WO2024065118A1

WO2024065118A1 - Decoding method in non-finite field, and communication apparatus

Info

Publication number: WO2024065118A1
Application number: PCT/CN2022/121491
Authority: WO
Inventors: 李源; 原帅; 秦康剑; 张华滋; 王俊; 杜颖钢; 闫桂英; 马志明
Original assignee: 华为技术有限公司; 中国科学院数学与系统科学研究院
Priority date: 2022-09-26
Filing date: 2022-09-26
Publication date: 2024-04-04

Abstract

Provided in the present application are a decoding method in a non-finite field, and a communication apparatus, which can solve the problem of high decoding complexity caused by iterative decoding, thus increasing the decoding efficiency, and same can be applied to a communication system. The method comprises: a receiving-end device acquiring a first sequence, wherein the first sequence comprises values of transmission bits in an encoded sequence, the first sequence has a length of N1, the encoded sequence is the sequence of a sequence to be encoded after same has been encoded, the sequence to be encoded has a length of N, N = 2n, n being a positive integer, and N1 being a positive integer less than N; and then, the receiving-end device determining a decoding result according to a signal probability distribution, a first set, and the values of the transmission bits in the encoded sequence, wherein the signal probability distribution comprises the probability distribution of the sequence to be encoded, and the first set indicates the position, in the encoded sequence, of each value in the first sequence.

Description

Decoding method and communication device under non-finite field

Technical Field

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

Background technique

In compressed sensing (CS), the basis pursuit (BP) algorithm is usually used to recover the real signal from the adopted data. Specifically, in the BP algorithm, the sampling matrix is used to complete the signal reconstruction through multiple iterations. The sampling matrix of the BP algorithm is randomly generated and the matrix is not fixed. In addition, the BP algorithm has the problem of many iterations and high computational complexity in the signal reconstruction process.

Summary of the invention

The present 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, the present application adopts the following technical solutions:

In a first aspect, a decoding method under a non-finite field is provided. The execution subject of the method may be a receiving device or a chip applied to the receiving device. The following description is made by taking the execution subject as an example of a receiving device. The method comprises: 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 N _1. The encoded sequence is a sequence after the sequence to be encoded is encoded, and the length of the sequence to be encoded is N, N=2 ⁿ , and n is a positive integer. N ₁ is a positive integer less than N. Then, the receiving device determines the decoding result according to 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 an embodiment of the present application, the encoded sequence includes the value of the transmission bit and the value of the bit to be restored. The reliability of the bit to be restored is higher than the reliability of the transmission bit. In this way, after obtaining the first sequence, the receiving device can determine the value of the bit to be restored by recursive operation in combination with the signal probability distribution and the first set, rather than by iterative operation. When the value of each transmission bit and the value of the bit to be restored are known, the receiving device can determine the decoding result. That is to say, in the above decoding process, the receiving device performs one operation for the value of each position, there is no iterative operation processing process, and the decoding complexity is low.

In a possible design, the first sequence is a real number sequence, and the decoding result is a real number sequence.

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

In one possible design, the receiving device determines the decoding result according to the signal probability distribution, the first set, and the value of the transmission bit in the encoded sequence, including: determining a decoding path according to the signal probability distribution, the first set, and the value of the transmission bit in the encoded sequence, and then determining the decoding result according to 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.

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 N ₁ .

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.

In a possible design, the number of bits to be recovered in the encoded sequence is N ₂ , where N ₂ 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 to improve the accuracy of decoding. Each decoding metric in the multiple decoding metrics is determined based on the following two items: signal probability distribution, and the value of each position before the jth bit to be recovered in the decoding path. Wherein, j is a positive integer less than or equal to N ₂ .

In one possible design, each decoding metric in the plurality of decoding metrics is determined through 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 the probability distribution of the third 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.

The first variable is the value of the t-th position in the s-th layer of the coding network, the second variable is the value of the t+2 ^ns -th position in the s-th layer, the third variable is the value of the t-th position in the s+1-th layer of the coding network, and the fourth variable is the value of the t+2 ^ns -th position in the s+1-th layer. The coding network includes n+1 layers, the first layer of the coding network is used to input the sequence to be encoded, the second to n-th layers of the coding network are used to encode the sequence to be encoded to obtain the encoded sequence, and the n+1-th layer of the coding 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 s-th parameter set, each parameter in the s-th parameter set indicates a position in the s-th layer, and the number of positions indicated by the s-th parameter set is N/2.

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.

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

The first term, A~P, P(a _i )＝ _pi ,i＝1,...,I. A represents the set of first variables, P represents the probability distribution of the first variables, a _i represents the i-th first variable in A, p _i represents the probability that the i-th first variable is a _i , and I represents the number of first variables.

The second term, B～Q, P(b _j )＝q _j ,j＝1,...,J. B represents the set of second variables, Q represents the probability distribution of the second variables, b _j represents the jth second variable in B, q _j represents the probability that the jth second variable is b _j , and J represents the number of second variables.

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

Where c _k is one of the IxJ values, and the IxJ values are the values of c _i,j when traversing i=1,...,I,j=1,...,J.

_fi,j = p _i q _j , fi _,j represents the probability of occurrence of c _i,j . When c _k is the same as L values among IxJ values, f _k is equal to the sum of the probability of occurrence of L values, and L is a positive integer less than or equal to IxJ. In other words, the IxJ values may be different from each other; or, the IxJ values may be all the same; or, some of the IxJ values may be the same, and the other values may be the same or different.

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.

In one possible design, the input to the g operation includes the following four items:

the third item,

C represents a set of third variables, and μ represents a first value of the third variable.

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

The outputs of the g operation include:

exist

The conditional probability distribution G at , G(d _m ) = g _m , g _m = p _i q _j /f, m = 1,...,M, D represents the set of fourth variables, G represents the probability distribution of the fourth variable, d _m represents the mth fourth variable in D, g _m represents the probability that the mth fourth variable is d _m , and M represents the number of fourth variables.

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.

First item,

A represents the first variable, η _P represents the first variable taken from

The probability,

Indicates that the first variable is taken from

In the case of , the probability that the first variable is a _i is p _i , and P represents the Gaussian parameter matrix of the first variable.

second section,

B represents the second variable, η _Q represents the second variable taken from

The probability,

Indicates that the second variable is taken from

In the case of , the probability that the second variable is b _j is q _j , where Q represents the Gaussian parameter matrix of the second variable.

The outputs of the f operation include:

The probability distribution of .

Among them, C represents the third variable, and the probability distribution of C satisfies:

Among them, η _U = η _P η _Q , η _U represents the third variable taken from

The probability.

Indicates that the third variable is taken from

In the case of , the probability that the third variable is _cm is f _m . U represents the Gaussian parameter matrix of the third variable.

and U are determined based on A and B.

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.

In one possible design, the values of the M third variables are different from each other. Wherein, _cm is one of the IxJ values, and the IxJ values are the values of c _i,j when traversing i=1,...,I, j=1,...,J.

_fi,j = p _i q _j , fi _,j represents the probability of occurrence of c _i,j . When c _m is the same as L values among IxJ values, f _m is equal to the sum of the probability of occurrence of L values, and L is a positive integer less than or equal to IxJ. In other words, the IxJ values may be different from each other; or, the IxJ values may be all the same; or, some of the IxJ values may be the same, and the other values may be the same or different.

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.

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

Wherein, K represents the number of first combinations. The first combination is a partial combination of IxG _Q +G _P xJ +G _P xG _Q Gaussian component combinations, the Gaussian components of the K first combinations are different from each other, and the IxG _Q +G _P xJ +G _P xG _Q Gaussian component combinations include the following three items:

The combination of t = 1 and traversing i = 1, ..., I, j = 1, ..., G _Q

Combinations when t=2 and traverse i=1,…, _GP ,j=1,…,J

At t=3, and traversing i=1,…,G _P , j=1,…,G _Q

Indicates the kth combination in the K first combinations

Sum.

When traversing i＝1,…,I,j＝1,…,G _Q ,

When traversing i=1,…, _GP ,j=1,…,J,

When traversing i=1,…,G _P , j=1,…,G _Q ,

G _P represents the number of columns in the Gaussian parameter matrix of the first variable, P _1,i represents the element in the first row and i-th column in the Gaussian parameter matrix of the first variable, P _2,i represents the element in the second row and i-th column in the Gaussian parameter matrix of the first variable, and P _3,i represents the element in the third row and i-th column in the Gaussian parameter matrix of the first variable.

G _Q represents the number of columns in the Gaussian parameter matrix of the second variable, Q _1,j represents the element in the first row and j column in the Gaussian parameter matrix of the second variable, Q _2,j represents the element in the second row and j column in the Gaussian parameter matrix of the second variable, and Q _3,j represents the element in the third row and j column in the Gaussian parameter matrix of the second variable.

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

First item,

A represents the first variable, η _P represents the first variable taken from

The probability,

Indicates that the first variable is taken from

second section,

The probability,

Indicates that the second variable is taken from

the third item,

Wherein, C represents the third variable.

The fourth item is the support {c ₁ ,c ₂ ,...,c _M } of the discrete part of C. The support {c ₁ ,c ₂ ,...,c _M } represents the M of ci _,j in the case of traversing i=1,...,I,j=1,...,J.

The elements in the support {c ₁ ,c ₂ ,...,c _M } are different from each other.

The outputs of the g operation include:

exist

D represents the fourth variable. The conditional probability distribution of the output of the g operation is determined based on μ and the support set {c ₁ ,c ₂ ,...,c _M }.

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 information.

In one possible design, when μ is an element in the support {c ₁ ,c ₂ ,...,c _M }, the conditional probability distribution satisfies:

in,

When traversing i＝1,...,I,j＝1,...,J, if

Then

That is, when μ is an element in the support {c ₁ , c ₂ , ..., c _M }, the conditional probability distribution of the g operation includes a discrete part.

In one possible design, when μ is outside the support {c ₁ ,c ₂ ,...,c _M }, the conditional probability distribution satisfies:

in,

When traversing i＝1,...,I,j＝1,...,J, if

Then

in,

That is, when μ is outside the support {c ₁ ,c ₂ ,...,c _M }, the conditional probability distribution of the g operation includes both discrete and continuous parts.

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 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.

The first variable is the value of the t-th position in the s-th layer of the encoding network, the second variable is the value of the t+2 ^ns -th position in the s-th layer, the third variable is the value of the t-th position in the s+1-th layer of the encoding network, and the fourth variable is the value of the t+2 ^ns -th position in the s+1-th layer.

The coding network includes n+1 layers, the first layer of the coding network is used to input the sequence to be coded, the second to nth layers of the coding network are used to encode the sequence to be coded to obtain the coded sequence, and the n+1th layer of the coding network is used to output the coded 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.

The first term, A～f _P.

Wherein, A represents the first variable, _fP represents the density function of the first variable, and P represents the sampling matrix of the first variable.

The second term, B~f _Q.

Wherein, 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.

The outputs of the f operation include:

The sampling matrix U of .

Where C represents the third variable,

in,

P _1,1 represents the element in the first row and first column of the sampling matrix P, and 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, and 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, and the n points are points equally spaced between [U _min ,U _max ], i=1,2,...,n.

d(t,P) represents the discretization function of the first variable,

Represents the discretized function of the second variable.

In one possible design, the input to the g operation includes the following three items:

The first term, A～f _P.

The second term, B~f _Q.

the third item,

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

The outputs of the g operation include:

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, and 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 n+2 column of the sampling matrix P.

_vi is the i-th point among n points, and the n points are points equally spaced between [V _min , V _max ], i=1, 2, ..., n.

in,

represents the discretized function of the first variable,

Represents the discretized function of the second variable.

In a second aspect, a communication device is provided, which 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 a module, unit, or means corresponding to the method, which may be implemented by hardware, software, or by hardware executing corresponding software. The hardware or software includes one or more modules or units corresponding to the functions.

In a third aspect, a communication device is provided, comprising: a processor; the processor is coupled to a memory, and after reading an instruction in the memory, executes the method as described in any of the above aspects according to the instruction. The communication device can be the receiving device in the first aspect, or a chip that implements the function of the receiving device.

In a 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.

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 arranged in the receiving device.

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 a module outside the chip. For example, the chip can be a chip that implements the function of a receiving device in the first aspect or any possible design of the first aspect. The processing circuit is used to run a computer program or instruction to implement the method in the first aspect or any possible design of the first aspect.

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 encoded to obtain a coded sequence. The length of the sequence to be encoded is N, N= ²ⁿ , and n is a positive integer. The transmitting device is also used to send the coded sequence. The receiving device is used to receive the coded sequence and determine a first sequence based on the received coded sequence. The first sequence includes the value of the transmission bit 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 also used to determine a decoding result based on a signal probability distribution, a first set, and the value of the transmission bit in the coded 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 coded sequence.

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

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

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.

In an eighth aspect, a circuit system is provided, wherein the circuit system includes a processing circuit, and the processing circuit is configured to execute any method in any of the above aspects.

Among them, the technical effects brought about by any design in the second to eighth aspects can refer to the beneficial effects in the corresponding methods provided above, and will not be repeated here.

BRIEF DESCRIPTION OF THE DRAWINGS

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

FIG2 is a schematic diagram of a basic flow of wireless communication provided in an embodiment of the present application;

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

FIG4 is a schematic diagram of a decoding process provided by an embodiment of the present application;

FIG5 is a flow chart of a decoding method under a non-finite field provided by an embodiment of the present application;

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

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

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

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

FIG9b is a schematic diagram of a function gradient provided in an embodiment of the present application;

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

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

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

FIG13 is a schematic diagram of the structure of a communication device provided in an embodiment of the present application;

FIG. 14 is a second schematic diagram of the structure of the communication device provided in an embodiment of the present application.

Detailed ways

FIG. 1 is a schematic diagram of the architecture of a communication system 1000 used in an embodiment of the present application. As shown in FIG. 1 , the communication system 1000 includes at least one network device (such as 110a and 110b in FIG. 1 ) and at least one terminal device (such as 120a-120j in FIG. 1 ). The terminal device is connected to the network device wirelessly. FIG. 1 is only a schematic diagram, and other network devices may also be included in the communication system, such as wireless relay devices and wireless backhaul devices, which are not shown in FIG. 1 .

The network equipment can be a base station, an evolved NodeB (eNodeB), a transmission reception point (TRP), a next generation base station (next generation NodeB, gNB) in the fifth generation (5G) mobile communication system, a next generation base station in the 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 can also be a module or unit that completes part of the functions of a base station, for example, it can be a centralized unit (CU) or a distributed unit (DU). Here, the CU completes the functions of the radio resource control (RRC) protocol and the packet data convergence layer 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 each of the above-mentioned protocol layers, reference can be made 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. 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 takes the network device as an example.

The terminal device may also be referred to as a terminal, user equipment (UE), mobile station, mobile terminal, etc. The terminal device 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, automatic driving, telemedicine, smart grid, smart furniture, smart office, smart wear, smart transportation, smart city, etc. The terminal device may be a mobile phone, a tablet computer, a computer with wireless transceiver function, a wearable device, a vehicle, a drone, a helicopter, an airplane, a ship, a robot, a mechanical arm, a smart home device, etc. The embodiments of the present application do not limit the specific technology and specific device form adopted by the terminal device.

The network equipment and terminal equipment can be fixed or movable. The network equipment and terminal equipment can be deployed on land, including indoors or outdoors, handheld or vehicle-mounted; they can also be deployed on the water surface; they can also be deployed on aircraft, balloons and artificial satellites in the air. The embodiments of the present application do not limit the application scenarios of the network equipment and terminal equipment.

The roles of network devices and terminal devices can be relative. For example, the helicopter or drone 120i in FIG1 can be configured as a mobile base station. For the terminal devices 120j that access the wireless access network through 120i, the terminal device 120i is a network device; but for the

network device

110a, 120i is a terminal device, that is, 110a and 120i communicate through the wireless air interface protocol. Of course, 110a and 120i can also communicate through the interface protocol between base stations. In this case, relative to 110a, 120i is also a network device. Therefore, network devices and terminal devices can be collectively referred to as communication devices. 110a and 110b in FIG1 can be referred to as communication devices with network device functions, and 120a-120j in FIG1 can be referred to as communication devices with terminal device functions.

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

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 including the network device function. The control subsystem including the network device function here may be a control center in the above-mentioned application scenarios such as smart grid, industrial control, smart transportation, smart city, etc. 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 including the terminal device function.

Next, the basic process of wireless communication is introduced.

FIG2 shows a basic process of wireless communication. At the transmitting device, the information source is sent out after being sequentially coded, channel coded and modulated, and then transmitted to the receiving device through the channel. At the receiving device, the information destination is outputted sequentially through demodulation, channel decoding and source decoding. In the uplink transmission, the transmitting device is the terminal device in FIG1, and the receiving device is the network device in FIG1. In the downlink transmission, the transmitting device is the network device in FIG1, and the receiving device is the terminal device in FIG1.

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.

It should be understood that the message name between the devices or the name of each parameter in the message in the embodiment of the present application is only an example, and other names may be used in the specific implementation. The embodiment of the present application does not specifically limit this.

In order to facilitate understanding of the embodiments of the present application, the following is a brief description of 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 to the present application.

1. Non-finite domain polarization

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

2. Polar codes on binary domain

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.

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

Source sequence

After encoding, the encoded sequence is obtained

Generally, the bits with higher reliability are set as the value to be restored, and the bits with lower reliability are set as the received value, which need to be transmitted from the transmitting device to the receiving device. As shown in Figure 3, the first four bits with higher reliability include: u ₃ , u ₅ , u ₆ , u ₇ , which are set as the value to be restored. The last four bits with lower reliability include: u ₀ , u ₁ , u ₂ , u ₄ , which are set as the received value. In other words, the source sequence

It is compressed into u ₀ , u ₁ , u ₂ , u ₄ , and the 8-long sequence is compressed into a 4-long sequence, thereby achieving the source compression requirement.

In order to restore the original source sequence from the compressed result (u ₀ ,u ₁ ,u ₂ ,u ₄ )

Polar code decoding requires using the compression result (i.e., the received value) and the distribution of the original source sequence to sequentially restore the value to be restored (u ₃ , u ₅ , u ₆ , u ₇ ), and then convert the coded sequence

Re-encoding to restore the original source sequence

3. Compressed sensing (CS)

Compressed sensing is a technique for finding sparse solutions in underdetermined linear systems. It has a wide range of applications in signal and image processing. In many practical problems in science and technology industries, people often need to recover the real signal from the sampled data. When the sampling system is linear, this problem can be regarded as a problem of solving a system of linear equations:

y＝Ah Formula (1-1)

Among them, ^y∈RM represents the sampled data, that is, a matrix with M rows and 1 column, A∈RM ^×N represents the sampling matrix, that is, a matrix with M rows and N columns, and ^h∈RN represents the real signal, that is, a matrix with N rows and 1 column.

When M<N, this is an underdetermined linear system, so it is impossible to accurately recover the signal h through y. However, if it is assumed that the signal h has a sparse structure, in other words, 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 technology that studies the solution of sparse signals in such underdetermined linear systems.

For example, see Fig. 4, which shows a model framework of compressed sensing. In Fig. 4, each square represents an element.

Since sparse signals are very common in practical engineering problems, compressed sensing technology is widely used, such as single-pixel imaging technology, 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 sampling data, thereby greatly reducing costs and effectively improving the accuracy of reconstructed images.

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 Figure 4 as an example, solving the sparse signal h that satisfies y = Ah can be transformed into the following optimization problem:

min||z|| ₀ subect to Ah＝y Formula (1-2)

Among them, ||z|| ₀ (L ₀ 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 real signal. Since the above L ₀ optimization problem is a non-convex optimization, it is difficult to find an efficient solution algorithm. In order to overcome this difficulty, the optimization problem can be relaxed and the L ₁ norm can be used to approximate the L ₀ norm, converting the problem into:

min||z|| ₁ subect to Ah＝y Formula (1-3)

in,

z _i represents the non-zero elements in the sparse signal h, and the L ₁ optimization problem is a convex optimization. Using the properties of the L ₁ norm, a low-complexity iterative algorithm can be designed to solve the L ₁ optimization problem. Once the solution to the L ₁ optimization problem is obtained, the reconstructed signal is obtained.

This process of recovering the sparse signal h is called the BP algorithm. According to the theory of compressed sensing, under certain regular conditions, it can be proved that the BP algorithm can accurately recover any sparse signal h, which provides a theoretical guarantee for the reliability of the BP algorithm. The BP algorithm is also the most common signal reconstruction method in practical applications.

In the process of obtaining the reconstructed signal by the BP algorithm, multiple iterative decoding is required, and the decoding complexity is high.

In view of this, an 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, a receiving device obtains 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 N _1. The coded sequence is a sequence after the sequence to be coded is coded, and the length of the sequence to be coded is N, N=2 ⁿ , and n is a positive integer. N ₁ is a positive integer less than N. Then, the receiving device determines the decoding result according to the signal probability distribution, the first set, and the value of the transmission bit 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. That is, the coded sequence includes the value of the transmission bit and the value of the bit to be restored. The reliability of the bit to be restored is higher than the reliability of the transmission bit. In this way, after obtaining the first sequence, the receiving device can determine the value of the bit to be restored by recursive operation in combination with the signal probability distribution and the first set. When the value of each transmission bit and the value of the bit to be restored 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, there is no iterative operation process, and the decoding complexity is low.

In the embodiment of the present application, the sequence to be encoded refers to the sequence before the transmitting device performs encoding. The encoded sequence refers to the sequence after the transmitting device encodes the sequence to be encoded. The value of the transmission bit in the encoded sequence constitutes the first sequence.

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

S501: A transmitting device encodes a sequence to be encoded to obtain an encoded sequence.

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.

The length of the sequence to be encoded is N, where N=2 ⁿ and n is a positive integer. For example, N=2, 4, 8, or 16. Taking FIG8 as an example, the sequence to be encoded includes

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 , _N1 and _N2 are positive integers.

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 previous position of the first bit to be restored in the encoded sequence is the transmission bit.

Taking Figure 8 as an example, the encoded sequence includes

That is, the encoded sequence in FIG8 has 4 positions, numbered 0 to 3. The value at the position of number 0 is z ₀ , the value at the position of number 1 is z ₁ , and the values at the positions of other numbers can be deduced by analogy, which will not be repeated. In the encoded sequence of FIG8 , the number of transmitted bits is 2, namely the positions of

number

0 and 2. In the encoded sequence of FIG8 , the number of bits to be restored is 2, namely the positions of number 1 and 3.

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

Exemplarily, 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 after demodulation.

It is easy to understand that the processing of the coded sequence before transmission through the channel, such as rate matching, precoding, interleaving, modulation, etc., is common knowledge to those skilled in the art and is not listed one by one. In the embodiments of the present application, the transmission of the coded sequence is taken as an example for introduction, which should not be understood as a limitation on the embodiments of the present application.

Exemplarily, 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.

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

The first sequence includes the value of each transmission bit in the coded sequence. The coded sequence includes N ₁ transmission bits, and accordingly, the length of the first sequence is N ₁ .

Taking FIG8 as an example, the first sequence includes [z ₀ , z ₂ ], that is, the first sequence includes the values of 2 transmission bits in the encoded sequence.

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].

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

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.

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

Exemplarily, the signal probability distribution includes: X~[-1+1; 0.5 0.5], that is, in FIG. 8

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.

Exemplarily, the signal probability distribution may be preconfigured.

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

Taking FIG8 as an example, the first set includes {0,2}. The first set {0,2} can be understood as that the positions of

sequence numbers

0 and 2 in the encoded sequence belong to the transmission bits. In addition, when the first sequence includes [z ₀ ,z ₂ ], the first value z ₀ in the first sequence is at the position of sequence number 0, and the second value z ₂ in the first sequence is at the position of sequence number 2.

Exemplarily, the first set may be preconfigured.

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.

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

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.

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,

Exemplarily, each position in the decoding path and the value at each position are introduced as follows:

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, where k is a positive integer less than or equal to N _1. That is, 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.

Taking Figure 8 as an example, k = 1, the first transmission bit is the position of sequence 0,

in,

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.

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 N ₂ .

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 at 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.

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

The first item is the signal probability distribution.

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

It is easy to understand that in some embodiments, the positions before the jth bit to be restored in the decoding path are all transmission bits. In this case, each position before the jth bit to be restored includes: each transmission bit before the jth bit to be restored. In other embodiments, the position before the jth bit to be restored in the decoding path includes both transmission bits and bits to be restored. Accordingly, each position before the jth bit to be restored includes: transmission bits and bits to be restored before the jth bit to be restored.

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

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

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

Step 2: The receiving device processes the signal probability distribution through the f operation to obtain the probability distribution of the value z ₁ at the first position of the encoded sequence. The receiving device determines

in,

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.

For the positions after the first position, such as the i-th position (i.e., the position of 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:

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.

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.

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 written as

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:

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

in,

satisfy:

in,

represents 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 probability that the value of the i-th position is z _{i is} ,

express

Maximize the conditional probability distribution of the i-th position.

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.

Step 5: Determine the receiving device

in,

represents the value of the i-th position indicated by the decoding path, and z _i represents the value of the i-th position indicated by the first sequence (the i-th position is the transmission bit).

For the receiving device, after the receiving device executes step 4 or step 5, if i is less than N, i is replaced by i+1 and step 3 is executed again. If i is equal to N, the receiving device executes step 6:

Step 6: Output of receiving device

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

It should be understood that in S5031, the f operation and the g operation are introduced as follows:

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, as described in the following Example 1 (or Example 2, or Example 3).

The input of 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, 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 1 (or Example 3) below. Alternatively, the input of 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.

Among them, the first variable is the value of the t-th position in the s-th layer of the coding network, the second variable is the value of the t+2 ^ns -th position in the s-th layer, the third variable is the value of the t-th position in the s+1-th layer of the coding network, and the fourth variable is the value of the t+2 ^ns -th position in the s+1-th layer. The coding network includes n+1 layers, the first layer of the coding network is used to input the sequence to be encoded, the second to n-th layers of the coding network are used to encode the sequence to be encoded to obtain the encoded sequence, and the n+1-th layer of the coding 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 s-th parameter set, each parameter in the s-th parameter set indicates a position in the s-th layer, and the number of positions indicated by the s-th parameter set is N/2.

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:

u _s,t is the value of the tth position in the sth layer of the coding network. Among them, u _1,1 ,…,u _1,N is the sequence to be encoded, and 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 .

The receiving device sequentially decodes u _n+1,1 ,…,u _n+1,N . When decoding u _n+1,1 , the receiving device performs N-1 f operations, and when decoding u _n+1,t , when t is greater than 1 and t is an even number, performs 1 g operation; when decoding u _n+1,t , when t is greater than 1 and t is an odd number, performs

g operations,

f operations, specifically:

When decoding u _n+1,1 , j traverses from 1 to n, i traverses from 1 to 2 ^ns , and the input of the operation f includes the probability distribution of the first variable u _j,i and the second variable

The output of the operation f includes the probability distribution of the third variable u _j+1,i .

When decoding u _n+1,t , t is greater than 1 and t is an even number, the input of the g operation includes the probability distribution of the first variable u _n,t-1 , the probability distribution of the second variable u _n,t , the probability distribution of the third variable, and the decoded value of the third variable

The output of the g operation includes the probability distribution of the third variable u _n+1,t , and then the decoded value is obtained.

When decoding u _n+1,t , t is greater than 1 and t is an odd number, the receiving device first performs

g operations, i traverses from t to

The input to the g operation consists of 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 operation, j traverses from no _t +2 to n, i traverses from t to t+2 ^nj -1, the input of f operation includes the probability distribution of the first variable u _j,i , the second variable

The output of the f operation includes the probability distribution of the third variable u _j+1,i , and then the decoded value is obtained.

Exemplarily, the coding network may be a butterfly structure. The number of layers of the coding network = log ₂ N + 1. Where N represents the length of the sequence to be coded. When the length of the sequence to be coded N = 4, the number of layers of the coding network is 3, as described in the following examples 1 to 3.

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

Taking Figure 7 as an example, the value indicated by the decoding path is recorded as

Receiving device pair

Perform inverse Hadamard transform to obtain the decoding result.

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

Example 1

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:

FIG8 shows a decoding process under a non-finite field. In FIG8 , the code length of the sequence to be encoded is N=4. x ₀ , x ₁ , x ₂ , x ₃ are the sequences to be encoded, and are also the values of the 1st, 2nd, 3rd, and 4th positions of the first layer in the encoding network. y ₀ , y ₁ , y ₂ , y ₃ are the values of the 1st, 2nd, 3rd, and 4th positions of the second layer in the encoding network. z ₀ , z ₂ are the values of the transmitted bits, z ₁ , z ₃ are the values of the bits to be recovered, and z ₀ , z ₁ , z ₂ , z ₃ are also the values of the 1st, 2nd, 3rd, and 4th positions of the third layer in the encoding network.

The input of the receiving device includes the following three items:

The first item, the first sequence [z ₀ ,z ₂ ]. In FIG8 , z ₀ =0, z ₂ =2.

The second item is the signal probability distribution. In FIG8 , the signal probability distribution of x ₀ , x ₁ , x ₂ , and x ₃ is P(-1)=1/4, P(1)=3/4).

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

The output of the receiving device includes:

First, we introduce the f operation and g operation applicable to discrete values. Among them, the f operation is used for convolution operation, and the g operation is used for conditional probability operation. Among them, the introduction of the f operation and the g operation is as follows:

1. f operation

The inputs to the operation f include the following two items:

The first item, A～P, P(a _i )＝ _pi , i＝1,...,I; A represents the set of first variables, P represents the probability distribution of the first variables, a _i represents the i-th first variable in A, p _i represents the probability that the i-th first variable is a _i , and I represents the number of first variables.

The second item, B～Q, P(b _j )＝q _j ,j＝1,...,J; B represents the set of second variables, Q represents the probability distribution of the second variables, b _j represents the jth second variable in B, q _j represents the probability that the jth second variable is b _j , and J represents the number of second variables.

The outputs of the f operation include:

C～F,F(c _k )＝f _k ,k＝1,...,K; C represents the set of third variables, F represents the probability distribution of the third variables, c _k represents the kth third variable in C, f _k represents the probability that the kth third variable is c _k , K represents the number of third variables, and the values of K third variables are different.

_fi,j ₌ _piqj , fi _,j represents the probability of occurrence of c _i,j . When c _k is the same as L values among IxJ values, f _k is equal to the sum of the probability of occurrence of the L values, and L is a positive integer less than or equal to IxJ.

In other words, the operation f includes step a1 and step b1:

Step a1, traverse i=1,...,I, j=1,...,J, and calculate the following two items:

_fi,j ₌ _piqj .

Step a2: for different i,j, the calculated c _i,j may be the same, and the c i, _j with the same value are merged. The merging can be understood as adding the fi _{,j corresponding to the c i,} _{j with} the same value.

2. g operation

The input to the g operation includes the following four items:

the third item,

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

The outputs of the g operation include:

exist

The conditional probability distribution G at , G(d _m ) = g _m , g _m = p _i q _j /f, m = 1,..., M, D represents the set of fourth variables, G represents the probability distribution of the fourth variable, d _m represents the mth fourth variable in D, g _m represents the probability that the mth fourth variable is d _m , and M represents the number of fourth variables.

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:

_gm ₌ _piqj /f.

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.

Next, the steps in Example 1 (hereinafter referred to as S11 to S18) are introduced:

S11, the receiving device performs f operation.

Exemplarily, the receiving device performs an f operation, the input of which includes the probability distribution of the first variable (the value x ₀ at the first position in the first layer of the coding network) and the probability distribution of the second variable (the value x ₂ at the third position in the first layer). The output of the f operation includes the probability distribution of the third variable (the value y ₀ at the first position in the second layer).

In S11, the inputs of the f operation include the following two items:

The first term, x ₀ ～P,P(a _i )＝p _i ,i＝1...I.

Specifically, the probability that _x0 is -1 is 1/4, and the probability that _x0 is 1 is 3/4.

For example, it can be written as: a ₁ = -1, a ₂ = 1.

p ₁ = 1/4, p ₂ = 3/4.

The second term, x ₂ ～Q, P(b _j )＝q _j ,j＝1...J.

Specifically, the probability that _x2 is -1 is 1/4, and the probability that _x2 is 1 is 3/4.

For example, it can be written as: b ₁ = -1, b ₂ = 1.

q ₁ = 1/4, q ₂ = 3/4.

In S11, the output of the f operation includes:

The conditional probability distribution F.

Specifically, in the process of traversing i=1...I=2, j=1...J=2, the following two items are calculated:

_fij = _piqj _.

For example, it can be written as:

c ₁₂ ＝0,c ₂₁ ＝0,

After merging, it can be recorded as:

c ₂ = 0,

In S11, the output of the operation f can be recorded as: y ₀ ~F,P(c _k )=f _k ,k=1,...,K,K=3.

S12, the receiving device performs f operation.

Exemplarily, the receiving device performs f operation, the input of f operation includes the probability distribution of the first variable (the value x ₁ at the second position in the first layer of the coding network), the probability distribution of the second variable (the value x ₃ at the fourth position in the first layer), and the output of f operation includes the probability distribution of the third variable (the value y ₁ at the second position in the second layer).

In S12, the inputs of operation f include the following two items:

The first term, x ₁ ～P,P(a _i )＝ _pi ,i＝1...I.

Specifically, the probability that _x1 is -1 is 1/4, and the probability that _x1 is 1 is 3/4.

For example, it can be written as: a ₁ = -1, a ₂ = 1.

p ₁ = 1/4, p ₂ = 3/4.

The second term, x ₃ ～Q, P(b _j )＝q _j ,j＝1...J.

Specifically, the probability that x ₃ is -1 is 1/4, and the probability that x ₃ is 1 is 3/4.

For example, it can be written as: b ₁ = -1, b ₂ = 1.

q ₁ = 1/4, q ₂ = 3/4.

In S12, the output of the f operation includes:

The conditional probability distribution F.

_fij = _piqj _.

For example, it can be written as:

c ₁₂ ＝0,c ₂₁ ＝0,

After merging, it can be recorded as:

c ₂ = 0,

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

S13, the receiving device performs f operation.

Exemplarily, the receiving device performs an f operation, the input of the f operation includes the probability distribution of the first variable (the value y ₀ at the first position in the second layer of the coding network), the probability distribution of the second variable (the value y ₁ at the second position in the second layer). The output of the f operation includes the probability distribution of the third variable (the value z ₀ at the first position in the third layer).

In S13, the inputs of operation f include the following two items:

The first term, y ₀ ～P,P(a _i )＝p _i ,i＝1...I.

Specifically, _y0 is

The probability that y 0 is 0 is 1/16, the probability that y ₀ is 0 is 6/16, and the probability that y ₀ is

The probability is 9/16.

For example, it can be written as:

a ₂ ＝0,

The second term, y ₁ ～Q, P(b _j )＝q _j ,j＝1...J.

Specifically, _y1 is

The probability that y 1 is 0 is 1/16, the probability that y ₁ is 0 is 6/16, and y ₁ is

The probability is 9/16.

For example, it can be written as:

_b2 ＝0,

In S13, the output of the f operation includes:

The conditional probability distribution F.

Specifically, in the process of traversing i=1...I=3,j=1...J=3, the following two items are calculated:

_fij = _piqj _.

For example, it can be written as:

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.

After merging, it can be recorded as: c ₁ = -2, c ₂ = -1, c ₃ = 0, c ₄ = 1, c ₅ = 2.

In S13, the output of the operation f can be recorded as: z ₀ ~F,P(c _k )=f _k ,k=1,...,K,K=5.

Since z ₀ = 0 is known,

S14, the receiving device performs g operation.

Exemplarily, the receiving device performs a g operation, and the input of the g operation includes the probability distribution of the first variable (the value y ₀ of the first position in the second layer of the coding network), the probability distribution of the second variable (the value y ₁ of the second position in the second layer), the probability distribution of the third variable (the value z ₀ of the first position in the third layer), and the decoded value of z ₀

The output of the g operation includes the fourth variable (the value z ₁ at the second position in the third layer) in

The conditional probability distribution at .

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

The first term, y ₀ ～P,P(a _i )＝p _i ,i＝1...I.

Specifically, _y0 is

The probability is 9/16.

For example, it can be written as:

a ₂ ＝0,

The second term, y ₁ ～Q, P(b _j )＝q _j ,j＝1...J.

Specifically, _y1 is

The probability of _y2 being 0 is 1/16, the probability of _y1 being

The probability is 9/16.

For example, it can be written as:

_b2 ＝0,

The third and fourth items,

In S14, the output of the g operation includes:

Given the conditional probability distribution G where z ₀ =0.

Specifically, in the process of traversing i=1...I=3,j=1...J=3, if

Then calculate the following two items:

_gm ₌ _piqj /f.

For example, it can be recorded as: d ₁ = -2, d ₂ = 0, d ₃ = 2.

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

Since z ₁ is to be restored,

That is to say,

is the value d _m corresponding to the maximum g _m .

because

so,

S15, the receiving device performs g operation.

Exemplarily, the receiving device performs a g operation, the input of which includes the probability distribution of the first variable (the value x ₀ at the first position in the first layer of the coding network), the probability distribution of the second variable (the value x ₂ at the third position in the first layer), the probability distribution of the third variable (the value y ₀ at the first position in the second layer), and the decoded value of y ₀

The output of the g operation includes the fourth variable (the value y ₂ at the third position in the second layer) in

The conditional probability distribution at .

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

The first term, x ₀ ～P,P(a _i )＝p _i ,i＝1...I.

For example, it can be written as: a ₁ = -1, a ₂ = 1.

p ₁ = 1/4, p ₂ = 3/4.

The second term, x ₂ ～Q, P(b _j )＝q _j ,j＝1...J.

For example, it can be written as: b ₁ = -1, b ₂ = 1.

q ₁ = 1/4, q ₂ = 3/4.

The third and fourth items,

In S15, the output of the g operation includes:

In the known

The conditional probability distribution G.

Specifically, in the process of traversing i=1...I=2,j=1...J=2, if

Then calculate the following two items:

_gm ₌ _piqj /f.

For example, it can be written as:

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

S16, the receiving device performs g operation.

Exemplarily, the receiving device performs a g operation, the input of which includes the probability distribution of the first variable (the value x ₁ at the second position in the first layer of the coding network), the probability distribution of the second variable (the value x ₃ at the fourth position in the first layer), the probability distribution of the third variable (the value y ₁ at the second position in the second layer), and the decoded value of y ₁

The output of the g operation includes the fourth variable (the value y ₃ at the fourth position in the second layer) in

The conditional probability distribution at .

In S16, the input of the g operation includes the following four items:

The first term, x ₁ ～P,P(a _i )＝ _pi ,i＝1...I.

For example, it can be written as: a ₁ = -1, a ₂ = 1.

p ₁ = 1/4, p ₂ = 3/4.

The second term, x ₃ ～Q, P(b _j )＝q _j ,j＝1...J.

For example, it can be written as: b ₁ = -1, b ₂ = 1.

q ₁ = 1/4, q ₂ = 3/4.

The third and fourth items,

In S16, the output of the g operation includes:

In the known

The conditional probability distribution G.

Specifically, in the process of traversing i=1...I=2,j=1...J=2, if

Then calculate the following two items:

_gm ₌ _piqj /f.

For example, it can be written as:

In S16, the output of the g operation can be recorded as: y ₃ ~G,P(d _m )=g _m ,m=1,...,M,M=2.

S17, the receiving device performs f operation.

Exemplarily, the receiving device performs an f operation, the input of the f operation includes the probability distribution of the first variable (the value y ₂ at the third position in the second layer of the coding network), the probability distribution of the second variable (the value y ₃ at the fourth position in the second layer), and the output of the f operation includes the probability distribution of the third variable (the value z ₂ at the third position in the third layer).

In S17, the inputs of the f operation include the following two items:

The first term, y ₂ ～P,P(a _i )＝p _i ,i＝1...I.

Specifically, _y2 is

The probability of y2 is 1/2, and _y2 is

The probability is 1/2.

For example, it can be written as:

p ₁ ＝1/2,p ₂ ＝1/2.

The second term, y ₃ ～Q,P(b _j )＝q _j ,j＝1...J.

Specifically, y ₃ is

The probability of y 1 is 1/2, and y ₁ is

The probability is 1/2.

For example, it can be written as:

q ₁ = 1/2,q ₂ = 1/2.

In S17, the output of the f operation includes:

The conditional probability distribution F.

_fij = _piqj _.

For example, it can be written as:

c ₁₂ ＝0,c ₂₁ ＝0,

After merging, it can be recorded as:

c ₂ = 0,

In S17, the output of the operation f can be recorded as: z ₂ ~F,P(c _k )=f _k ,k=1,...,K,K=3.

Since z ₂ = 2,

S18, the receiving device performs g operation.

Exemplarily, the receiving device performs a g operation, the input of which includes the probability distribution of the first variable (the value y ₂ at the third position in the second layer of the coding network), the probability distribution of the second variable (the value y ₃ at the fourth position in the second layer), the probability distribution of the third variable (the value z ₂ at the third position in the third layer), and the decoded value of z ₂

The output of the g operation includes the fourth variable (the value z ₃ at the fourth position in the third layer) in

The conditional probability distribution at .

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

The first term, y ₂ ～P,P(a _i )＝p _i ,i＝1...I.

Specifically, _y2 is

The probability of y2 is 1/2, and _y2 is

The probability is 1/2.

For example, it can be written as:

p ₁ ＝1/2,p ₂ ＝1/2.

The second term, y ₃ ～Q,P(b _j )＝q _j ,j＝1...J.

Specifically, y ₃ is

The probability of y2 is 1/2, and _y2 is

The probability is 1/2.

The third and fourth items,

In S18, the output of the g operation includes:

In the known

The conditional probability distribution G.

Specifically, in the process of traversing i=1...I=2,j=1...J=2, if

Then calculate the following two items:

_gm ₌ _piqj /f.

For example, it can be written as: d ₁ =0.

g ₁ =1.

In S18, the output of the g operation can be recorded as: z ₃ ~G,P(d _m )=g _m ,m=1,...,M,M=1.

Since z ₃ is to be restored,

That is to say,

is the value d _m corresponding to the maximum g _m .

After the above S11 to S18,

Calculate:

Depend on

Calculate:

Depend on

Calculate:

In this way, the receiving device obtains the decoding result

Example 2

In Example 2, the first sequence is a real number sequence, and the decoding result is a complex number sequence. The decoding process is described below using continuous values as an example:

FIG9a shows a decoding process under a non-finite field. In FIG9a, the code length of the sequence to be encoded is N=4. x ₀ , x ₁ , x ₂ , x ₃ are the sequences to be encoded, and are also the values of the 1st, 2nd, 3rd, and 4th positions of the first layer in the encoding network. y ₀ , y ₁ , y ₂ , y ₃ are the values of the 1st, 2nd, 3rd, and 4th positions of the second layer in the encoding network. z ₀ , z ₂ are the values of the transmitted bits, z ₁ , z ₃ are the values of the bits to be recovered, and z ₀ , z ₁ , z ₂ , z ₃ are also the values of the 1st, 2nd, 3rd, and 4th positions of the third layer in the encoding network.

The input of the receiving device includes the following three items:

The first term, the first sequence [z ₀ ,z ₂ ]. In FIG9 a , z ₀ = 0.50, z ₂ = −0.67.

The second item is signal probability distribution. In Figure 9a, taking the complex signal c ₀ = x ₀ + x ₁ i, c ₁ = x ₂ + x ₃ i as an example, the signal probability distribution includes: x ₀ , x ₁ , x ₂ , x ₃ are independent and identically distributed, and obey a bimodal Gaussian distribution with a variance of 0.1.

Wherein, φ(x; μ, σ) represents a Gaussian distribution density function with a mean of μ and a variance of σ.

The third item is the transmission bit position number {0,2}.

The output of the receiving device includes:

Estimated value of complex signal c ₀ ,c ₁

First, define the sampling matrix and discretization function:

Definition 1, sampling matrix

Given a sampling interval [a, b] and n sampling points a<c ₁ <c ₂ <...< _cn <b, the sampling matrix P of the density function f _X (x) is a 2×(n+2) matrix that stores the sampling interval and the values of the density function f _X (x) at the sampling points, that is:

In the first column of the sampling matrix P, a represents an endpoint value of the sampling interval, and the value of the density function f _X (x) at the endpoint a is 0. In the i+1th column of the sampling matrix P, the value of the density function f _X (x) at the sampling point c _i is p _i . 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 another endpoint value of the sampling interval, and the value of the density function f _X (x) at the endpoint b is 0.

Definition 2: Discretization function

Given a sampling matrix P and a real number x, the discretization function d(x,P) is defined as:

In the discretization function d(x,P), P _1,1 represents the element in the 1st row and 1st column of the sampling matrix P, that is, the endpoint value a. _{P 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. _{P 1,i} represents the element in the 1st row and i-th column of the sampling matrix P, that is, the sampling point c _i-1 . P _2,j represents the element in the 2nd row and j-th column of the sampling matrix P, that is, the sampling point p _i-1 .

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 distance between the sampling point P _1,j of the sampling matrix P and x is the smallest.

It is easy to understand that the discretization function d(x,P) is a step function approximation of the density function _fX (x), as shown in FIG9b.

Then, define the f operation and the g operation:

1. f operation:

The input to the f operation includes the following three items:

The first term, A～f _P.

The second term, B~f _Q.

The third item is the number of sampling points n.

The outputs of the f operation include:

The sampling matrix U of .

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

Step 1, determine the sampling point:

make

Select n points with equal spacing in the interval [U _min ,U _max ], denoted as u ₁ ,u ₂ ,u ₃ ,…, _un .

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

The sample values near the i-th sampling point

satisfy:

d(·,·) is a discretization function, see the introduction of formula (3-2), which will not be repeated here.

Step 3,

Do normalization calculation

make

Then, according to the normalized _fi , we get the sampling matrix U:

2. g operation:

The input to the g operation includes the following four items:

The first term, A～f _P.

The second term, B~f _Q.

the third item,

Wherein, C represents the third variable, and μ represents the first value of the third variable.

The fourth item is the number of sampling points n.

The outputs of the g operation include:

exist

The conditional probability distribution V at .

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

in,

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.

represents the discretized function of the first variable,

Represents the discretized function of the second variable.

In other words, the g operation involves:

Step b1, determine the sampling point

make

Select n points with equal spacing in the interval [V _min ,V _max ], denoted as v ₁ ,v ₂ ,v ₃ ,…,v _n .

Step b2, let

Step b3,

Do normalization

calculate

make

Output

Among them, the above-mentioned first variable to fourth variable can refer to the introduction of S5031, which will not be repeated here.

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

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

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

S21, the receiving device performs f operation.

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

First item,

second section,

The third item, the number of sampling points n=4.

In S21, the output of the f operation includes:

The sampling matrix U.

Specifically, first, the receiving device calculates

Then determine the sampling points, that is, u ₁ = -1.6971, u ₂ = -0.5657, u ₃ = 0.5657, u ₄ = 1.6971.

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

To get:

After normalization, calculate

make

To get:

f ₁ = 0.1636, f ₂ = 0.1966, f ₃ = 0.1966, f ₄ = 0.1636.

In S21, the output of the f operation can be written as:

S22, the receiving device performs f operation.

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

First item,

second section,

The third item, the number of sampling points n=4.

In S22, the output of the f operation includes:

The sampling matrix U.

Specifically, first, the receiving device calculates

corresponding,

After normalization, calculate

make

To get:

f ₁ = 0.1636, f ₂ = 0.1966, f ₃ = 0.1966, f ₄ = 0.1636.

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

S23, the receiving device performs f operation.

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

First item,

second section,

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

In S23, the output of the f operation includes:

The sampling matrix U.

Specifically, first, the receiving device calculates

Then determine the sampling points, that is, u ₁ = -2.4, u ₂ = -0.8, u ₃ = 0.8, u ₄ = 2.4.

To get:

After normalization, calculate

make

To get:

f ₁ ＝0.0844,f ₂ ＝0.1859,f ₃ ＝0.1859,f ₄ ＝0.0844.

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

Since z ₀ = 0.5 is known,

S24, the receiving device performs g operation.

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

First item,

second section,

the third item,

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

In S24, the output of the g operation includes:

The conditional distribution sampling matrix V is known to be z ₀ = 0.5.

Specifically, first, the receiving device calculates

Then determine the sampling points, that is, v ₁ = -2.1, v ₂ = -0.7, v ₃ = 0.7, v ₄ = 2.1.

To get:

After normalization, calculate

make

To get:

g ₁ = 0.1213, g ₂ = 0.1752, g ₃ = 0.1752, g ₄ = 0.1213

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

Since z ₁ is to be restored,

because

so,

S25, the receiving device performs g operation.

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

First item,

second section,

the third item,

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

In S25, the output of the f operation includes:

The conditional distribution sampling matrix V is known to be y ₀ = -0.1414.

Specifically, first, the receiving device calculates

Then determine the sampling points, that is, v ₁ = -1.6122, v ₂ = -0.5374, v ₃ = 0.5374, v ₄ = 1.6122.

To obtain: g ₁ = 0.2667, g ₂ = 0.0109, g ₃ = 0.0109, g ₄ = 0.2667.

After normalization, calculate

make

To get:

g ₁ = 0.3019, g ₂ = 0.0123, g ₃ = 0.0123, g ₄ = 0.3019

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

S26, the receiving device performs g operation.

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

First item,

second section,

the third item,

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

In S26, the output of the g operation includes:

The conditional distribution sampling matrix V is known to be y ₁ = 0.8485.

Specifically, first, the receiving device calculates

Then determine the sampling points, that is, v ₁ = -1.1879, v ₂ = -0.3960, v ₃ = 0.3960, v ₄ = 1.1879.

To obtain: g ₁ = 0.0539, g ₂ = 0.0539, g ₃ = 0.0539, g ₄ = 0.0539.

After normalization, calculate

make

To get:

g ₁ = 0.2525, g ₂ = 0.2525, g ₃ = 0.2525, g ₄ = 0.2525

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

S27, the receiving device performs f operation.

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

First item,

second section,

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

In S27, the output of the f operation includes:

Sampling matrix U.

Specifically, first, the receiving device calculates

Then determine the sampling points, that is, u ₁ = -1.98, u ₂ = -0.66, u ₃ = 0.66, u ₄ = 1.98.

To get:

After normalization, calculate

make

To get:

f ₁ = 0.1487, f ₂ = 0.1557, f ₃ = 0.1557, f ₄ = 0.1487.

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

Since z ₂ = -0.67 is known,

S28, the receiving device performs g operation.

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

First item,

second section,

the third item,

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

In S28, the output of the g operation includes:

The conditional distribution sampling matrix V is known to have z ₂ = -0.67.

Specifically, first, the receiving device calculates

Then determine the sampling points, that is, v ₁ = -2.078, v ₂ = -1.026, v ₃ = 0.026, v ₄ = 1.078.

To obtain: g ₁ = 0.0762, g ₂ = 0.0762, g ₃ = 0.0031, g ₄ = 0.0031.

After normalization, calculate

make

To get:

g ₁ = 0.3653, g ₂ = 0.3653, g ₃ = 0.0149, g ₄ = 0.0149

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

Since z ₃ is to be restored,

Depend on

Calculate:

Depend on

Calculate:

Depend on

Calculate:

In this way, the receiving device can get an estimate

Example 3

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:

FIG10 shows a decoding process under a non-finite field. In FIG10 , the code length of the sequence to be encoded is N=4. x ₀ , x ₁ , x ₂ , x ₃ are the sequences to be encoded, and are also the values of the 1st, 2nd, 3rd, and 4th positions of the first layer in the encoding network. y ₀ , y ₁ , y ₂ , y ₃ are the values of the 1st, 2nd, 3rd, and 4th positions of the second layer in the encoding network. z ₀ , z ₂ are the values of the transmitted bits, z ₁ , z ₃ are the values of the bits to be recovered, and z ₀ , z ₁ , z ₂ , z ₃ are also the values of the 1st, 2nd, 3rd, and 4th positions of the third layer in the encoding network.

The input of the receiving device includes the following three items:

The first term, the first sequence [z ₀ ,z ₂ ]. In FIG10 , z ₀ = 0.60, z ₂ = -0.60.

The second item is the signal probability distribution. In Figure 10, the signal probability distribution P is 0.5δ ₀ +0.5φ(x; 0, 1), that is, P is taken 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.

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

The output of the receiving device includes:

Consider the continuous part of the signal to be a mixed Gaussian distribution,

In the embodiment of the present application,

Represents the Gaussian distribution density function with mean μ and variance σ.

For a mixed Gaussian distribution

It is represented by a 3×G matrix P:

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 proportional coefficient. It is easy to understand that the mixed Gaussian distribution remains a mixed Gaussian distribution after the f and g operations, but the mean and variance change.

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

1. f operation

The inputs to the operation f include the following two items:

First item,

Where A represents the first variable, η _P represents the first variable taken from

The probability,

Indicates that the first variable is taken from

second section,

Where B represents the second variable, η _Q represents the second variable taken from

The probability,

Indicates that the second variable is taken from

The outputs of the f operation include:

The probability distribution of .

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

The f operation includes the following steps:

Step 1: Determine the ratio of the discrete parts, let η _U ＝η _P η _Q .

Step 2, determine the discrete part:

When traversing i＝1,…,I,j＝1,…,J, calculate

f _ij = p _i q _j . For different i, j, the calculated c _ij may be the same, merge the same c _ij . The merged value is recorded as c ₁ ,…,c _M ; f ₁ ,…,f _M .

Step 3, determine the continuous part:

When traversing i＝1,…,I,j＝1,…,G _Q , calculate

When traversing i=1,…, _GP ,j=1,…,J, calculate

When traversing i=1,…,G _P , j=1,…,G _Q , calculate

Step 4, merge the continuous parts:

For different i,j,t, Gaussian components

May be the same, merge the same

Suppose there are K Gaussian components after merging (μ ₁ ,σ ₁ ,λ ₁ ),…,(μ _K ,σ _K ,λ _K ), let

make

2. g operation

The input to the g operation includes the following four items:

First item,

The probability,

Indicates that the first variable is taken from

second section,

The probability,

Indicates that the second variable is taken from

the third item,

The fourth term is the support of the discrete part of C {c ₁ ,c ₂ ,...,c _M }.

The support set {c ₁ ,c ₂ ,...,c _M } represents the M of c _i,j in the case of traversing i＝1,...,I,j＝1,...,J.

The outputs of the g operation include:

exist

The conditional probability distribution of . Where D represents the fourth variable.

The processing steps of the g operation include:

If u∈{c ₁ ,c ₂ ,…,c _M }, that is, u is in the discrete support of operation f, then the processing steps of operation g include:

When traversing i＝1,…,I,j＝1,…,J, if

Then

g _m = p _i q _j . Let

corresponding,

if

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

Step 1, determine the proportion of discrete parts:

calculate

F(u)＝F ₁ (u)+F ₂ (u)+F ₃ (u). Let

Step 2, determine the discrete part:

calculate

make

Step 3, determine the continuous part:

When traversing i=1,…,G _P , j=1,…,G _Q , the following three items are calculated:

Step 4, merge the continuous parts:

For different i, j, the Gaussian components (μ _ij ,σ _ij ) may be the same, and the same (μ _ij ,σ _ij ) are merged.

make

corresponding,

Next, the steps in Example 3 (S31 to S38 described below) are introduced:

S31, the receiving device performs f operation.

In S31, the input of operation f includes the following two items:

First item,

second section,

In S31, the output of the f operation includes:

Distribution.

Specifically, calculate η _U =η _P η _Q =0.5*0.5=0.25.

f ₁ ＝p ₁ q ₁ ＝1.

calculate

Merge the same Gaussian components and normalize them to get

In S31, the output of operation f can be recorded as: y ₀ ～0.25δ ₀ +0.75U.

S32, the receiving device performs f operation.

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

First item,

second section,

In S32, the output of the f operation includes:

Distribution.

Specifically, calculate η _U =η _P η _Q =0.5*0.5=0.25.

f ₁ ＝p ₁ q ₁ ＝1.

calculate

Merge the same Gaussian components and normalize them to get

In S32, the output of operation f can be recorded as: y ₁ ～0.25δ ₀ +0.75U.

S33, the receiving device performs f operation.

In S33, the inputs of the f operation include the following two items:

First item,

second section,

In S33, the output of the f operation includes:

Distribution.

Specifically, calculate η _U =η _P η _Q =0.25*0.25=0.0625.

f ₁ ＝p ₁ q ₁ ＝1.

Traverse i＝1,j＝1,2, calculate

Traverse i＝1,2,j＝1, calculate

Traverse i＝1,2,j＝1,2, calculate

Merge the same Gaussian components and normalize them to get

In S33, the output of the f operation can be recorded as: z ₀ ～0.0625δ ₀ +0.9375U.

Since z ₀ = 0.6 is known, we can

S34, the receiving device performs g operation.

In S34, the input of the g operation includes the following four items:

First item,

second section,

The third term, z ₀ = 0.6.

The fourth term is the support {0} of the discrete part of z ₀ .

In S34, the output of the g operation includes:

Conditional distribution at z ₀ = 0.6.

because

Therefore, the receiving device determines:

F(z ₀ )＝F ₁ (z ₀ )+F ₂ (z ₀ )+F ₃ (z ₀ )＝0.3561, let

calculate

After normalizing g _i , we get g ₁ = g ₂ = 0.5.

Traverse i＝1,2,j＝1,2, calculate

μ ₁₁ ＝0,σ ₁₁ ＝0.5,λ ₁₁ ＝0.4690；μ ₁₂ ＝-0.2,

λ ₁₂ =0.2159;

μ ₂₁ = 0.2,

λ ₂₁ ＝0.2159；μ ₂₂ ＝0,σ ₂₂ ＝1,λ ₂₂ ＝0.0993.

Combining the same Gaussian components, we get

Output

Since z ₁ needs to be restored, if z ₁ takes a discrete distribution, it is most likely to take -0.6 = {d _m :max g _m }, and the probability is p _d = η _V *max g _m = 0.4108*0.5 = 0.2054.

If z ₁ takes a continuous distribution, the most likely distribution is a Gaussian distribution with a mean of 0 = {V _1,m :max V _3,m }, with a probability of p _c = (1-η _V )*max V _3,m = 0.5892*0.4690 = 0.2763.

Since p _c > p _d , we get

Depend on

Calculate

S35, the receiving device performs g operation.

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

First item,

second section,

The third term, y ₀ = 0.4243.

The fourth term is the support {0} of the discrete part of y ₀ .

In S35, the output of the g operation includes:

Conditional distribution at y ₀ = 0.4243.

because

Therefore, the receiving device determines:

F(y ₀ )＝F ₁ (y ₀ )+F ₂ (y ₀ )+F ₃ (y ₀ )＝0.3268, let

calculate

After normalizing g _i , we get g ₁ = g ₂ = 0.5.

calculate

λ ₁₁ = 1, we get

Output

S36, the receiving device performs g operation.

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

First item,

second section,

The third term, y ₁ = 0.4243.

The fourth term is the support {0} of the discrete part of y ₁ .

In S36, the output of the g operation includes:

Conditional distribution at y ₁ = 0.4243.

because

Therefore, the receiving device determines:

F(y ₁ )＝F ₁ (y ₁ )+F ₂ (y ₁ )+F ₃ (y ₁ )＝0.3268, let

calculate

After normalizing g _i , we get g ₁ = g ₂ = 0.5.

calculate

λ ₁₁ = 1, we get

Output

S37, the receiving device performs f operation.

In S37, the inputs of the f operation include the following two items:

First item,

second section,

In S37, the output of the f operation includes:

Distribution.

Specifically, the receiving device calculates η _U =η _P η _Q =0.7211*0.7211=0.5199. Iterates through i=1,2,j=1,2, and calculates

_fij = _piqj _, to obtain:

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. Combining the same c _ij gives c ₁ = -0.6, f ₁ = 0.25; c ₂ = 0, f ₂ = 0.5; c ₃ = 0.6, f ₃ = 0.25.

Traverse i＝1,2,j＝1, calculate

Traverse i＝1,j＝1,2, calculate

Traverse i＝1,j＝1, calculate

Merge the same Gaussian components and normalize them to get

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

Since z ₂ = 0.6 is known,

S38, the receiving device performs g operation.

In S38, the input of the g operation includes the following four items:

First item,

second section,

The third term, z ₂ = 0.6.

The fourth term, the support of the discrete part of z ₂ is {-0.6, 0.6, 0}.

In S38, the output of the g operation includes:

Conditional distribution at z ₂ = 0.6.

z ₂ = 0.6∈{-0.6,0.6,0}. Traverse i=1,2,j=1,2, if

but

g _m = p _i q _j :

d ₁ = 0, g ₁ = 0.25, after normalization, we get d ₁ = 0, g ₁ = 1.

Output

z ₃ is to be restored, and the conditional distribution of z ₃ takes 0 with probability 1, so

Depend on

Calculate

Depend on

Calculate

Depend on

Calculate

In this way, the receiving device obtains the decoding result

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.

Exemplarily, FIG. 11 and FIG. 12 correspond to the compression effect when the code length N = {128, 512}, respectively. In FIG. 11 and FIG. 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 FIG. 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 FIG. 4. Among them, the broken line indicated by the letter A in FIG. 11 and FIG. 12 represents the performance effect of the method shown in FIG. 4, and the broken line indicated by the letter B in FIG. 11 and FIG. 12 represents the performance effect of the decoding method 500 under the non-finite field of the embodiment of the present application.

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 taken as an example for introduction.

It should be understood that the decoding method 500 under the non-finite field of the embodiment of the present application can be applied to source decoding or channel decoding. In the case where the decoding method of the embodiment of the present application performs source decoding, the source coding can be encoded using Hadamard transform. In the case where the decoding method of the embodiment of the present application performs channel decoding, the channel coding can be encoded using Hadamard transform, and in addition to Hadamard transform, other technologies still need to be used for processing to complete channel coding.

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

On the originating device side, record the message sequence w = (w ₀ ,…,w _K-1 ). Where, w _k = 0, or, w _k = 1, 0≤k≤K-1, k is an integer. The originating device performs the following steps (steps 1 to 3 below):

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

Among them, the codeword index

It can be understood that the message sequence w is the binary representation of the codeword index I.

Step 2: The transmitting device determines the sequence to be encoded according to the codeword index.

Among them, the sequence to be encoded

i≠I, which can be understood as, in the sequence to be encoded x, the value of the I+1th position is 1, and the remaining positions are 0. The length of the sequence to be encoded is: 2 ^K -1.

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

Exemplarily, the transmitting device performs Hadamard transform on the sequence to be coded x to obtain the coded sequence

The transmission bit sequence is {i ₀ ,…,i _M-1 }, 1≤M≤2 ^K . Correspondingly, the first sequence, i.e., the value of the transmission bit

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

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

Message A, received value

Where _ni represents the normally distributed noise with mean 0 and variance ^a2 , 0≤i≤M-1.

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

For example, in the information B of the receiving device, the signal probability distribution P may be a bimodal Gaussian distribution, denoted as

Where φ(x; μ, σ) represents the Gaussian distribution density function with mean μ and variance σ ² .

Information C, the sequence number of the transmitted bit.

In the embodiment of the present application, in combination with step 3 of the transmitting device, the sequence number of the transmission bits is {i ₀ ,…,i _M-1 }.

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

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 transmission bit.

For example, the process of step 4 can be referred to the introduction of example 2, which will not be repeated here.

Exemplarily, the decoding result of step 4 is recorded as

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

Exemplary, codeword index estimation

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

Exemplarily, the receiving device determines

The binary representation of the message sequence

for

The binary representation of .

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

It is easy to understand that in the embodiment of the present application, the received value, or the 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 according to the received encoded sequence. For details, see the introduction of S502a and S502b, which will not be repeated here.

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 to 14.

For example, Fig. 13 is a schematic diagram of the structure of a communication device provided in an embodiment of the present application. As shown in Fig. 13, a communication device 1300 includes: a processing module 1301 and a transceiver module 1302. For ease of description, Fig. 13 only shows the main components of the communication device 1300.

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

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 N ₁ . The coded sequence is a sequence after the sequence to be coded is coded, and the length of the sequence to be coded is N, N=2 ⁿ , and n is a positive integer. N ₁ is a positive integer less than N.

The processing module 1301 is used to determine the decoding result according to 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 one possible design, the processing module 1301 is used to determine a decoding result according to the signal probability distribution, the first set, and the value of the transmission bit in the encoded sequence, including: determining a decoding path according to the signal probability distribution, the first set, and the value of the transmission bit in the encoded sequence. The decoding path indicates the value of each position in the encoded sequence; and determining a decoding result according to the decoding path.

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, and i is a positive integer less than or equal to N ₁ .

In one possible design, the number of bits to be restored in the encoded sequence is N ₂ , where N ₂ is a positive integer less than N.

The value of the jth bit to be restored 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: signal probability distribution, and the value of each position before the jth bit to be restored in the decoding path. Wherein, j is a positive integer less than or equal to N ₂ .

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 the probability distribution of the third 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. The first value is the decoded value of the third variable.

The coding network includes n+1 layers, the first layer of the coding network is used to input the sequence to be coded, the second to nth layers of the coding network are used to encode the sequence to be coded to obtain a coded sequence, and the n+1th layer of the coding network is used to output the coded 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.

A～P, P(a _i )＝ _pi ,i＝1,...,I. A represents the set of first variables, P represents the probability distribution of the first variables, a _i represents the i-th first variable in A, p _i represents the probability that the i-th first variable is a _i , and I represents the number of first variables.

B～Q, P(b _j )＝q _j ,j＝1,...,J. B represents the set of second variables, Q represents the probability distribution of the second variables, b _j represents the j-th second variable in B, q _j represents the probability that the j-th second variable is b _j , and J represents the number of second variables.

The outputs of the f operation include:

C～F, F(c _k )＝f _k , k＝1,...,K. C represents the set of third variables, F represents the probability distribution of the third variables, c _k represents the kth third variable in C, f _k represents the probability 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.

_fi,j ₌ _piqj , fi _,j represents the occurrence probability of c _i,j .

When c _k is the same as L values out of IxJ values, f _k is equal to the sum of the occurrence probabilities of the L values, and L is a positive integer less than or equal to IxJ.

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.

The outputs of the g operation include:

exist

A represents the first variable, η _P represents the first variable taken from

The probability,

Indicates that the first variable is taken from

The probability,

Indicates that the second variable is taken from

The outputs of the f operation include:

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

Wherein, η _U = η _P η _Q . _{η U} represents the third variable taken from

The probability.

Indicates that the third variable is taken from

and U are determined based on A and B.

_fi,j ₌ _piqj , fi _,j represents the probability of occurrence of c _i,j . When c _m is the same as L values among IxJ values, f _m is equal to the sum of the probability of occurrence of the L values, and L is a positive integer less than or equal to IxJ.

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

Wherein, K represents the number of first combinations, the first combination is a partial combination of IxG _Q +G _P xJ +G _P xG _Q Gaussian component combinations, the Gaussian components of the K first combinations are different from each other, and the IxG _Q +G _P xJ +G _P xG _Q Gaussian component combinations include the following three items: combinations when t=1 and traversing i=1,…,I,j=1,…,G _Q

Combinations when t=2 and traverse i=1,…, _GP ,j=1,…,J

At t=3, and traversing i=1,…,G _P , j=1,…,G _Q

Indicates the kth combination in the K first combinations

Sum.

When traversing i＝1,…,I,j＝1,…,G _Q ,

When traversing i=1,…, _GP ,j=1,…,J,

When traversing i=1,…,G _P , j=1,…,G _Q ,

A represents the first variable, η _P represents the first variable taken from

The probability,

Indicates that the first variable is taken from

The probability,

Indicates that the second variable is taken from

and the support {c ₁ ,c ₂ ,...,c _M } of the discrete part of C, where C represents the third variable and the support {c ₁ ,c ₂ ,...,c _M } represents the M of ci _,j when traversing i=1,...,I,j=1,...,J.

The outputs of the g operation include:

exist

in,

When traversing i＝1,...,I,j＝1,...,J, if

Then

in,

When traversing i＝1,...,I,j＝1,...,J, if

Then

in,

The input of 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.

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, and Q represents the sampling matrix of the second variable.

The outputs of the f operation include:

The sampling matrix U of . C represents the third variable,

in,

d(t,P) represents the discretization function of the first variable,

Represents the discretized function of the second variable.

The outputs of the g operation include:

exist

in,

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.

represents the discretized function of the first variable,

Represents the discretized function of the second variable.

Optionally, the transceiver module 1302 may include a receiving module and a sending module (not shown in FIG. 13 ). The transceiver module 1302 is used to implement the sending function and the receiving function of the communication device 1300 .

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

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.

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 including the receiving device, which is not limited in the present application.

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.

Exemplarily, FIG14 is a second structural diagram of a communication device provided in an embodiment of the present application. The communication device may be a receiving device, or a chip (system) or other component or assembly that may be provided in the receiving device. As shown in FIG14 , a 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, such as by a communication bus.

The following is a detailed introduction to the various components of the communication device 1400 in conjunction with FIG14:

The processor 1401 is the control center of the communication device 1400, which may be a processor or a general term for multiple processing elements. For example, the processor 1401 is one or more central processing units (CPUs), or 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).

Optionally, the processor 1401 may perform 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 .

In a specific implementation, as an embodiment, the processor 1401 may include one or more CPUs, such as CPU0 and CPU1 shown in FIG. 14 .

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 FIG. 14. Each of these processors may be a single-core processor (single-CPU) or a multi-core processor (multi-CPU). The processor here may refer to one or more devices, circuits, and/or processing cores for processing data (e.g., computer program instructions).

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, which will not be repeated here.

Optionally, the memory 1402 may be a read-only memory (ROM) or other types of static storage devices that can store static information and instructions, a random access memory (RAM) or other types of dynamic storage devices 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, optical disc storage (including compressed optical 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 the 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 may exist independently and be coupled to the processor 1401 through an interface circuit (not shown in FIG. 14 ) of the communication device 1400, which is not specifically limited in the embodiments of the present application.

The transceiver 1403 is used for communication with other communication devices. For example, the communication device 1400 is a receiving device, and the transceiver 1403 can be used to communicate with a transmitting device. For another example, the communication device 1400 is a transmitting device, and the transceiver 1403 can be used to communicate with a receiving device.

Optionally, the transceiver 1403 may include a receiver and a transmitter (not shown separately in FIG. 14 ), wherein the receiver is used to implement a receiving function, and the transmitter is used to implement a sending function.

Optionally, the transceiver 1403 may be integrated with the processor 1401, or may 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 the embodiments of the present application.

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

In addition, the technical effects of the communication device 1400 can refer to the technical effects of the method described in the above method embodiment, which will not be repeated here.

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. A general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

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).

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 programs 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 site, computer, server or data center to another website site, computer, server or data center by wired (such as infrared, wireless, microwave, etc.). 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 hard disk.

It should be understood that the term "and/or" in this article is only a description of the association relationship of associated objects, indicating that there can be three relationships. For example, A and/or B can represent: A exists alone, A and B exist at the same time, and B exists alone. A and B can be singular or plural. In addition, the character "/" in this article generally indicates that the associated objects before and after are in an "or" relationship, but it may also indicate an "and/or" relationship. Please refer to the context for specific understanding.

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, a-b, a-c, b-c, or a-b-c, where a, b, c can be single or multiple.

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.

Those of ordinary skill 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 to be beyond the scope of this application.

Those skilled in the art can 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.

In the several embodiments provided in the present 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 only schematic. For example, the division of the units is only a logical function division. There may be other division methods in actual implementation, 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.

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

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.

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 can be essentially or partly embodied in the form of a software product that contributes to the prior art. The computer software product is stored in a storage medium and includes several instructions for a computer device (which can be a personal computer, server, or communication device, etc.) to perform all or part of the steps of the methods described in each embodiment of the present application. The aforementioned storage media include: U disk, mobile hard disk, read-only memory (ROM), random access memory (RAM), disk or optical disk, and other media that can store program codes.

The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art who is familiar with the present technical field can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

A decoding method under a non-finite field, characterized in that it is applied to a receiving device, and the method comprises:

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 N 1 ; the encoded sequence is a 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; N 1 is a positive integer less than N;

A decoding result is determined according to 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.
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.
The method according to claim 1 or 2, characterized in that the step of determining the decoding result according to the signal probability distribution, the first set and the value of the transmission bit in the encoded sequence comprises:

Determining a decoding path according to the signal probability distribution, the first set and the value of the transmission bit in the encoded sequence; the decoding path indicates the value of each position in the encoded sequence;

The decoding result is determined according to the decoding path.
The method according to claim 3 is 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, and i is a positive integer less than or equal to N 1 .
The method according to claim 4, characterized in that the number of bits to be restored in the encoded sequence is N 2 , where N 2 is a positive integer less than N;

The value of the jth bit to be restored in the decoding path corresponds to the maximum decoding metric among multiple decoding metrics; each decoding metric among the multiple decoding metrics is determined according to the following two items:

The 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 N 2 .
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 t-th position in the s-th layer of the coding network, the second variable is the value of the t+2 ns -th position in the s-th layer, the third variable is the value of the t-th position in the s+1-th layer of the coding network, and the fourth variable is the value of the t+2 ns- th position in the s+1-th layer;

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.
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 )＝ pi ,i＝1,…,I; A represents the set of the first variables, P represents the probability distribution of the first variables, a i represents the i-th first variable in A, p i represents the probability that the i-th first variable is a i , and I represents the number of the first variables;

B～Q, P(b j )＝q j , j＝1,…,J; B represents the set of the second variables, Q represents the probability distribution of the second variables, b j represents the j-th second variable in B, q j represents the probability that the j-th second variable is b j , and J represents the number of the second variables;

The output of the f operation includes:

C～F,F(c k )＝f k ,k＝1,…,K; C represents the set of the third variables, F represents the probability distribution of the third variables, c k represents the kth third variable in C, f k represents the probability 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;

Wherein, c k is one of IxJ values, and the IxJ values are the values of c i,j when traversing i=1,…,I,j=1,…,J,
fi ,j = piqj , fi ,j represents the probability of occurrence of c i,j ;

When c k is the same as L values among the IxJ values, f k is equal to the sum of the occurrence probabilities of the L values, and L is a positive integer less than or equal to IxJ.
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 )＝ pi ,i＝1,…,I; A represents the set of the first variables, P represents the probability distribution of the first variables, a i represents the i-th first variable in A, p i represents the probability that the i-th first variable is a i , and I represents the number of the first variables;

B～Q, P(b j )＝q j , j＝1,…,J; B represents the set of the second variables, Q represents the probability distribution of the second variables, b j represents the j-th second variable in B, q j represents the probability that the j-th second variable is b j , and J represents the number of the second variables;

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 at , G(d m ) = g m , g m = p i q j /f, m = 1,…, M, D represents the set of the fourth variables, G represents the probability distribution of the fourth variables, d m represents the mth fourth variable in D, g m represents the probability that the mth fourth variable is d m , and M represents the number of the fourth variables.
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 represents the first variable is taken from
The probability,
Indicates that the first variable is taken from
In the case of , the probability that the first variable is a i is p i , and P represents the Gaussian parameter matrix of the first variable;

B represents the second variable, η Q represents the second variable is taken from
The probability,
Indicates that the second variable is taken from
In the case of , the probability that the second variable is b j is q j , where 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:

Wherein, η U =η P η Q ; η U represents the third variable is taken from
The probability;
Indicates that the third variable is taken from
In the case of , the probability that the third variable is cm is f m ; U represents the Gaussian parameter matrix of the third variable;
and U are determined based on A and B.
The method according to claim 9, characterized in that the values of the M third variables are different from each other;

Wherein, cm is one of IxJ values, and the IxJ values are the values of c i,j when traversing i=1,…,I,j=1,…,J;
fi ,j = piqj , fi ,j represents the probability of occurrence of c i,j ;

When c m is the same as L values among the IxJ values, f m is equal to the sum of the occurrence probabilities of the L values, and L is a positive integer less than or equal to IxJ.
The method according to claim 9, characterized in that

The Gaussian parameter matrix U satisfies:

Wherein, K represents the number of first combinations, the first combination is a partial combination of IxG Q +G P xJ +G P xG Q Gaussian component combinations, the Gaussian components of the K first combinations are different from each other, and the IxG Q +G P xJ +G P xG Q Gaussian component combinations include the following three items: combinations when t=1 and traversing i=1,…,I,j=1,…,G Q
Combinations when t=2 and traverse i=1,…, GP ,j=1,…,J
At t=3, and traversing i=1,…,G P , j=1,…,G Q

Indicates the kth combination in the K first combinations corresponds to
Sum;

When traversing i＝1,…,I,j＝1,…,G Q ,

When traversing i=1,…, GP ,j=1,…,J,

When traversing i=1,…,G P , j=1,…,G Q ,

G P represents the number of columns of the Gaussian parameter matrix of the first variable, P 1,i represents the element in the first row and the i-th column of the Gaussian parameter matrix of the first variable, P 2,i represents the element in the second row and the i-th column of the Gaussian parameter matrix of the first variable, and P 3,i represents the element in the third row and the i-th column of the Gaussian parameter matrix of the first variable;

G Q represents the number of columns of the Gaussian parameter matrix of the second variable, Q 1,j represents the element in the first row and j column of the Gaussian parameter matrix of the second variable, Q 2,j represents the element in the second row and j column of the Gaussian parameter matrix of the second variable, and Q 3,j represents the element in the third row and j column of the Gaussian parameter matrix of the second variable.
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 represents the first variable is taken from
The probability,
Indicates that the first variable is taken from
In the case of , the probability that the first variable is a i is p i , and P represents the Gaussian parameter matrix of the first variable;

B represents the second variable, η Q represents the second variable is taken from
The probability,
Indicates that the second variable is taken from
In the case of , the probability that the second variable is b j is q j , where Q represents the Gaussian parameter matrix of the second variable;

and a support {c 1 ,c 2 ,…,c M } of the discrete part of C, where C represents the third variable, and the support {c 1 ,c 2 ,…,c M } represents M of c i,j when traversing i=1,…,I,j=1,…,J,
The elements in the support set {c 1 ,c 2 ,…,c M } are different from each other;

The output of the g operation includes:

exist
D represents the fourth variable, and the conditional probability distribution of the output of the g operation is determined according to μ and the support {c 1 , c 2 , …, c M }.
The method according to claim 12, characterized in that, when μ is an element in the support {c 1 ,c 2 ,…,c M }, the conditional probability distribution satisfies:

in,
When traversing i＝1,…,I,j＝1,…,J, if
Then
The method according to claim 12, characterized in that, when μ is outside the support {c 1 ,c 2 ,…,c M }, the conditional probability distribution satisfies:

in,
When traversing i＝1,…,I,j＝1,…,J, if
Then

in,
F(u)＝ F1 (u)+ F2 (u)+ F3 (u),

G P represents the number of columns of the Gaussian parameter matrix of the first variable, P 1,i represents the element in the first row and the i-th column of the Gaussian parameter matrix of the first variable, P 2,i represents the element in the second row and the i-th column of the Gaussian parameter matrix of the first variable, and P 3,i represents the element in the third row and the i-th column of the Gaussian parameter matrix of the first variable;

G Q represents the number of columns of the Gaussian parameter matrix of the second variable, Q 1,j represents the element in the first row and j column of the Gaussian parameter matrix of the second variable, Q 2,j represents the element in the second row and j column of the Gaussian parameter matrix of the second variable, and Q 3,j represents the element in the third row and j column of the Gaussian parameter matrix of the second variable.
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 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;

The first variable is the value of the t-th position in the s-th layer of the coding network, the second variable is the value of the t+2 ns -th position in the s-th layer, the third variable is the value of the t-th position in the s+1-th layer of the coding network, and the fourth variable is the value of the t+2 ns- th position in the s+1-th layer;

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.
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~ fQ ; B represents the second variable, fQ represents the density function of the second variable, and Q represents the sampling matrix of the second variable;

The output of the f operation includes:

The sampling matrix U of ; C represents the third variable,

in,
P 1,1 represents the element in the first row and first column of the sampling matrix P, and 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, and 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 points equally spaced between [U min ,U max ], i=1, 2, ..., n;

d(t,P) represents the discretization function of the first variable,
represents a discretized function of the second variable.
The method according to claim 15, characterized in that the input of the g operation includes 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~ fQ ; B represents the second variable, fQ represents the density function of the second variable, and 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, and 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 n+2 column of the sampling matrix P;

vi is the i-th point among n points, wherein the n points are points equally spaced between [V min , V max ], i=1, 2, ..., n;

represents the discretized function of the first variable,
represents a discretized function of the second variable.
A communication device, characterized in that it includes: a processor, the 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 as described in any one of claims 1-17.
A communication device, characterized in that the communication device includes a processor and a transceiver, the transceiver is used for information exchange between the communication device and other communication devices, and the processor executes program instructions to execute the method as described in any one of claims 1-17.
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 described in any one of claims 1-17 through logic circuits or execution code instructions.
A computer-readable storage medium, characterized in that the computer-readable storage medium stores a computer program, and when the computer program is run on a communication device, the communication device executes the method according to any one of claims 1 to 17.
A communication system, characterized in that it comprises a transmitting device and a receiving device; wherein:

The transmitting device is used to perform Hadamard transform on the sequence to be encoded to obtain an encoded sequence; the length of the sequence to be encoded is N, N=2 n , and n is a positive integer;

The transmitting device is further used to send the encoded sequence;

The receiving device is used to receive the coded sequence and determine a first sequence according to the received coded sequence; wherein the first sequence includes the value of the transmission bit in the coded sequence, and the length of the first sequence is N 1 ; N 1 is a positive integer less than N;

The receiving device is further used to execute the method as described in any one of claims 1-17 according to the first sequence.