(y0)=0.3268, let

[0726] calculate

[0727]

[0728] For g i After normalization, we get g1 = g2 = 0.5.

[0729] calculate λ 11 =1, we get

[0730] Output

[0731] S36: The receiving device performs g operation.

[0732] In S36, the input of the g operation includes the following four items:

[0733] The first item,

[0734] The second item,

[0735] The third term, y1 = 0.4243.

[0736] The fourth term is the support {0} of the discrete part of y1.

[0737] In S36, the output of the g operation includes: Conditional distribution when y1=0.4243.

[0738] because Therefore, the receiving device determines:

[0739]

[0740]

[0741]

[0742] F(y1)=F1(y1)+F2(y1)+F3(y1)=0.3268, let

[0743] calculate

[0744]

[0745] For g i After normalization, we get g1 = g2 = 0.5.

[0746] calculate λ 11 =1, we get

[0747] Output

[0748] S37, the receiving device performs f operation.

[0749] In S37, the inputs to the f operation include the following two items:

[0750] The first item,

[0751] The second item,

[0752] In S37, the output of the f operation includes: The distribution of .

[0753] Specifically, the receiving device calculates η U =η P η Q =0.7211*0.7211=0.5199. Traverse i=1,2,j=1,2, calculate f ij =p i q j , to obtain:

[0754] c 11 =-0.6,f 11 =0.25; c 12 =0,f 12 =0.25; c 21 =0,f 21 =0.25; c 22 =0.6,f 22 =0.25. Merge the same c ij We get c1 = -0.6, f1 = 0.25; c2 = 0, f2 = 0.5; c3 = 0.6, f3 = 0.25.

[0755] Traverse i=1,2,j=1, calculate

[0756]

[0757] Traverse i=1,j=1,2, calculate

[0758]

[0759] Traverse i=1,j=1, calculate

[0760] Merge the same Gaussian components and normalize to get

[0761] In S37, the output of the f operation can be expressed as:

[0762]

[0763] Since z2=0.6, we know that

[0764] S38, the receiving device performs g operation.

[0765] In S38, the inputs to the g operation include the following four items:

[0766] The first item,

[0767] The second item,

[0768] The third term, z2 = 0.6.

[0769] The fourth term is the support of the discrete part of z2, {-0.6, 0.6, 0}.

[0770] In S38, the output of the g operation includes: Conditional distribution at z2=0.6.

[0771] z2=0.6∈{-0.6,0.6,0}. Traverse i=1,2,j=1,2, if but g m =p i q j :

[0772] d1=0,g1=0.25, after normalization we get d1=0,g1=1.

[0773] Output

[0774] z3 is to be restored, and the conditional distribution of z3 takes 0 with probability 1, so

[0775] Depend on Calculate

[0776] Depend on Calculate

[0777] Depend on Calculate

[0778] In this way, the receiving device obtains the decoding result

[0779] In Example 3, the receiving device uses the recursive structure of Hadamard transform to recover the sparse signal. Compared with the traditional BP algorithm, the decoding process of Example 3 does not require iteration, has low complexity, and has better signal recovery effect.

[0780] For example, Figures 11 and 12 correspond to the compression effect when the code length N = {128, 512}, respectively. In Figures 11 and 12, the horizontal axis is the compression rate (i.e., the ratio of the number of bits retained after compression to the total number of bits), and the vertical axis is the compression performance, i.e., the normalized mean square error (NMSE). Comparing the decoding method 500 under the non-finite field of the embodiment of the present application with the method shown in Figure 4, under the same compression rate, the decoding method 500 under the non-finite field of the embodiment of the present application has a lower NMSE than the method shown in Figure 4. Among them, the broken line indicated by the letter A in Figures 11 and 12 represents the performance effect of the method shown in Figure 4, and the broken line indicated by the letter B in Figures 11 and 12 represents the performance effect of the decoding method 500 under the non-finite field of the embodiment of the present application.

[0781] It should be understood that in the embodiment of the present application, the execution subject of the decoding method 500 under the non-finite field can be a receiving device, such as a decoder in the receiving device, or other modules capable of implementing the decoding function. In the embodiment of the present application, the receiving device is used as an example for description.

[0782] It should be understood that the decoding method 500 under a non-finite field according to the embodiment of the present application can be applied to both source decoding and channel decoding. When the decoding method according to the embodiment of the present application performs source decoding, the source coding can be performed using a Hadamard transform. When the decoding method according to the embodiment of the present application performs channel decoding, the channel coding can be performed using a Hadamard transform, and in addition to the Hadamard transform, other techniques may still be used to complete the channel coding.

[0783] Next, an introduction to the channel coding and channel decoding process is given:

[0784] On the sending device side, the message sequence w=(w0,…,w K-1 ). Among them, w k =0, or w k =1, 0≤k≤K-1, k is an integer. The emitting device performs the following steps (steps 1 to 3 below):

[0785] Step 1: The transmitting device determines the codeword index according to the message sequence.

[0786] Among them, the codeword index It can be understood that the message sequence w is the binary representation of the codeword index I.

[0787] Step 2: The transmitting device determines the sequence to be encoded based on the codeword index.

[0788] Among them, the sequence to be coded i≠I, which means that in the sequence to be encoded, the value of the I+1 position is 1, and the rest of the positions are 0. The length of the sequence to be encoded is: 2 K -1.

[0789] Step 3: The transmitting device encodes the sequence to be encoded to obtain an encoded sequence.

[0790] Exemplarily, the transmitting device performs Hadamard transform on the sequence to be coded x to obtain the coded sequence Among them, the serial number of the transmission bit is {i0,…,i M-1}, 1≤M≤2 K . Accordingly, the first sequence, i.e. the value of the transmitted bit

[0791] It is easy to understand that in steps 1 to 3 executed by the transmitting device, the length of the sequence to be encoded can be 4, that is, 2 K -1=4. The sequence number of the transmission bit can be {0,2}, that is, the position of sequence number 0 and the position of sequence number 2. Correspondingly, the first sequence is

[0792] On the receiving device side, the receiving device obtains the following three pieces of information:

[0793] Message A, received value

[0794] Among them, n i Indicates that the mean is 0 and the variance is a 2 Normally distributed noise, 0≤i≤M-1.

[0795] Information B, signal probability distribution P of the signal to be encoded.

[0796] For example, in the information B of the receiving device, the signal probability distribution P can be a bimodal Gaussian distribution, which is expressed as Among them, φ(x; μ, σ) means the mean is μ and the variance is σ 2 Gaussian distribution density function.

[0797] Information C, the sequence number of the transmitted bit.

[0798] In the embodiment of the present application, in combination with step 3 of the transmitting device, the sequence number of the transmission bit is {i0, ..., i M-1}.

[0799] The receiving device performs the following steps (steps 4 to 6 below):

[0800] Step 4: The receiving device determines the decoding result based on the received value r, the signal probability distribution P and the sequence number of the transmitted bit.

[0801] For example, the process of step 4 can be referred to the introduction of example 2 and will not be repeated here.

[0802] For example, the decoding result of step 4 is recorded as

[0803] Step 5: The receiving device determines an estimate of the codeword index based on the decoding result.

[0804] Example, codeword index estimation

[0805] Step 6: The receiving device determines the message sequence based on the estimated codeword index.

[0806] For example, the receiving device determines The binary representation of the message sequence for The binary representation of .

[0807] It can be seen from the above steps 1 to 6 that the decoding method 500 under non-finite fields in the embodiment of the present application can also be applied to channel decoding.

[0808] It is readily understood that in this embodiment of the present application, the received value, or received value r, can be understood as the value of the transmission bit indicated by the first sequence. For the receiving device, the receiving device receives the encoded sequence from the transmitting device and determines the first sequence based on the received encoded sequence. For details, see S502a and S502b, which will not be further described here.

[0809] The method provided by the embodiment of the present application is described in detail above in conjunction with Figures 5 to 12. The communication device for executing the method provided by the embodiment of the present application is described in detail below in conjunction with Figures 13 and 14.

[0810] For example, Figure 13 is a structural diagram of a communication device according to an embodiment of the present application. As shown in Figure 13, the communication device 1300 includes a processing module 1301 and a transceiver module 1302. For ease of illustration, Figure 13 only shows the main components of the communication device 1300.

[0811] In some embodiments, the communication apparatus 1300 may be applicable to the communication system shown in FIG. 1 , and perform the functions of a receiving device in the method shown in FIG. 5 , FIG. 6 , or FIG. 7 .

[0812] The transceiver module 1302 is used to obtain a first sequence. The first sequence includes the value of the transmission bit in the coded sequence, and the length of the first sequence is N1. The coded sequence is the sequence after the sequence to be coded is coded, and the length of the sequence to be coded is N, where N=2 n , n is a positive integer. N1 is a positive integer less than N.

[0813] Processing module 1301 is configured to determine a decoding result based on the signal probability distribution, the first set, and the values ​​of the transmission bits in the encoded sequence. The signal probability distribution includes the probability distribution of the sequence to be encoded, and the first set indicates the position of each value in the first sequence in the encoded sequence.

[0814] In one possible design, the first sequence is a real number sequence, and the decoding result is a real number sequence.

[0815] In a possible design, the first sequence is a real number sequence, and the decoding result is a complex number sequence.

[0816] In one possible design, processing module 1301 is configured to determine a decoding result based on the signal probability distribution, the first set, and the values ​​of the transmitted bits in the coded sequence, including determining a decoding path based on the signal probability distribution, the first set, and the values ​​of the transmitted bits in the coded sequence. The decoding path indicates the value of each position in the coded sequence; and determining a decoding result based on the decoding path.

[0817] In one possible design, the value of the i-th transmission bit in the decoding path is the same as the value of the i-th transmission bit in the first sequence, where i is a positive integer less than or equal to N1.

[0818] In one possible design, the number of bits to be restored in the encoded sequence is N2, where N2 is a positive integer less than N.

[0819] The value of the jth bit to be recovered in the decoding path corresponds to the maximum decoding metric among the multiple decoding metrics. Each decoding metric in the multiple decoding metrics is determined based on the following two items: the signal probability distribution and the value of each position before the jth bit to be recovered in the decoding path. Where j is a positive integer less than or equal to N2.

[0820] In one possible design, each decoding metric in the plurality of decoding metrics is determined through an f operation and a g operation.

[0821] The input of the f operation includes the probability distribution of the first variable and the probability distribution of the second variable. The output of the f operation includes the probability distribution of the third variable, which is the convolution of the probability distribution of the first variable and the probability distribution of the second variable.

[0822] The inputs to the g operation include the probability distributions of the first variable, the second variable, and the third variable, as well as the first value of the third variable. The output of the g operation includes the conditional probability distribution of the fourth variable at the first value of the third variable. The first value is the decoded value of the third variable.

[0823] The first variable is the value of the t-th position in the s-th layer of the encoding network, and the second variable is the value of the t+2-th position in the s-th layer. n-s The third variable is the value of the tth position in the s+1th layer of the encoding network, and the fourth variable is the value of the tth position in the s+1th layer. n-s The value of the position.

[0824] The encoding network includes n+1 layers, the first layer of the encoding network is used to input the sequence to be encoded, the second to nth layers of the encoding network are used to encode the sequence to be encoded to obtain the encoded sequence, and the n+1th layer of the encoding network is used to output the encoded sequence.

[0825] s is a positive integer less than or equal to n. t is a positive integer, and t traverses each parameter in the sth parameter set, each parameter in the sth parameter set indicates a position in the sth layer, and the number of positions indicated by the sth parameter set is N / 2.

[0826] In one possible design, the inputs to the f operation include the following two items:

[0827] A~P,P(a i )=p i,i=1,...,I. A represents the set of the first variable, P represents the probability distribution of the first variable, a i represents the first variable i in A, p i Indicates that the first variable of the i-th is a i The probability of , I represents the number of the first variable.

[0828] B~Q,P(b j )=q j ,j=1,...,J. B represents the set of the second variable, Q represents the probability distribution of the second variable, b j represents the j-th second variable in B, q j Indicates that the jth second variable is b j The probability of , J represents the number of second variables.

[0829] The outputs of the f operation include:

[0830] C~F,F(c k )=f k ,k=1,...,K. C represents the set of the third variable, F represents the probability distribution of the third variable, c k represents the kth third variable in C, f k Indicates that the kth third variable is c k , K represents the number of third variables, and the values ​​of K third variables are different from each other.

[0831] Among them, c k is one of the IxJ values, where IxJ values ​​are obtained when i=1,...,I ​​and j=1,...,J are traversed. i,j The value of f i,j =p i q j , f i,j Indicates c i,j probability of occurrence.

[0832] In c k When L values ​​are the same as L values ​​in IxJ values, f k It is equal to the sum of the occurrence probabilities of L values, where L is a positive integer less than or equal to IxJ.

[0833] In one possible design, the inputs to the g operation include the following four items:

[0834] A~P,P(a i )=p i ,i=1,...,I. A represents the set of the first variable, P represents the probability distribution of the first variable, a i represents the first variable i in A, p iIndicates that the first variable of the i-th is a i The probability of , I represents the number of the first variable.

[0835] B~Q,P(b j )=q j ,j=1,...,J. B represents the set of the second variable, Q represents the probability distribution of the second variable, b j represents the j-th second variable in B, q j Indicates that the jth second variable is b j The probability of , J represents the number of second variables.

[0836] P(μ)=f. C represents a set of third variables, μ represents a first value of the third variable, and P(μ) represents a value of the probability distribution of the third variable at μ.

[0837] The outputs of the g operation include:

[0838] exist The conditional probability distribution G,G(d m )=g m ,g m =p i q j / f,m=1,...,M, D represents the set of the fourth variable, G represents the probability distribution of the fourth variable, d m represents the mth fourth variable in D, g m Indicates that the mth fourth variable is d m The probability of , M represents the number of the fourth variable.

[0839] In one possible design, the inputs to the f operation include the following two items:

[0840] A represents the first variable, η P Indicates that the first variable is taken from The probability of Indicates that the first variable is taken from In the case of i The probability is p i , P represents the Gaussian parameter matrix of the first variable.

[0841] B represents the second variable, η Q Indicates that the second variable is taken from The probability of Indicates that the second variable is taken from In the case of j The probability is q j, Q represents the Gaussian parameter matrix of the second variable.

[0842] The outputs of the f operation include:

[0843] The probability distribution of . C represents the third variable, and the probability distribution of C satisfies:

[0844] Among them, η U =η P η Q η U Indicates that the third variable is taken from probability. Indicates that the third variable is taken from In the case of m The probability is f m U represents the Gaussian parameter matrix of the third variable. and U are determined based on A and B.

[0845] In one possible design, the values ​​of the M third variables are different from each other. m is one of the IxJ values, where IxJ values ​​are obtained when i=1,...,I ​​and j=1,...,J are traversed. i,j The value of . f i,j =p i q j , f i,j Indicates c i,j The probability of occurrence. m When L values ​​are the same as L values ​​in IxJ values, f m It is equal to the sum of the occurrence probabilities of L values, where L is a positive integer less than or equal to IxJ.

[0846] In one possible design, the Gaussian parameter matrix U satisfies:

[0847] Among them, K represents the number of the first combination, the first combination is IxG Q +G P xJ+G P xG Q The Gaussian components of the K first combinations are different from each other, and IxG Q +G P xJ+G P xG Q The Gaussian component combination includes the following three items: at t = 1, and traversing i = 1, ..., I, j = 1, ..., G Q Combination of cases At t=2, and traversing i=1,…,G P ,j=1,…,J At t=3, and traversing i=1,…,G P ,j=1,…,G Q Combination of cases

[0848] Indicates the kth combination in the K first combinations sum.

[0849] When traversing i=1,…,I,j=1,…,G Q In the case of

[0850] When traversing i=1,…,G P ,j=1,…,J,

[0851] When traversing i=1,…,G P ,j=1,…,G Q In the case of

[0852] G P The number of columns of the Gaussian parameter matrix representing the first variable, P 1,i The element in the first row and column i of the Gaussian parameter matrix of the first variable, P 2,i The element in the second row and column i of the Gaussian parameter matrix of the first variable, P 3,i Represents the element in the third row and i column of the Gaussian parameter matrix of the first variable.

[0853] G Q The number of columns in the Gaussian parameter matrix representing the second variable, Q 1,j The element in the first row and j column of the Gaussian parameter matrix representing the second variable, Q 2,j The element in the second row and j column of the Gaussian parameter matrix of the second variable, Q 3,j The element in the third row and j column of the Gaussian parameter matrix representing the second variable.

[0854] In one possible design, the inputs to the g operation include the following four items:

[0855] A represents the first variable, η P Indicates that the first variable is taken from The probability of Indicates that the first variable is taken from In the case of i The probability is p i , P represents the Gaussian parameter matrix of the first variable.

[0856] B represents the second variable, η Q Indicates that the second variable is taken from The probability of Indicates that the second variable is taken from In the case of j The probability is q j , Q represents the Gaussian parameter matrix of the second variable.

[0857] and the support of the discrete part of C {c1,c2,...,c M}, C represents the third variable, the support set {c1,c2,...,c M} means that when traversing i=1,...,I,j=1,...,J, c i,j M of them, Support {c1,c2,...,c M The elements in} are different from each other.

[0858] The outputs of the g operation include: exist The conditional probability distribution of . D represents the fourth variable. The conditional probability distribution of the output of the g operation is based on μ and the support {c1, c2, ..., c M}OK.

[0859] In one possible design, in μ, there is a support set {c1,c2,...,c M}, the conditional probability distribution satisfies:

[0860] in, When traversing i=1,...,I,j=1,...,J, if Then order

[0861] In one possible design, in μ, in the support set {c1,c2,...,c M}, the conditional probability distribution satisfies:

[0862] in, When traversing i=1,...,I,j=1,...,J, if Then order

[0863] in,

[0864]

[0865]

[0866]

[0867] G P The number of columns of the Gaussian parameter matrix representing the first variable, P 1,i The element in the first row and column i of the Gaussian parameter matrix of the first variable, P 2,i The element in the second row and column i of the Gaussian parameter matrix of the first variable, P 3,i Represents the element in the third row and i column of the Gaussian parameter matrix of the first variable.

[0868] G Q The number of columns in the Gaussian parameter matrix representing the second variable, Q 1,j The element in the first row and j column of the Gaussian parameter matrix representing the second variable, Q 2,j The element in the second row and j column of the Gaussian parameter matrix of the second variable, Q 3,j The element in the third row and j column of the Gaussian parameter matrix representing the second variable.

[0869] In one possible design, each decoding metric in the plurality of decoding metrics is determined through an f operation and a g operation.

[0870] The input of the f operation includes the probability distribution of the first variable and the probability distribution of the second variable. The output of the f operation includes the probability distribution of the third variable, which is the convolution of the probability distribution of the first variable and the probability distribution of the second variable.

[0871] The inputs to the g operation include the probability distribution of the first variable, the probability distribution of the second variable, and the first value. The output of the g operation includes the conditional probability distribution of the fourth variable at the first value. The first value is the decoded value of the third variable.

[0872] The first variable is the value of the t-th position in the s-th layer of the encoding network, and the second variable is the value of the t+2-th position in the s-th layer. n-s The third variable is the value of the tth position in the s+1th layer of the encoding network, and the fourth variable is the value of the tth position in the s+1th layer. n-s The value of the position.

[0873] The encoding network includes n+1 layers, the first layer of the encoding network is used to input the sequence to be encoded, the second to nth layers of the encoding network are used to encode the sequence to be encoded to obtain the encoded sequence, and the n+1th layer of the encoding network is used to output the encoded sequence.

[0874] s is a positive integer less than or equal to n. t is a positive integer, and t traverses each parameter in the sth parameter set, each parameter in the sth parameter set indicates a position in the sth layer, and the number of positions indicated by the sth parameter set is N / 2.

[0875] In one possible design, the inputs to the f operation include the following two items:

[0876] A~f P . A represents the first variable, f P represents the density function of the first variable, and P represents the sampling matrix of the first variable.

[0877] B~f Q . B represents the second variable, f Q represents the density function of the second variable, and Q represents the sampling matrix of the second variable.

[0878] The outputs of the f operation include:

[0879] The sampling matrix U. C represents the third variable,

[0880] in, P 1,1 Represents the element in the first row and first column of the sampling matrix P, Q 1,1 Represents the element in the first row and first column of the sampling matrix Q.

[0881] P 1,n+2 Represents the element in the first row and n+2 column of the sampling matrix P, Q 1,n+2 Represents the element in the first row and n+2 column of the sampling matrix Q.

[0882] u i is the i-th point among n points, and n points are [U min ,U max ] are points equally spaced between them, i = 1, 2, ..., n.

[0883] d(t,P) represents the discretization function of the first variable, Represents the discretized function of the second variable.

[0884] In one possible design, the inputs to the g operation include the following three items:

[0885] A~f P . A represents the first variable, f P represents the density function of the first variable, and P represents the sampling matrix of the first variable.

[0886] B~f Q . B represents the second variable, f Q represents the density function of the second variable, and Q represents the sampling matrix of the second variable.

[0887] C represents a third variable, and μ represents a first value of the third variable.

[0888] The outputs of the g operation include:

[0889] exist The conditional probability distribution V at ; D represents the fourth variable,

[0890]

[0891] in, P 1,1 Represents the element in the first row and first column of the sampling matrix P, Q 1,n+2 Represents the element in the first row and n+2 column of the sampling matrix Q.

[0892] Q 1,1 Represents the element in the first row and first column of the sampling matrix Q.

[0893] P 1,n+2 Represents the element in the first row and n+2 column of the sampling matrix P.

[0894] v i is the i-th point among n points, and n points are [V min ,V max ] are points equally spaced between them, i = 1, 2, ..., n.

[0895] represents the discretized function of the first variable, Represents the discretized function of the second variable.

[0896] Optionally, the transceiver module 1302 may include a receiving module and a sending module (not shown in FIG13 ). The transceiver module 1302 is used to implement the sending function and the receiving function of the communication device 1300 .

[0897] Optionally, the communication device 1300 may further include a storage module (not shown in FIG. 13 ) storing a program or instruction. When the processing module 1301 executes the program or instruction, the communication device 1300 may perform the functions of the receiving device in the method shown in any one of FIG. 5 , FIG. 6 , or FIG. 7 .

[0898] It should be understood that the processing module 1301 involved in the communication device 1300 can be implemented by a processor or a processor-related circuit component, which can be a processor or a processing unit; the transceiver module 1302 can be implemented by a transceiver or a transceiver-related circuit component, which can be a transceiver or a transceiver unit.

[0899] It is easy to understand that the communication device 1300 can be a receiving device, or a chip (system) or other parts or components that can be set in the receiving device, or a device that includes a receiving device. This application does not limit this.

[0900] In addition, the technical effects of the communication device 1300 can refer to the technical effects of the method shown in any one of Figures 5, 6, or 7, and will not be repeated here.

[0901] For example, Figure 14 is a second structural diagram of a communication device provided in an embodiment of the present application. The communication device can be a receiving device, or a chip (system) or other component or assembly that can be provided in the receiving device. As shown in Figure 14, the communication device 1400 may include a processor 1401. Optionally, the communication device 1400 may also include a memory 1402 and / or a transceiver 1403. The processor 1401 is coupled to the memory 1402 and the transceiver 1403, for example, via a communication bus.

[0902] The following is a detailed introduction to the various components of the communication device 1400 with reference to FIG14 :

[0903] The processor 1401 is the control center of the communication device 1400 and can be a single processor or a collective term for multiple processing elements. For example, the processor 1401 can be one or more central processing units (CPUs), an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of the present application, such as one or more digital signal processors (DSPs) or one or more field programmable gate arrays (FPGAs).

[0904] Optionally, the processor 1401 may execute various functions of the communication device 1400 by running or executing a software program stored in the memory 1402 and calling data stored in the memory 1402 .

[0905] In a specific implementation, as an embodiment, the processor 1401 may include one or more CPUs, such as CPU0 and CPU1 shown in FIG14 .

[0906] In a specific implementation, as an embodiment, the communication device 1400 may also include multiple processors, such as the processor 1401 and the processor 1404 shown in FIG14 . Each of these processors may be a single-core processor (single-CPU) or a multi-core processor (multi-CPU). The processor herein may refer to one or more devices, circuits, and / or processing cores for processing data (e.g., computer program instructions).

[0907] The memory 1402 is used to store the software program for executing the solution of the present application, and the execution is controlled by the processor 1401. The specific implementation method can refer to the above method embodiment and will not be repeated here.

[0908] Alternatively, the memory 1402 may be a read-only memory (ROM) or other type of static storage device that can store static information and instructions, a random access memory (RAM) or other type of dynamic storage device that can store information and instructions, or an electrically erasable programmable read-only memory (EEPROM), a compact disc read-only memory (CD-ROM) or other optical disc storage, an optical disc storage (including a compact disc, laser disc, optical disc, digital versatile disc, Blu-ray disc, etc.), a magnetic disk storage medium or other magnetic storage device, or any other medium that can be used to carry or store desired program code in the form of instructions or data structures and can be accessed by a computer, but is not limited thereto. The memory 1402 may be integrated with the processor 1401 or exist independently and be coupled to the processor 1401 via an interface circuit (not shown in FIG. 14 ) of the communication device 1400, which is not specifically limited in this embodiment of the present application.

[0909] Transceiver 1403 is used for communication with other communication devices. For example, if communication device 1400 is a receiving device, transceiver 1403 can be used to communicate with a transmitting device. For another example, if communication device 1400 is a transmitting device, transceiver 1403 can be used to communicate with a receiving device.

[0910] Optionally, the transceiver 1403 may include a receiver and a transmitter (not shown separately in FIG14 ), wherein the receiver is used to implement a receiving function, and the transmitter is used to implement a sending function.

[0911] Optionally, the transceiver 1403 can be integrated with the processor 1401, or can exist independently and be coupled to the processor 1401 through the interface circuit of the communication device 1400 (not shown in Figure 14), which is not specifically limited in this embodiment of the present application.

[0912] It is easy to understand that the structure of the communication device 1400 shown in Figure 14 does not constitute a limitation on the communication device. The actual communication device may include more or fewer components than shown in the figure, or combine certain components, or arrange the components differently.

[0913] In addition, the technical effects of the communication device 1400 can refer to the technical effects of the methods described in the above method embodiments, and will not be repeated here.

[0914] It should be understood that the processor in the embodiments of the present application may be a central processing unit (CPU), and the processor may also be other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or any conventional processor, etc.

[0915] It should also be understood that the memory in the embodiments of the present application may be a volatile memory or a non-volatile memory, or may include both volatile and non-volatile memories. Among them, the non-volatile memory may be a read-only memory (ROM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electrically erasable programmable read-only memory (EEPROM), or a flash memory. The volatile memory may be a random access memory (RAM), which is used as an external cache. By way of example and not limitation, many forms of random access memory (RAM) are available, such as static RAM (SRAM), dynamic random access memory (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), and direct rambus RAM (DR RAM).

[0916] The above embodiments can be implemented in whole or in part by software, hardware (such as circuits), firmware or any other combination. When implemented using software, the above embodiments can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions or computer programs. When the computer instructions or computer program are loaded or executed on a computer, the process or function described in the embodiment of the present application is generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another computer-readable storage medium. For example, the computer instructions can be transmitted from one website, computer, server or data center to another website, computer, server or data center via a wired (such as infrared, wireless, microwave, etc.) method. The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device such as a server or data center that contains one or more available media sets. The available medium can be a magnetic medium (for example, a floppy disk, a hard disk, a tape), an optical medium (for example, a DVD), or a semiconductor medium. The semiconductor medium can be a solid-state drive.

[0917] It should be understood that the term "and / or" as used herein simply describes a relationship between associated objects, indicating that three possible relationships exist. For example, "A and / or B" can represent: A alone, A and B together, or B alone. A and B can be singular or plural. Furthermore, the character " / " as used herein generally indicates an "or" relationship between the associated objects, but it may also indicate an "and / or" relationship. For specific understanding, please refer to the context.

[0918] In this application, "at least one" means one or more, and "plurality" means two or more. "At least one of the following" or similar expressions refers to any combination of these items, including any combination of single or plural items. For example, at least one of a, b, or c can mean: a, b, c, ab, ac, bc, or abc, where a, b, and c can be single or plural.

[0919] It should be understood that in the various embodiments of the present application, the size of the serial numbers of the above-mentioned processes does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present application.

[0920] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0921] Those skilled in the art will clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0922] In the several embodiments provided in this application, it should be understood that the disclosed systems, devices and methods can be implemented in other ways. For example, the device embodiments described above are merely schematic. For example, the division of the units is merely a logical function division. In actual implementation, there may be other division methods, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0923] The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of these units may be selected to achieve the purpose of this embodiment according to actual needs.

[0924] In addition, each functional unit in each embodiment of the present application may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit.

[0925] If the functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or communication device, etc.) to execute all or part of the steps of the method described in each embodiment of the present application. The aforementioned storage medium includes various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.

[0926] The above description is merely a specific embodiment of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of this application. Therefore, the scope of protection of this application should be based on the scope of protection of the claims.

Claims

1. A decoding method under a non-finite field, characterized in that: Applied to a receiving device, the method includes: Obtain a first sequence; the first sequence includes the value of the transmission bit in the encoded sequence, and the length of the first sequence is N1; the encoded sequence is the sequence after the sequence to be encoded is encoded, and the length of the sequence to be encoded is N, N=2 n , n is a positive integer; N1 is a positive integer less than N; Determine a decoding result based on a signal probability distribution, a first set, and a value of a transmission bit in the encoded sequence; the signal probability distribution includes a probability distribution of the sequence to be encoded, and the first set indicates a position of each value in the first sequence in the encoded sequence.

2. The method according to claim 1, characterized in that The first sequence is a real number sequence, and the decoding result is a real number sequence; or, The first sequence is a real number sequence, and the decoding result is a complex number sequence.

3. The method according to claim 1 or 2, characterized in that The determining of a decoding result according to the signal probability distribution, the first set, and the value of the transmission bit in the encoded sequence includes: determining a decoding path based on the signal probability distribution, the first set, and the value of the transmitted bit in the coded sequence; the decoding path indicating the value of each position in the coded sequence; The decoding result is determined according to the decoding path.

4. The method according to claim 3, characterized in that The value of the i-th transmission bit in the decoding path is the same as the value of the i-th transmission bit in the first sequence, where i is a positive integer less than or equal to N1.

5. The method according to claim 4, characterized in that The number of bits to be restored in the encoded sequence is N2, where N2 is a positive integer less than N; The value of the jth to-be-recovered bit in the decoding path corresponds to a maximum decoding metric among a plurality of decoding metrics; each of the plurality of decoding metrics is determined according to the following two items: said signal probability distribution; The value of each position before the j-th bit to be restored in the decoding path; Wherein, j is a positive integer less than or equal to N2.

6. The method according to claim 5, characterized in that Each decoding metric in the plurality of decoding metrics is determined by an f operation and a g operation; The input of the f operation includes the probability distribution of the first variable and the probability distribution of the second variable; the output of the f operation includes the probability distribution of the third variable, and the probability distribution of the third variable is the convolution of the probability distribution of the first variable and the probability distribution of the second variable; The input of the g operation includes the probability distribution of the first variable, the probability distribution of the second variable, the probability distribution of the third variable, and a first value; the output of the g operation includes the conditional probability distribution of the fourth variable at the first value; the first value is the decoded value of the third variable; The first variable is the value of the tth position in the sth layer of the encoding network, and the second variable is the value of the t+2th position in the sth layer. n-s The third variable is the value of the tth position in the s+1th layer of the encoding network, and the fourth variable is the value of the tth position in the s+1th layer. n-s The value of the position; The encoding network includes n+1 layers, the first layer of the encoding network is used to input the sequence to be encoded, the second to nth layers of the encoding network are used to encode the sequence to be encoded to obtain the encoded sequence, and the n+1th layer of the encoding network is used to output the encoded sequence; s is a positive integer less than or equal to n; t is a positive integer, and t traverses each parameter in the sth parameter set, each parameter in the sth parameter set indicates a position in the sth layer, and the number of positions indicated by the sth parameter set is N / 2.

7. The method according to claim 6, characterized in that The input of the f operation includes the following two items: A~P,P(a i )=p i , i=1,…,I; A represents the set of the first variables, P represents the probability distribution of the first variables, a i represents the first variable i in A, p i Indicates that the i-th first variable is a i The probability of , I represents the number of the first variable; B~Q,P(b j )=q j ,j=1,…,J; B represents the set of the second variable, Q represents the probability distribution of the second variable, b j represents the j-th second variable in B, q j Indicates that the j-th second variable is b j The probability of , J represents the number of the second variable; The output of the f operation includes: C~F,F(c k )=f k , k=1,…,K; C represents the set of the third variable, F represents the probability distribution of the third variable, c k represents the kth third variable in C, f k Indicates that the kth third variable is c k , K represents the number of the third variables, and the values ​​of the K third variables are different from each other; Among them, c k is one of the IxJ values, wherein c is the value of i,j The value of f i,j =p i q j , f i,j Indicates c i,j probability of occurrence; In c k When L values ​​are the same as those in the 1xJ values, f k is equal to the sum of the occurrence probabilities of the L values, where L is a positive integer less than or equal to 1xJ.

8. The method according to claim 6, characterized in that The input of the g operation includes the following four items: A~P,P(a i )=p i , i=1,…,I; A represents the set of the first variables, P represents the probability distribution of the first variables, a i represents the first variable i in A, p i Indicates that the i-th first variable is a i The probability of , I represents the number of the first variable; B~Q,P(b j )=q j ,j=1,…,J; B represents the set of the second variable, Q represents the probability distribution of the second variable, b j represents the j-th second variable in B, q j Indicates that the j-th second variable is b j The probability of , J represents the number of the second variable; P(μ)=f; C represents the set of the third variable, μ represents the first value of the third variable, and P(μ) represents the value of the probability distribution of the third variable at μ; The output of the g operation includes: exist The conditional probability distribution G,G(d m )=g m ,g m =p i q j / f,m=1,…,M, D represents the set of the fourth variable, G represents the probability distribution of the fourth variable, d m represents the mth fourth variable in D, g m Indicates that the mth fourth variable is d m The probability of M represents the number of the fourth variable.

9. The method according to claim 6, characterized in that The input of the f operation includes the following two items: A represents the first variable, η P Indicates that the first variable is taken from The probability of Indicates that the first variable is taken from In the case where the first variable is a i The probability is p i , P represents the Gaussian parameter matrix of the first variable; B represents the second variable, η Q Indicates that the second variable is taken from The probability of Indicates that the second variable is taken from In the case of j The probability is q j , Q represents the Gaussian parameter matrix of the second variable; The output of the f operation includes: The probability distribution of C represents the third variable, and the probability distribution of C satisfies: Among them, η U =η P η Q η U Indicates that the third variable is taken from probability; Indicates that the third variable is taken from In the case of m The probability is f m ; U represents the Gaussian parameter matrix of the third variable; and U are determined based on A and B.

10. The method according to claim 9, characterized in that The values ​​of the M third variables are different from each other; Among them, c m is one of the IxJ values, wherein c is the value of i,j The value of f i,j =p i q j , f i,j Indicates c i,j probability of occurrence; In c m When L values ​​are the same as those in the 1xJ values, f m is equal to the sum of the occurrence probabilities of the L values, where L is a positive integer less than or equal to 1xJ.

11. The method according to claim 9, characterized in that The Gaussian parameter matrix U satisfies: Wherein, K represents the number of first combinations, and the first combination is 1×G Q +G P xJ+G P xG Q The Gaussian components of the K first combinations are different from each other. Q +G P xJ+G P xG Q The Gaussian component combination includes the following three items: at t = 1, and traversing i = 1, ..., I, j = 1, ..., G Q Combination of cases At t=2, and traversing i=1,…,G P ,j=1,…,J At t=3, and traversing i=1,…,G P ,j=1,…,G Q Combination of cases Indicates the kth combination in the K first combinations corresponding to sum; When traversing i=1,…,I,j=1,…,G Q In the case of When traversing i=1,…,G P ,j=1,…,J, When traversing i=1,…,G P ,j=1,…,G Q In the case of G P The number of columns of the Gaussian parameter matrix representing the first variable, P 1,i The element in the first row and column i of the Gaussian parameter matrix of the first variable, P 2,i The element in the second row and column i of the Gaussian parameter matrix representing the first variable, P 3,i The element in the third row and i column of the Gaussian parameter matrix representing the first variable; G Q The number of columns of the Gaussian parameter matrix representing the second variable, Q 1,j The element in the first row and j column of the Gaussian parameter matrix of the second variable, Q 2,j The element in the second row and j column of the Gaussian parameter matrix of the second variable, Q 3,j The element in the third row and j column of the Gaussian parameter matrix representing the second variable.

12. The method according to claim 6, characterized in that The input of the g operation includes the following four items: A represents the first variable, η P Indicates that the first variable is taken from The probability of Indicates that the first variable is taken from In the case where the first variable is a i The probability is p i , P represents the Gaussian parameter matrix of the first variable; B represents the second variable, η Q Indicates that the second variable is taken from The probability of Indicates that the second variable is taken from In the case of j The probability is q j , Q represents the Gaussian parameter matrix of the second variable; and the support of the discrete part of C {c1,c2,…,c M }, C represents the third variable, the support {c1, c2, ..., c M } means that when traversing i=1,…,I,j=1,…,J, c i,j M of them, The support {c1, c2, ..., c M The elements in} are different from each other; The output of the g operation includes: exist D represents the fourth variable, the conditional probability distribution of the g operation output is based on μ and the support {c1, c2, ..., c M }OK.

13. The method according to claim 12, characterized in that In μ, the support {c1,c2,…,c M }, the conditional probability distribution satisfies: in, When traversing i=1,…,I,j=1,…,J, if Then order 14. The method according to claim 12, characterized in that In μ, the support set {c1,c2,…,c M }, the conditional probability distribution satisfies: in, When traversing i=1,…,I,j=1,…,J, if Then order in, F(u)=F1(u)+F2(u)+F3(u), G P The number of columns of the Gaussian parameter matrix representing the first variable, P 1,i The element in the first row and column i of the Gaussian parameter matrix of the first variable, P 2,i The element in the second row and column i of the Gaussian parameter matrix representing the first variable, P 3,i The element in the third row and i column of the Gaussian parameter matrix representing the first variable; G Q The number of columns of the Gaussian parameter matrix representing the second variable, Q 1,j The element in the first row and j column of the Gaussian parameter matrix of the second variable, Q 2,j The element in the second row and j column of the Gaussian parameter matrix of the second variable, Q 3,j The element in the third row and j column of the Gaussian parameter matrix representing the second variable.

15. The method according to claim 5, characterized in that Each decoding metric in the plurality of decoding metrics is determined by an f operation and a g operation; The input of the f operation includes the probability distribution of the first variable and the probability distribution of the second variable; the output of the f operation includes the probability distribution of the third variable, and the probability distribution of the third variable is the convolution of the probability distribution of the first variable and the probability distribution of the second variable; The input of the g operation includes the probability distribution of the first variable, the probability distribution of the second variable, and a first value; the output of the g operation includes the conditional probability distribution of the fourth variable at the first value; the first value is the decoded value of the third variable; The first variable is the value of the tth position in the sth layer of the encoding network, and the second variable is the value of the t+2th position in the sth layer. n-s The third variable is the value of the tth position in the s+1th layer of the encoding network, and the fourth variable is the value of the tth position in the s+1th layer. n-s The value of the position; The encoding network includes n+1 layers, the first layer of the encoding network is used to input the sequence to be encoded, the second to nth layers of the encoding network are used to encode the sequence to be encoded to obtain the encoded sequence, and the n+1th layer of the encoding network is used to output the encoded sequence; s is a positive integer less than or equal to n; t is a positive integer, and t traverses each parameter in the sth parameter set, each parameter in the sth parameter set indicates a position in the sth layer, and the number of positions indicated by the sth parameter set is N / 2.

16. The method according to claim 15, characterized in that The input of the f operation includes the following two items: A~f P ; A represents the first variable, f P represents the density function of the first variable, and P represents the sampling matrix of the first variable; B~f Q ; B represents the second variable, f Q represents the density function of the second variable, Q represents the sampling matrix of the second variable; The output of the f operation includes: The sampling matrix U; C represents the third variable, in, P 1,1 Represents the element in the first row and first column of the sampling matrix P, Q 1,1 Represents the element in the first row and first column of the sampling matrix Q; P 1,n+2 Represents the element in the first row and n+2 column of the sampling matrix P, Q 1,n+2 Represents the element in the first row and n+2 column of the sampling matrix Q; u i is the i-th point among n points, wherein the n points are [U min ,U max ] points are equally spaced between them, i = 1, 2, …, n; d(t,P) represents the discretization function of the first variable, represents the discretized function of the second variable.

17. The method according to claim 15, characterized in that The inputs to the g operation include the following three items: A~f P ; A represents the first variable, f P represents the density function of the first variable, and P represents the sampling matrix of the first variable; B~f Q ; B represents the second variable, f Q represents the density function of the second variable, Q represents the sampling matrix of the second variable; C represents the third variable, and μ represents the first value of the third variable; The output of the g operation includes: exist The conditional probability distribution V at ; D represents the fourth variable, in, P 1,1 Represents the element in the first row and first column of the sampling matrix P, Q 1,n+2 Represents the element in the first row and n+2 column of the sampling matrix Q; Q 1,1 Represents the element in the first row and first column of the sampling matrix Q; P 1,n+2 Represents the element in the first row and the n+2th column of the sampling matrix P; v i is the i-th point among n points, wherein the n points are [V min ,V max ] points are equally spaced between them, i = 1, 2, …, n; represents the discretized function of the first variable, represents the discretized function of the second variable.

18. A communication device, characterized in that: include: A processor is coupled to a memory; the memory stores program instructions, and when the program instructions stored in the memory are executed by the processor, the communication device executes the method according to any one of claims 1 to 17.

19. A communication device, characterized in that: The communication device includes a processor and a transceiver, the transceiver is used to exchange information between the communication device and other communication devices, and the processor executes program instructions to perform the method according to any one of claims 1 to 17.

20. A chip, characterized in that: It includes a processor and an input / output interface, wherein the input / output interface is used to receive signals from other devices outside the chip and transmit them to the processor or send signals from the processor to other devices outside the chip, and the processor is used to implement the method according to any one of claims 1 to 17 through logic circuits or execution code instructions.

21. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, and when the computer program is executed on a communication device, the communication device is caused to perform the method according to any one of claims 1 to 17.

22. A communication system, characterized in that: Including the sending end equipment and the receiving end equipment; among which, The transmitting device is used to perform Hadamard transform on the sequence to be coded to obtain a coded sequence; the length of the sequence to be coded is N, N=2 n , n is a positive integer; The transmitting device is further configured to send the encoded sequence; The receiving device is configured to receive the coded sequence and determine a first sequence based on the received coded sequence; wherein the first sequence includes values ​​of transmission bits in the coded sequence and has a length of N1, where N1 is a positive integer less than N; The receiving device is further configured to execute the method according to any one of claims 1 to 17 according to the first sequence.

Images