WO2024065119A1

WO2024065119A1 - Decoding method in non-finite field, and communication apparatus

Info

Publication number: WO2024065119A1
Application number: PCT/CN2022/121492
Authority: WO
Inventors: 秦康剑; 李源; 张华滋; 王俊
Original assignee: 华为技术有限公司
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 error propagation during decoding so as to improve the decoding efficiency, and can be applied in a communication system. The method comprises: a receiving-end device acquiring a signal probability distribution and a first set, wherein the first set is used for determining the position of each bit to be recovered that is in a coded sequence, the coded sequence is the sequence obtained after a sequence to be coded is coded, and the length of the sequence to be coded is N, N = 2n, n being a positive integer; then, the receiving-end device determining X Nth candidate paths according to the signal probability distribution and the first set, wherein one or more said bits of different candidate paths among the X Nth candidate paths correspond to different values, X being a positive integer greater than 1, but smaller than or equal to M, and each said bit in the coded sequence corresponds to at most M candidate values, M being a positive integer greater than 1; and then, the receiving-end device determining a decoding result according to the X Nth candidate paths.

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

At present, the transmitting device can use Hadamard transform to encode the sequence to be encoded to obtain the encoded sequence, and then send the encoded sequence to the receiving device. The length of the sequence to be encoded is N. Correspondingly, the receiving device can use the successive cancellation (SC) decoding algorithm under a non-finite field to decode the encoded sequence. Specifically, when decoding the i-th position in the encoded sequence, the receiving device needs to know the values of the first i-1 positions in the encoded sequence. Wherein, i is a positive integer less than or equal to N. If the i-1th position is decoded incorrectly, the i-th position will also be decoded incorrectly, that is, error propagation occurs. How to reduce the error propagation phenomenon in the decoding process is an urgent problem to be solved.

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 error propagation in the decoding process, thereby improving the 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 includes: the receiving device obtains a signal probability distribution and a first set. The first set is used to determine the position of each bit to be recovered in the coded sequence, the coded sequence is a sequence after the coded sequence is coded, and the length of the coded sequence is N, N= ²ⁿ , and n is a positive integer. Then, the receiving device determines X Nth candidate paths according to the signal probability distribution and the first set. Each candidate path in the X Nth candidate paths indicates the value of each position in the coded sequence, and one or more bits to be recovered in different candidate paths in the X Nth candidate paths have different values, X is a positive integer greater than 1 and less than or equal to M, and each bit to be recovered in the coded sequence corresponds to at most M candidate values, and the M candidate values are values determined by the receiving device, and M is a positive integer greater than 1. Afterwards, the receiving device determines the decoding result according to the X Nth candidate paths.

That is to say, the receiving device determines multiple Nth candidate paths. In this way, the possibility of retaining the correct decoding path increases. Correspondingly, for a certain position to be restored, the possibility of retaining the candidate value corresponding to the position also increases, and the probability of decoding errors at this position is reduced. This also reduces the problem of error propagation caused by decoding errors at a certain position (or positions) to a certain extent, thereby improving decoding efficiency.

In a possible design, the receiving device determines X N-th candidate paths according to the signal probability distribution and the first set, including: when the i-th position of the receiving device is a to-be-recovered bit, the receiving device determines Yi _{,k i-th candidate paths according to the signal probability distribution, the first set and the k} -th i-1 candidate path among Yi _- _{1 i-1 candidate paths. Each i-1 candidate path among Yi-1} _i -1 candidate paths indicates the value of the first i-1 positions in the encoded sequence, and different i-1 candidate paths among Yi- ₁ i-1 candidate paths have different values in one or more to-be-recovered bits. Each i-th candidate path in Yi _{,k i-th} candidate paths indicates the value of the first i positions in the encoded sequence, the value of the first i-1 position indicated by each i-th candidate path in Yi _{,k i} -th candidate paths is the same as the value of the first i-1 position indicated by the k-th i-1-th candidate path, the values corresponding to the i-th positions of different candidate paths in Yi _,k i-th candidate paths are different, i is a positive integer greater than 1 and less than or equal to N, k is a positive integer less than or equal to _Yi-1 , and _Yi-1 is a positive integer less than or equal to M.

The receiving device determines X Nth candidate paths according to Yi _,k th candidate paths corresponding to each i _- 1 th candidate path among Yi-1 th candidate paths when i is equal to N. Alternatively, the receiving device determines X _Nth candidate paths according to the signal probability distribution, the first set, and Yi _,k th candidate paths corresponding to each i-1 th candidate path among Yi-1 th candidate paths when i is less than N.

In this way, when the values corresponding to the i-th positions of different candidate paths in the Yi _,k i-th candidate paths are different, the receiving device retains multiple candidate values for the i-th position, thereby increasing the possibility of the position being correctly decoded.

In a possible design, the receiving device determines X N-th candidate paths according to Yi _{,k i} -th candidate paths corresponding to each i-1-th candidate path in Yi- ₁ i-1-th candidate paths, including: when a first condition is met, determining that Yi _, _{k i-th} candidate paths corresponding to each i-1-th candidate path in Yi-1 i-1-th candidate paths all belong to the X N-th candidate paths. The first condition includes: the total number of i-th candidate paths is less than or equal to M.

That is, when the total number of the i-th candidate paths is less than or equal to M, the receiving device does not need to perform a pruning operation so that each transmission bit retains more candidate values.

In a possible design, the receiving device determines X N-th candidate paths according to Yi _{,k i} -th candidate paths corresponding to each i-1-th candidate path in Yi- ₁ i-1-th candidate paths, including: when the second condition is met, according to the path metric PM value of each i-th candidate path, determining X N-th candidate paths from Yi _{,k i-} th candidate paths corresponding to each i-1-th candidate path in Yi _-1 i-1-th candidate paths. The second condition includes: the total number of i-th candidate paths is greater than M.

That is, when the total number of the i-th candidate paths is greater than M, the receiving device performs a pruning operation so that the transmission bits retain values with greater probability, thereby improving the accuracy of decoding.

In a possible design, the PM value of the mth i-th candidate path determined based on the kth i-1th candidate path satisfies:

PM(k+m,i)＝PM(k,i-1)+lnP(yi _,m |yi _-1,k ,…,y1 _,k )

Wherein, PM(k+m,i) represents the PM value of the mth i-th candidate path determined based on the kth i-1th candidate path, PM(k,i-1) represents the PM value of the kth i-1th candidate path, the kth i-1th candidate path indicates that the values of the first i-1 positions in the encoded sequence are y _i-1,k ,…,y _1,k , lnP(y _i,m |y _i-1,k ,…,y _1,k ) represents the natural logarithm of P(y _i,m |y _i-1,k ,…,y _1,k ), P(y _i,m |y _i-1,k ,…,y _1,k ) represents the probability that the value of the i-th position is y i,m when the mth i-th candidate path indicates that the values of the first i-1 positions in the encoded sequence are y _i-1,k ,…,y _1,k , _and the value of the i-th position in the encoded sequence is y The probability of _i,m is one of the conditional probability distributions of the i-th position, and is the m-th probability in the conditional probability distribution of the i-th position arranged in descending order, where m is a positive integer less than or equal to M.

In one possible design, the PM value of the first candidate path is determined based on the conditional probability distribution of the first position in the encoded sequence.

In a possible design, the conditional probability distribution of the sth position in the encoded sequence is discrete, and the discrete conditional probability distribution includes K ₁ values of the sth position and the probability of occurrence of each of the K ₁ values, where K ₁ is a positive integer. Wherein, s is a positive integer less than or equal to N.

In a possible design, the conditional probability distribution of the sth position in the encoded sequence is continuous, and the continuous conditional probability distribution includes _K2 peak points, each of the _K2 peak points indicates a value of the sth position and the probability of the value occurring, and _K2 is a positive integer. Wherein, s is a positive integer less than or equal to N.

In a possible design, the conditional probability distribution of the sth position in the encoded sequence is continuous, and the continuous conditional probability distribution includes K ₃ reference points in the first confidence interval, each of the K ₃ reference points indicates a value of the sth position and the probability of the value occurring, and K ₃ is a positive integer. Wherein, s is a positive integer less than or equal to N.

In a possible design, the receiving device determines X N-th candidate paths according to the signal probability distribution and the first set, including: when the j-th position of the receiving device is a transmission bit, the receiving device determines the p-th j _- th candidate path according to the signal probability distribution, the first set and the p-th i-1-th candidate path among Y _j-1 j-1-th candidate paths. Each j-1-th candidate path among Y j-1 j-1-th candidate paths indicates the value of the first j-1 position in the coded sequence, and different j-1-th candidate paths among Y _j-1 j-1-th candidate paths have different values in one or more bits to be restored. The p-th j-th candidate path indicates the value of the first j positions in the coded sequence, the value of the first j-1 position indicated by the p-th j-th candidate path is the same as the value of the first j-1 position indicated by the p-th j-1-th candidate path, and is the same as the value corresponding to the j-th position of the j-th candidate path corresponding to different p, j is a positive integer greater than 1 and less than or equal to N, p is a positive integer less than or equal to Y _j-1 , and Y _j-1 is a positive integer less than or equal to M.

The receiving device determines X Nth candidate paths according to the jth candidate path corresponding to each j-1th candidate path among Y _j-1 j-1th candidate paths when j is equal to N. Alternatively, the receiving device determines X Nth candidate paths according to the signal probability distribution, the first set, and the jth candidate path corresponding to each j-1th candidate path among Y _j-1 j-1th candidate paths when j is less than N.

In the present application, the j-th position and the i-th position are different positions in the encoded sequence, in other words, j≠i.

That is to say, when the j-th position is a transmission bit, the value of the j-th position indicated by different j-th candidate paths is the same, and there is no path extension phenomenon.

In one possible design, the PM value of the p-th j-th candidate path satisfies:

PM(p,j)＝PM(p,j-1)+lnP(y _j |y _j-1,p ,…,y _1,p )

Among them, PM(p,j) represents the PM value of the p-th j-th candidate path, PM(p,j-1) represents the PM value of the p-th j-1-th candidate path among Y _j-1 -th j- _{1-th candidate paths, the p-th j-1-th candidate path among Y j-} 1-th j-1-th candidate paths indicates that the values of the first i-1 positions in the encoded sequence are y _j-1,p ,…,y _1,p , lnP(y _j |y j _-1,p ,…,y _1,p ) represents the natural logarithm of (y _j |y _j-1,p ,…,y _1,p ), and P(y _j |y _j-1,p ,…,y _1,p ) represents the probability that the value of the j-th position is y j when the p-th _j -th candidate path indicates that the values of the first j-1 positions in the encoded sequence are y _j-1,p ,…,y _1,p .

In one possible design, when the encoded sequence includes at least one transmission bit, the method further includes: the receiving device obtains a first sequence, wherein the first sequence includes the value of each transmission bit in the at least one transmission bit, so that the receiving device determines the value of the transmission bit in the decoding path according to the first sequence.

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

In a second 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 determines L sub-blocks corresponding to the coded sequence according to the distribution of transmission bits and/or bits to be recovered in the coded sequence. 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= ²ⁿ , and n and L are positive integers. Then, the receiving device uses _the _Lith matrix corresponding to the Lith sub-block in the L sub-blocks to perform matrix operations on the Lith sub _- block to obtain a decoding sequence of the Lith _sub- block. Wherein, i is a positive integer less than or equal to L, the number of rows and columns of the _Lith matrix is determined according to the number of positions in the coded sequence corresponding to the _Lith sub-block, and the elements of the _Lith matrix are determined according to the butterfly operation corresponding to the Lith sub _- block. Afterwards, the receiving device determines the decoding result according to the decoding sequence of each sub-block in the L sub-blocks.

That is to say, the receiving device uses matrix operations to obtain the values at different positions in the encoded sequence, without the need to sequentially calculate the probability distribution of different positions in the encoded sequence through recursive operations, thus avoiding the problem of large decoding delay caused by serial decoding, thereby improving decoding efficiency.

In a possible design, the L _i matrix is an M×M matrix, where M is the number of positions in the encoded sequence corresponding to the L _i sub-block. That is, the receiving device determines the number of rows and columns of the matrix corresponding to the sub-block according to the number of positions of the L _i sub-block.

In one possible design, the L sub-blocks include a first type of sub-block, each of which includes one or more consecutive transmission bits in the encoded sequence. And/or, the L sub-blocks include a second type of sub-block, each of which includes one or more consecutive bits to be recovered in the encoded sequence.

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

In a third 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 receiving device in the second aspect or any possible design of the second 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 fourth aspect, a communication device is provided, comprising: a processor; the processor is used to couple with a memory, and after reading an instruction in the memory, execute the method as described in any of the above aspects according to the instruction. The communication device can be a receiving device in the above first aspect or any possible design of the first aspect, or a receiving device in the above second aspect or any possible design of the second aspect, or a chip that implements the functions of the above receiving device.

In a possible design, the communication device described in the fourth 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 fourth aspect to communicate with other communication devices.

In a fifth 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 may 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. For another example, the chip may be a chip that implements the function of a receiving device in the second aspect or any possible design of the second aspect. The processing circuit is used to run a computer program or instruction to implement the method in the second aspect or any possible design of the second 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 third 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 a decoding process provided by an embodiment of the present application;

FIG4 is a schematic diagram of another decoding process provided in 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 another decoding method under a non-finite field provided in an embodiment of the present application;

FIG9 is a flowchart of another decoding method under a non-finite field provided in an embodiment of the present application;

FIG10 is a simulation result provided by an embodiment of the present application;

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

FIG14 is a flowchart of another decoding method under a non-finite field provided in an embodiment of the present application;

FIG15 is a schematic diagram of another decoding process provided in an embodiment of the present application;

FIG16 is another simulation result provided by an embodiment of the present application;

FIG17 is a schematic structural diagram of a communication device provided in an embodiment of the present application;

FIG18 is a schematic diagram of the structure of another 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), the next generation NodeB (gNB) in the fifth generation (5G) mobile communication system, the 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 third 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 is taken as an example of a network device.

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 FIG. 1 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 FIG. 1 can be referred to as communication devices with network device functions, and 120a-120j in FIG. 1 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 source coding, channel coding and modulation, and then transmitted to the receiving device through the channel. At the receiving device, the information destination is output 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 decoding method 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 under the non-finite field 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 under the non-finite field 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.

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. Successive cancellation decoding (SC) decoding under non-finite fields

SC decoding in a non-finite field can be applied to SC decoding in a real number field, and can also be applied to SC decoding in a complex number field. In the embodiment of the present application, SC decoding in a real number field is taken as an example for introduction.

FIG3 shows an SC decoding process under a non-finite field. In FIG3 , the code length before compression is 8, and the code length after compression is 2. The 8 boxes on the far left represent the signal probability distribution corresponding to the data to be compressed, and the 8 boxes on the far right represent the output probability distribution of the data after real number domain encoding. Real number domain polarization is to use Hadamard transform to obtain 8 real numbers on the right side from the data on the left side that obeys a certain signal probability distribution (such as {-1, +1} and other probability distributions). Among them, the output probability distribution of the 8 real numbers on the right is different from the signal probability distribution of the 8 real numbers on the left. In FIG3 , the output probability distributions of the 8 real numbers on the right are different from each other, and the 8 real numbers on the right have different entropies. Generally speaking, the higher the position, the higher the conditional entropy and the greater the uncertainty; the lower the position, the lower the conditional entropy and the smaller the uncertainty.

The core idea of using real-domain polarization for compressed sensing is to set the data on the high-entropy bit as the transmission bit and place the received (or observed) data; set the data on the low-entropy bit as the bit to be recovered, and obtain the data on the low-entropy bit through SC decoding under a non-finite field.

Specifically, in the SC decoding process under a non-finite field, the input of the SC decoding under a non-finite field includes: the signal probability distribution of N positions on the left (such as N=8 in Figure 3) (such as the probability distribution of {+1, -1} in Figure 3), and the data at the (N-K) known high entropy positions on the right (such as the value of 0 at the first position and the value of 0 at the second position in Figure 3). The output of the SC decoding under a non-finite field includes: data at K low entropy positions. Among them, N is the encoding code length, K is the number of low entropy bits, and 1≤K≤N.

In order to obtain the real number data on the low entropy bit (such as the 3rd to 8th positions in Figure 3), it is necessary to recursively calculate the data on the i-th (i=1, 2, ..., N) position. Specifically, when decoding the i-th position, it is necessary to know the value of the previous (i-1) position. If the i-th position is a transmission bit, the value of the position is directly set to the observed value; if the i-th position is a bit to be restored, the output probability distribution of the position is calculated according to the recursive operation criterion, and then the value with the largest output probability at this position is taken out as the decoding result of the position. The decoding starts from i=1 and ends at i=N. After obtaining the data on all low entropy bits, combined with the known data on the (N-K) high entropy bits, the data on the rightmost position can be obtained. After the Hadamard inverse transform, the leftmost real number can be obtained, thereby completing the decoding.

For example, in FIG3 , taking the third position of the encoded sequence as an example, the conditional probability distribution of the third position includes: P(-2)=0.06, P(-1)=0.25, P(0)=0.37, P(+1)=0.25, P(+2)=0.06. In this case, the maximum probability is 0.37, and the value of the third position in the encoded sequence is 0.

The following describes the decoding process using discrete values as an example:

FIG4 shows a decoding process under a non-finite field. In FIG4 , 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 FIG4 , z ₀ =0, z ₂ =2.

The second item is the signal probability distribution. In Figure 4, the signal probability distribution of x ₀ , x ₁ , x ₂ , 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.

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 ₌ _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,

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.

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 to fourth variables can be found in the following descriptions of S11 to S18, which will not be repeated here.

Next, the various steps in the decoding process described in FIG. 4 (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 which includes the probability distribution of the first variable (the value y ₀ at the first position in the second layer of the coding network) and 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 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

From the above process, it can be seen that if the i-th position is decoded incorrectly, the i+1-th position will also be decoded incorrectly, causing error propagation.

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 signal probability distribution and a first set. The first set is used to determine the position of each to-be-recovered bit in the coded sequence, the coded sequence is a sequence after the to-be-recovered sequence is coded, and the length of the to-be-recovered sequence is N, N= ²ⁿ , and n is a positive integer. Then, the receiving device determines X Nth candidate paths according to the signal probability distribution and the first set. Each candidate path in the X Nth candidate paths indicates the value of each position in the coded sequence, and one or more to-be-recovered bits corresponding to different candidate paths in the X Nth candidate paths have different values, X is a positive integer greater than 1 and less than or equal to M, M indicates the maximum number of values corresponding to each to-be-recovered bit in the coded sequence, and M is a positive integer greater than 1. Afterwards, the receiving device determines the decoding result according to the X Nth candidate paths. That is, the receiving device determines multiple Nth candidate paths, so that the possibility of retaining the correct path increases, and the problem of error propagation caused by decoding errors at a certain (some) position is effectively reduced.

In an embodiment of the present application, the sequence to be encoded refers to the sequence before the transmitting device performs encoding. The length of the sequence to be encoded is N, N= ²ⁿ , and n is a positive integer. 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. In some embodiments, the transmitting device sends the encoded sequence to the receiving device, so that the receiving device determines the first sequence based on the encoded sequence, and then determines the decoding path based on the first sequence, and then determines the decoding result based on the decoding path.

5 to 13, 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 receiving device obtains a signal probability distribution and a first set.

In the uplink transmission, the receiving device is the network device in Figure 1. In the downlink transmission, the receiving device is the terminal device in Figure 1.

The signal probability distribution can be understood as the signal probability distribution of each position in the N positions of the sequence to be encoded. N = 2 ⁿ , n is a positive integer. For example, N = 2, 4, 8, or 16.

Exemplarily, taking Figure 6 as an example, the signal probability distribution includes: X~[-1 +1; 0.5 0.5], that is, the probability that the value of each position shown by the solid line box on the left side of Figure 6 is -1 is 0.5, and the probability that the value of each position is +1 is 0.5.

The first set is used to determine the position of each bit to be restored in the encoded sequence. The number of bits to be restored in the encoded sequence is one or more. The first set is introduced below through three examples (Examples 1 to 3 below):

Example 1: The first set indicates the position of each to-be-recovered bit in the encoded sequence.

Specifically, when the coded sequence includes one or more bits to be restored, or when the coded sequence includes one or more bits to be restored and one or more transmission bits, the first set indicates the position of each bit to be restored in the coded sequence.

Exemplarily, taking FIG. 6 as an example, the first set indicates that the 3rd to 8th positions in the encoded sequence are the bits to be restored, as shown by the dotted box on the right side of FIG. 6 .

Example 2: The first set indicates the position of each transmission bit in the encoded sequence. Accordingly, the receiving device can determine the position of each bit to be recovered in the encoded sequence.

Specifically, when the encoded sequence includes one or more bits to be restored and one or more transmission bits, the first set indicates the position of each transmission bit in the encoded sequence, so that the receiving device determines the position of each bit to be restored in the encoded sequence.

Exemplarily, taking FIG6 as an example, the first set indicates that the first to second positions in the encoded sequence are transmission bits, as shown in the solid line box on the right side of FIG6. Accordingly, the receiving device can also determine that the remaining positions in the encoded sequence (such as the third to eighth positions on the right side of FIG6) are bits to be recovered.

Optionally, in S501, the signal probability distribution and the first set may be preconfigured.

It should be understood that, in the case where the encoded sequence includes one or more transmission bits, the decoding method 500 under the non-finite field in the embodiment of the present application includes S502a, S502b and S502c:

S502a: The transmitting device encodes the 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, N = 2 ⁿ , and n is a positive integer. For example, N = 2, 4, 8, or 16. Taking Figure 4 as an example, the sequence to be encoded includes

Exemplarily, the transmitting device performs Hadamard transform on the sequence to be encoded to obtain a coded sequence, wherein the coded sequence includes _N1 transmission bits and _N2 bits to be restored. N = _N1 + _N2 , where _N1 and _N2 are 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 4 as an example, the encoded sequence includes

That is, the encoded sequence in FIG4 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, and will not be repeated. In the encoded sequence of FIG4 , the number of transmitted bits is 2, namely the positions of

number

0 and 2. In the encoded sequence of FIG4 , the number of bits to be restored is 2, namely the positions of

number

1 and 3.

S502b: 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.

S502c: 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 FIG4 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, taking FIG. 6 as an example, the originating device treats the coding sequence (such as

) is encoded, such as by performing Hadamard transform, to obtain a coded sequence. In the coded sequence, the box where the letter F is located represents the transmission bit, and the box where the letter I is located represents the bit to be restored. Accordingly, the first sequence includes u1u2. When the values of the first position and the second position in the coded sequence are 0, the first sequence is 00.

For the receiving device, the receiving device executes S503 after executing S502c, or, in the case where the encoded sequence does not include a transmission bit, after the receiving device obtains the signal probability distribution and the first set, the receiving device executes S503:

S503: The receiving device determines X Nth candidate paths according to the signal probability distribution and the first set.

Each candidate path in the X N-th candidate paths indicates the value of each position in the encoded sequence.

In the case where the encoded sequence includes at least one bit to be restored, the values corresponding to the one or more bits to be restored of different candidate paths among the X N-th candidate paths are different.

Optionally, when the encoded sequence further includes one or more transmission bits, the values corresponding to the same transmission bits of different candidate paths among the X Nth candidate paths are the same.

Exemplarily, taking FIG. 6 as an example, the first and second positions in the encoded sequence are transmission bits, and the third to eighth positions in the encoded sequence are bits to be restored. In the case of X=2, the value indicated by one of the X(X=2) Nth candidate paths is as follows: 00110011, which can be understood as the values of the first, second, fifth and sixth positions in the encoded sequence are 0, and the values of the third, fourth, seventh and eighth positions in the encoded sequence are 1. The value indicated by another of the X(X=2) Nth candidate paths is as follows: 00111111, which can be understood as the values of the first and second positions in the encoded sequence are 0, and the values of the third, fourth, fifth, sixth, seventh and eighth positions in the encoded sequence are 1.

From the above example, it can be seen that the 5th and 6th positions in the encoded sequence are bits to be restored, the values corresponding to the 5th position indicated by the above two candidate paths are different, and the values corresponding to the 6th position indicated by the above two candidate paths are also different. The 1st and 2nd positions in the encoded sequence are transmission bits, the values corresponding to the 1st position indicated by the above two candidate paths are the same, and the values corresponding to the 2nd position indicated by the above two candidate paths are also the same.

Where X is a positive integer greater than 1 and less than or equal to M. Each bit to be restored in the encoded sequence corresponds to at most M candidate values. The M candidate values are values determined by the receiving device, and M is a positive integer greater than 1. M can be a preconfigured value, such as 3.

In some embodiments, the implementation process of S503 is introduced:

In order to more clearly introduce the implementation process of S503, the conditional probability distribution of each position in the encoded sequence is first introduced, as described in the following three examples (Examples 1 to 3 below):

Example 1: The conditional probability distribution of the s-th position in the encoded sequence is discrete, and the discrete conditional probability distribution includes K ₁ values of the s-th position and the probability of occurrence of each of the K ₁ values, K ₁ is a positive integer, and s is a positive integer less than or equal to N. For example, the process of determining the conditional probability distribution of each position in the encoded sequence can be referred to the introduction of FIG. 3, which will not be repeated here.

Example 2: The conditional probability distribution of the sth position in the encoded sequence is continuous, and the continuous conditional probability distribution includes K ₂ peak points, each of the K ₂ peak points indicates a value at the sth position and the probability of the value occurring, K ₂ is a positive integer, and s is a positive integer less than or equal to N. The value indicated by each peak point can be understood as the value with the highest probability at the sth position in the local range.

Example 3: The conditional probability distribution of the sth position in the encoded sequence is continuous, and the continuous conditional probability distribution includes K ₃ reference points in the first confidence interval, each of the K ₃ reference points indicates a value of the sth position and the probability of the value occurring, K ₃ is a positive integer, and s is a positive integer less than or equal to N. The first confidence interval can be determined according to the 3σ criterion (Laida criterion).

It is easy to understand that in the above examples 1 to 3, s is a positive integer traversing from 1 to N. That is, the conditional probability distribution of each position in the encoded sequence is discrete, satisfying Example 1. The conditional probability distribution of each position in the encoded sequence is continuous, satisfying Example 2. Alternatively, the conditional probability distribution of each position in the encoded sequence is continuous, satisfying Example 3.

It should be understood that the conditional probability distribution of each position in the encoded sequence is determined by the receiving device according to the signal probability distribution and the first set. When the signal takes a discrete value, the determination process of the conditional probability distribution of each position can be referred to the introduction of FIG. 3, which will not be repeated here.

Next, let’s introduce the implementation process of S503:

For the first position in the encoded sequence, the value of this position is described as follows:

When the position is a transmission bit, the value of the position is the same as the value of the first transmission bit in the first sequence. For example, taking FIG6 as an example, the value of the first transmission bit in the first sequence is 0, and correspondingly, the value of the first position in the encoded sequence is 0.

Correspondingly, the first candidate path indicates the value of the first position in the encoded sequence. The PM value of the first candidate path is determined according to the conditional probability distribution of the first position in the encoded sequence.

Exemplarily, referring to FIG6 , the first position is the transmission bit, and the PM value of the first candidate path is {ln 0.195}.

In the case where the position is a bit to be restored, the value of the position is determined based on the conditional probability distribution of the first position in the encoded sequence. For example, the conditional probability distribution of the first position in the encoded sequence includes: P(-2) = 1/8, P(-1) = 1/8, P(0) = 1/4, P(+1) = 1/2. When M is 3, that is, each bit to be restored in the encoded sequence retains a maximum of 3 values, the value of the first position in the encoded sequence includes: {-1, 0, +1}.

Correspondingly, the first candidate path indicates the value of the first position in the encoded sequence. The PM value of the first candidate path is as follows:

The PM value of the first candidate path is determined based on the conditional probability distribution of the first position in the encoded sequence. For example, let Y ₁ be the total number of first candidate paths, and the PM value of each candidate path in the Y ₁ first candidate paths is equal to a probability, and the probability is one of the first M in the order from large to small in the conditional probability distribution of the first position in the encoded sequence. In other words, the PM value of each candidate path in the Y ₁ first candidate paths is equal to a probability, and the probability is one of the last M in the order from small to large in the conditional probability distribution of the first position in the encoded sequence.

Exemplarily, still taking the case where the value of the first position in the encoded sequence includes: {-1, 0, +1}, when the value of the first position in the encoded sequence is -1, the PM value of the first candidate path is equal to 1/8. When the value of the first position in the encoded sequence is 0, the PM value of the first candidate path is equal to 1/4. When the value of the first position in the encoded sequence is +1, the PM value of the first candidate path is equal to 1/2.

For the position after the first position in the encoded sequence, such as the i-th position, as shown in FIG7 , the receiving device executes S5031 and S5032a, or the receiving device executes S5031 and S5032b. Wherein, i is a positive integer greater than 1 and less than or equal to N. In the process of determining the value of the i-th position of the encoded sequence, the candidate path determined by the receiving device is described as the i-th candidate path. And, the number of the i-th candidate paths retained is recorded as _Yi . S5031, S5032a and S5032b are introduced as follows:

S5031. The receiving device determines Yi _,k _i- th candidate paths according to the signal probability distribution, the first set, and the k-th i-1-th candidate path among Yi-1 i-1-th candidate paths.

Among them, the signal probability distribution and the first set in S5031 can be found in the introduction of S501, and will not be repeated here.

Among them, the introduction of the i-1th candidate path is as follows: the number of the i-1th candidate paths is Yi _-1 , _{and Yi-1} is a positive integer less than or equal to M.

In an embodiment of the present application, each _{i-1th candidate path in Yi i-1} i-1th candidate paths indicates the value of the first i-1th position in the encoded sequence. In the case where the first i-1th position in the encoded sequence includes one or more bits to be restored, different i-1th candidate paths in Yi _i-1 i-1th candidate paths have different values in one or more bits to be restored. And/or, in the case where the first i-1th position in the encoded sequence includes one or more transmission bits, different i _{-1th candidate paths in Yi i-} 1 i-1th candidate paths have the same value in the same transmission bit.

Exemplarily, still taking FIG. 6 as an example, the first and second positions in the encoded sequence are transmission bits, and the third to eighth positions in the encoded sequence are bits to be restored. In the case of _Yi-1 = 2, taking the fifth candidate path as an example, the value indicated by one fifth candidate path is as follows: 00110, which can be understood as the values of the first, second and fifth positions in the encoded sequence are 0, and the values of the third and fourth positions in the encoded sequence are 1. The value indicated by another fifth candidate path is as follows: 00111, which can be understood as the values of the first and second positions in the encoded sequence are 0, and the values of the third, fourth and fifth positions in the encoded sequence are 1.

It can be seen from the above example that the fifth position in the encoded sequence is a position to be restored, and the values corresponding to the fifth positions indicated by the above two candidate paths are different.

The first position and the second position in the encoded sequence are transmission bits, the values corresponding to the first position indicated by the above two candidate paths are the same, and the values corresponding to the second positions indicated by the above two candidate paths are also the same.

The following describes S5031 in two cases (case 1 and case 2):

Case 1: when the i-th position in the encoded sequence is a transmission bit, Yi _,k is equal to 1. It can be understood that the i-th candidate path determined in S5031 is the k-th i-th candidate path.

In case 1, the introduction of the k-th i-th candidate path is as follows:

The kth i-th candidate path indicates the value of the first i positions in the encoded sequence, and the value of the first i-1 position indicated by the kth i-th candidate path is the same as the value of the first i-1 position indicated by the kth i-1th candidate path. In the case of different k, the value corresponding to the i-th position of the i-th candidate path corresponding to different k is the same, and k is a positive integer less than or equal to _Yi-1 .

It is easy to understand that in case 1, the i-th position in the encoded sequence is a transmission bit, and the value of this position is determined by the value received by the receiving device. In other words, each i-th candidate path has a value at the i-th position, which is the same as the value of the i-th position in the first sequence. Correspondingly, the number of i-1 candidate paths is the same as that of the i-th candidate path, and there is no path expansion phenomenon.

Exemplarily, taking FIG. 8 as an example, the first position and the second position in the encoded sequence are transmission bits. Taking the first candidate path and the second candidate path as an example, the number of the first candidate path (used to indicate the value of the first position in the encoded sequence) is 1. The number of the second candidate path (used to indicate the value of the first position in the encoded sequence and the value of the second position) is also 1.

Case 2: When the i-th position in the encoded sequence is a bit to be restored, Yi _,k is a positive integer greater than 1.

In case 2, the introduction of Yi _{,k i} -th candidate paths is as follows:

Each i-th candidate path in Yi _{,k i-th} candidate paths indicates the value of the first i positions in the encoded sequence, the value of the first i-1 position indicated by each i-th candidate path in Yi _{,k i} -th candidate paths is the same as the value of the first i-1 position indicated by the k-th i-1-th candidate path, and the values corresponding to the i-th positions of different candidate paths in Yi _,k i-th candidate paths are different. k is a positive integer less than or equal to Yi _-1 . For Yi _,k i-th candidate paths, the probability of occurrence of the value of the i-th position of each candidate path is one of the top M values with larger probabilities in the conditional probability distribution of the i-th position. For example, the conditional probability distribution of the i-th position includes: P(-2) = 1/8, P(-1) = 1/4, P(0) = 1/4, P(+1) = 1/4, P(+2) = 1/8. When M is equal to 3, _Yi,k is equal to 3. Among the three i-th candidate paths, the value of the i-th position of the first candidate path is -1, the value of the i-th position of the second candidate path is 0, and the value of the i-th position of the third candidate path is +1.

It is easy to understand that in case 2, the i-th position in the encoded sequence is a position to be restored, and there is a phenomenon of path extension.

Exemplarily, taking FIG8 as an example, the second position in the encoded sequence is a transmission bit, and the third position is a bit to be restored. Taking the second candidate path and the third candidate path as examples, the number of the second candidate path (used to indicate the value of the first position in the encoded sequence and the value of the second position) is 1, and the number of the third candidate path (used to indicate the values of the first three positions in the encoded sequence) is 3.

For the receiving device, when k traverses 1, 2, 3, ..., _Yi-1 , after the receiving device determines _{Yi, k i} -th candidate paths, when i=N, the receiving device executes S5032a, and when i<N, the receiving device executes S5032b. S5032a and S5032b are described as follows:

S5032a. The receiving device determines X N-th candidate paths according to Yi _,k i-th candidate paths corresponding to each i-1-th candidate path in Yi _-1 i-1-th candidate paths.

Among them, the total number of Yi _{,k i} -th candidate paths corresponding to each i-1-th candidate path in Yi- ₁ i-1-th candidate paths is recorded as

in,

satisfy:

in,

represents the total number of i-th candidate paths determined by the receiving device when k traverses 1, 2, 3, ..., Yi _-1 . _Yi,k represents the number of i-th candidate paths determined by the receiving device according to the signal probability distribution, the first set and the k-th i-1-th candidate paths among Yi _-1 i-1-th candidate paths, k = 1, 2, ..., _Mi-1 .

Optionally, when the first condition is met, S5032a includes: the receiving device determines

That is, the receiving device determines that the Yi _, k i-th candidate paths corresponding to each i _{-1-th candidate path in the Yi-1} _i -1-th candidate paths all belong to the X N-th candidate paths.

The first condition includes:

Less than or equal to M. That is, the number of candidate paths does not exceed M, and there is no need to perform sorting and pruning operations, and as many candidate paths as possible can be retained to increase the possibility of retaining the correct candidate paths.

It is easy to understand that when the first condition is met, X is less than or equal to M.

Optionally, when the second condition is met, S5032a includes: the receiving device receives the

The path-metric (PM) value of each i-th candidate path in the i-th candidate paths is obtained from

Select X N-th candidate paths from the i-th candidate paths.

The second condition includes:

Greater than M.

Exemplarily, the receiving device performs a sorting operation and a pruning operation from

Select X N-th candidate paths from the i-th candidate paths.

Specifically, the receiving device follows

The PM value of each candidate path in the i-th candidate path is

Then, the receiving device deletes

The i-th candidate path

The absolute value of the PM value of each candidate path in the X N-th candidate paths is greater than

The absolute value of the PM value of each candidate path in the i-th candidate path,

Is a positive integer.

It is easy to understand that in the present application, the sorting operation may include sorting from small to large or from large to small, and the present embodiment does not limit this. When the second condition is met, X is equal to M.

That is to say, the receiving device can retain as many candidate paths as possible, and the absolute values of the PM values of the retained candidate paths are larger, so as to improve the decoding accuracy.

S5032b. The receiving device determines X Nth candidate paths according to the signal probability distribution, the first set, and Yi _,k i _- th candidate paths corresponding to each i-1th candidate path in Yi-1 i-1th candidate paths.

Please refer to the introduction of formula (1) for details.

Optionally, when the first condition is met, the receiving device replaces i in S5031, S5032a and S5032b with i+1. That is, for the i+1th position in the encoded sequence, the above steps are repeated until the Nth candidate path is determined. The first condition can be referred to in the introduction of S5032a.

Optionally, when the second condition is met, S5032b includes: the receiving device receives the

The PM value of each i-th candidate path in the i-th candidate path is obtained through sorting and pruning operations.

Select _Yi Nth candidate paths from the i-th candidate paths. In this case, _Yi is equal to M. The second condition can be referred to in the introduction of S5032a. Then, the receiving device replaces i in S5031, S5032a and S5032b with i+1. That is, for the i+1th position in the encoded sequence, the above steps are repeated until the Nth candidate path is determined.

Next, let's introduce the PM value of the candidate path:

When the i-th position in the encoded sequence is a transmission bit, the PM value of the k-th i-th candidate path determined based on the k-th i-1-th candidate path satisfies:

PM(k,i)＝PM(k,i-1)+lnP(y _i |y _i-1,k ,…,y _1,k ) Formula (2)

Wherein, PM(k,i) represents the PM value of the kth i-th candidate path, PM(k,i-1) represents the PM value of the kth _i-1th candidate path among Yi-1th i-1th candidate paths, the kth _i-1th candidate path among Yi-1th i-1th candidate paths indicates that the values of the first i-1 positions in the encoded sequence are y _i-1,k ,…,y _1,k , lnP(y _i |y _i-1,k ,…,y _1,k ) represents the natural logarithm of (y _j |y _j-1,p ,…,y _1,p ), and P(y _i |y _i-1,k ,…,y _1,k ) represents the probability that the value of the i-th position is y i when the value of the first i-1 positions in the encoded sequence indicated by the kth i-th candidate path is y _i _-1,k ,…,y _1,k .

When the i-th position in the encoded sequence is the bit to be restored,

Among the i-th candidate paths, the PM value of the m-th i-th candidate path determined based on the k-th i-1-th candidate path satisfies:

PM(k+m,i)＝PM(k,i-1)+lnP(y _i,m |y _i-1,k ,…,y _1,k ) Formula (3)

Wherein, PM(k+m,i) represents the PM value of the mth i-th candidate path determined based on the kth i-1th candidate path, PM(k,i-1) represents the PM value of the kth i-1th candidate path, the kth i-1th candidate path indicates that the values of the first i-1 positions in the encoded sequence are y _i-1,k ,…,y _1,k , lnP(y _i,m |y _i-1,k ,…,y _1,k ) represents the natural logarithm of P(y _i,m |y _i-1,k ,…,y _1,k ), P(y _i,m |y _i-1,k ,…,y _1,k ) represents the probability that the value of the i-th position is y i,m when the mth i-th candidate path indicates that the values of the first i-1 positions in the encoded sequence are y _i-1,k ,…,y _1,k , _and the value of the i-th position in the encoded sequence is y The probability of _i,m is one of the conditional probability distributions of the i-th position, and is the m-th probability in the conditional probability distribution of the i-th position arranged in descending order.

For example, referring to FIG6 , in the case where M is equal to 3, the PM value of the first candidate path is {ln0.195}, based on the first candidate path and formula (2), the PM value of the second candidate path is {ln0.195+ln0.275}, based on the second candidate path and formula (3), the number of third candidate paths is 3, and the PM value of the first third candidate path is {ln0.195+ln0.275+ln0.37,ln0.195+ln0.275+ln0.25,ln0.195+ln0.275+ln0.25}.

For the receiving device, after the receiving device determines X Nth candidate paths, S504 is executed:

S504: The receiving device determines a decoding result according to the X Nth candidate paths.

Exemplarily, when X=2, the receiving device selects an Nth candidate path from two Nth candidate paths through verification, and then determines the value of each position in the encoded sequence based on the selected Nth candidate path. After the receiving device performs an inverse Hadamard transform on the value of each position in the encoded sequence, it obtains the decoding result, thereby completing the decoding.

Next, in conjunction with FIG. 6 to FIG. 9 , the decoding method 500 under a non-finite field according to an embodiment of the present application is introduced:

S901. The receiving device controls the decoder to input the following information: a first sequence, a signal probability distribution and a first set.

Exemplarily, the first sequence includes two values. The signal probability distribution includes probability distributions of four positions in FIG8 (such as the first position, the second position, the third position, and the fourth position in FIG8). The first set indicates that the first value in the first sequence is the value of the first position in FIG8, and the first set indicates that the second value in the first sequence is the value of the second position in FIG8.

S902. The decoder of the receiving device determines the conditional probability distribution of the i-th position of the encoded sequence according to the first sequence, the signal probability distribution and the first set.

Where i is a positive integer ranging from 1 to 4.

The implementation process of S902 can be found in the introduction of FIG. 3 , and will not be described in detail here.

For the decoder of the receiving device, if the i-th position is not a transmission bit (i.e., the i-th position is a bit to be restored), the decoder of the receiving device executes S903, and if the i-th position is a transmission bit, the decoder of the receiving device executes S908. S903 is described as follows:

S903: The decoder of the receiving device performs path extension.

Exemplarily, taking i equal to 3 as an example, the conditional probability distribution of the third position includes: P(-2) = 0.06, P(-1) = 0.25, P(0) = 0.37, P(+1) = 0.25, P(+2) = 0.06. When M is equal to 3, the decoder of the receiving device performs path expansion according to {x3 = -1, x3 = 0, x3 = +1}. Among them, x3 = -1 can be understood as the value of the third position is -1. X3 = 0 and x3 = +1 can be deduced and will not be repeated.

S904: The decoder of the receiving device updates the PM value.

Exemplarily, the decoder of the receiving device uses formula (3) to update the PM value of each candidate path in S903.

Taking Figure 8 as an example, in the dotted box with i=3, the PM value of the first third candidate path is recorded as PM(1), PM(1)=a+ln0.25. The PM value of the second third candidate path is recorded as PM(2), PM(2)=a+ln0.37. The PM value of the third third candidate path is recorded as PM(3), PM(3)=a+ln0.25. Where a represents the PM value of the second candidate path. a=ln0.195+ln0.275.

S905: The decoder of the receiving device performs a sorting operation.

When the candidate paths determined in S903 are greater than M, the decoder of the receiving device sorts the candidate paths determined in S903 according to the PM values determined in S904.

Taking Figure 8 as an example, when i=4, the PM value of the 1st third candidate path is recorded as PM(1), the PM value of the 2nd third candidate path is recorded as PM(2), and the PM value of the 3rd third candidate path is recorded as PM(3).

In S905, the decoder of the receiving device determines that there are 5 candidate paths, and the PM values of the 5 candidate paths are recorded as: PM(1,1), PM(1,2), PM(2,2), PM(1,3), PM(2,3). The decoder of the receiving device sorts the 5 candidate paths according to their PM values.

S906: The decoder of the receiving device performs a pruning operation.

Exemplarily, the decoder of the receiving device deletes a part of the candidate paths from the candidate paths determined in S903.

Taking Fig. 8 as an example, the decoder of the receiving device deletes some candidate paths from the candidate paths sorted in S905 and retains the candidate paths with larger PM values. For example, in the dotted box where i=4, there are 3 fourth candidate paths.

When i is equal to N, the decoder of the receiving device executes S907. When i is less than N, the decoder of the receiving device replaces i with i+1 and re-executes S902. S907 is described as follows:

S907: The decoder of the receiving device determines the decoding result.

Exemplarily, the decoder of the receiving device determines a decoding result according to the candidate path determined in S906.

In addition, when the i-th position is a transmission bit, the decoder of the receiving device executes S908 and S909:

S908. The decoder of the receiving device determines the value of the i-th position according to the first sequence.

Exemplarily, the decoder of the receiving device uses the value of the i-th position in the first sequence as the value of the i-th transmission bit in the encoded sequence.

S909: The decoder of the receiving device updates the PM value.

Exemplarily, the decoder of the receiving device uses formula (2) to update the PM value of each candidate path in S908.

Taking Figure 6 as an example, when i=1, the conditional probability distribution of the first position is shown as P(u1) in Figure 6. The PM value of the first candidate path is equal to ln0.195. When i=1, the conditional probability distribution of the second position is shown as P(u2) in Figure 6. The PM value of the second candidate path is equal to ln0.195+ln0.275.

When i is equal to N, the decoder of the receiving device executes S907. When i is less than N, the decoder of the receiving device replaces i with i+1 and re-executes S902.

Combined with Figures 10 to 13, the performance effect of the decoding method 500 under the non-finite field of the embodiment of the present application is introduced. After adopting the decoding method 500 under the non-finite field of the embodiment of the present application, a lower mean square error (MSE) can be obtained under the same compression rate; under the same MSE, a higher compression rate can be obtained. Figures 10 to 13 correspond to the compression effect when the code length N = {16, 32, 64, 128}, respectively. The horizontal axis is the number of bits after compression (i.e., the data of the transmission bit), and the vertical axis is the compression performance MSE. The smaller the MSE, the better the performance. In Figures 10 to 13, the letter A indicates the performance effect of the decoding method shown in Figure 3, and the letter B indicates the performance effect of the decoding method 500 under the non-finite field of the embodiment of the present application.

In addition, the decoding process shown in FIG. 3 can be understood as serial decoding, that is, when decoding the i-th position, it is necessary to wait for the decoding result of the previous (i-1) position, resulting in a large decoding delay and high complexity.

In view of this, an embodiment of the present application provides another decoding method under a non-finite field, which can be applied to the communication system of Figure 1. In an embodiment of the present application, the receiving device determines L sub-blocks according to the distribution of transmission bits and/or bits to be recovered in the coded sequence. Wherein, 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= ²ⁿ , and n and L are positive integers. Then, the receiving device uses the _Lith matrix corresponding to the Lith sub-block in the _L sub-blocks to perform matrix operations on the Lith _sub -block to obtain a decoding sequence of the Lith sub _- block. Wherein, i is a positive integer less than or equal to L, the number of rows and columns of the _Lith matrix is determined according to the number of positions in the coded sequence corresponding to the _Lith sub-block, and the elements of the _Lith matrix are determined according to the butterfly operation corresponding to the Lith sub _- block. Afterwards, the receiving device determines the decoding result according to the decoding sequence of each sub-block in the L sub-blocks. That is to say, the receiving device uses matrix operations to obtain the values at different positions in the encoded sequence, and there is no need to sequentially calculate the probability distribution of different positions in the encoded sequence through recursive operations, thereby avoiding the problem of large decoding delay caused by serial decoding, reducing decoding complexity, and improving decoding efficiency.

14 to 16, the decoding method 1400 under a non-finite field proposed in the embodiment of the present application is described in detail. The decoding method 1400 under a non-finite field proposed in the embodiment of the present application includes the following steps:

S1401. A receiving device determines the position distribution of _N1 transmission bits and/or _N2 to-be-recovered bits in a coded sequence.

Exemplarily, S1401 includes: the receiving device obtains a first set, and determines the position distribution of N ₁ transmission bits and/or N ₂ to-be-recovered bits in the encoded sequence according to the first set.

The first set is used to determine the position of each to-be-recovered bit in the coded sequence. The first set and the coded sequence can be referred to in the introduction of S501, which will not be described here.

S1402: The receiving device determines L sub-blocks corresponding to the coded sequence according to the position distribution of the _N1 transmission bits and/or the _N2 to-be-recovered bits in the coded sequence.

The L sub-blocks include a sub-block of the first type, each sub-block of the first type includes the value of each transmission bit in at least one transmission bit. The transmission bits corresponding to each sub-block of the first type are continuous. And/or, the L sub-blocks include a sub-block of the second type, each sub-block of the second type includes the value of each to-be-recovered bit in at least one to-be-recovered bit. The to-be-recovered bits corresponding to each sub-block of the second type are continuous.

Exemplarily, if the continuous M (M = 2 ^q , 0≤q≤log ₂ N) positions starting from the i-th position (i = 2 ⁿ , 0≤n≤log ₂ N) in the encoded sequence are all transmission bits, then the bit sequence consisting of x _i , x _i+1 , x _i+2 , …, x _i+M is recorded as a first type of sub-block. Similarly, if the continuous M (M = 2 ^q , 0≤q≤log ₂ N) positions starting from the i-th position (i = 2 ⁿ , 0≤n≤log ₂ N) in the encoded sequence are all to-be-recovered bits, then the bit sequence consisting of x _i , x _i+1 , x _i+2 , …, x _i+M is recorded as a second type of sub-block.

Taking Figure 15 as an example, the encoded sequence is the sequence on the right, i.e., u1, u2, u3, u4, u5, u6, u7, u8, recorded as

The box where the letter F is located indicates that the position is a transmission bit, and the box where the letter I is located indicates that the position is a bit to be restored. The values of the first 4 positions in the encoded sequence constitute the first type of sub-block, and the values of the last 4 positions in the encoded sequence constitute the second type of sub-block.

It should be understood that in the embodiment of the present application, the sub-block may also be replaced by other names, such as a node. In the embodiment of the present application, the sub-block is introduced as an example and should not be understood as a limitation on the embodiment of the present application. Specifically, in the encoded sequence, one or more consecutive bits to be restored may be referred to as a rate-0 node. One or more consecutive frozen bits may be referred to as a rate-1 node.

S1403. The receiving device uses the L _{i th} matrix corresponding to the L _i th sub-block among the L sub-blocks to perform a matrix operation on the L _i th sub-block to obtain a decoding sequence of the L _i th sub-block.

Wherein, i is a positive integer less than or equal to L. For example, i=1,2,3,···,L-1,L.

The number of rows and columns of the _Lith matrix is determined according to the number of positions in the N positions corresponding to the _Lith sub-block. For example, the _Lith matrix is an M×M matrix, where M is the number of positions in the N positions corresponding to the Lith _sub- block. The elements of the _Lith matrix are determined according to the butterfly operation corresponding to the _Lith sub-block.

Taking Figure 15 as an example, when _Li = 1, the first matrix corresponding to the first sub-block is a 4X4 matrix, and the value of each element in the matrix is determined by the butterfly operation shown in the first dotted box. After obtaining {V1V2V3V4}, the receiving device performs a matrix operation on {V1V2V3V4} and the first matrix to obtain {u1u2u3u4} of the first sub-block. Among them, {V1V2V3V4} represents the value in the decoding process, and {u1u2u3u4} represents the value of the first 4 positions in the encoded sequence.

In the case of _Li = 2, the second matrix corresponding to the second sub-block is also a 4X4 matrix, and the value of each element in the matrix is determined by the butterfly operation shown in the second dotted box. After obtaining {g1g2g3g4}, the receiving device performs a matrix operation on {g1g2g3g4} and the second matrix to obtain {u5u6u7u8} of the second sub-block. Among them, {g1g2g3g4} represents the value in the decoding process, and {u5u6u7u8} represents the value of the last 4 positions in the encoded sequence.

It should be understood that in the embodiment of the present application, in the encoded sequence, one or more consecutive transmission bits can be called rate-0 nodes (i.e., the first sub-block mentioned above), and one or more consecutive frozen bits can be called rate-1 nodes (i.e., the second sub-block mentioned above).

That is to say, the receiving device aggregates the bits to be recovered and the bits to be transmitted in the coded sequence into different sub-blocks according to the code rate.

The decoding sequences at the N positions include the decoding sequence of each sub-block in the L sub-blocks.

S1404. The receiving device determines a decoding result according to a decoding sequence of each sub-block in the L sub-blocks.

Exemplarily, when L=2, the decoder of the receiving device determines the coded sequence based on the decoding sequences of the two sub-blocks (i.e., {u1u2u3u4} and {u5u6u7u8} mentioned above), and then performs an inverse Hadamard transform on the coded sequence to obtain the decoding result, thereby completing the decoding.

In this way, the receiving device uses matrix operations to obtain values at different positions in the encoded sequence, without the need to sequentially calculate the probability distribution of different positions in the encoded sequence through recursive operations, thus avoiding the problem of large decoding delay caused by serial decoding.

Exemplarily, taking FIG. 16 as an example, the length of the encoded sequence N=1024, the decoding method 1400 under the non-finite field of the embodiment of the present application is compared with the decoding method shown in FIG. 3. When the number of transmission bits is the same, the decoding method 1400 under the non-finite field of the embodiment of the present application has a lower decoding delay than the decoding method shown in FIG. 3. Among them, the letter A in FIG. 16 indicates the performance effect of the decoding method shown in FIG. 3, and the letter B in FIG. 16 indicates the performance effect of the decoding method 1400 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 a non-finite field and the decoding method 1400 under a non-finite field can be a receiving device, such as a decoder in the receiving device, or other modules capable of implementing a decoding function. In the embodiment of the present application, the receiving device is taken as an example for introduction.

The method provided by the embodiment of the present application is described in detail above in conjunction with Figures 5 to 16. The communication device for executing the method provided by the embodiment of the present application is described in detail below in conjunction with Figures 17 to 18.

For example, Fig. 17 is a schematic diagram of the structure of a communication device provided in an embodiment of the present application. As shown in Fig. 17, a communication device 1700 includes: a processing module 1701 and a transceiver module 1702. For ease of description, Fig. 17 only shows the main components of the communication device 1700.

In some embodiments, the communication device 1700 may be applicable to the communication system shown in FIG. 1 to perform the functions of the receiving device in the method shown in FIG. 5 (or FIG. 7 , or FIG. 9 ).

Processing module 1701 is used to obtain signal probability distribution and a first set, wherein the first set is used to determine the position of each bit to be restored in the coded sequence, 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= ²ⁿ , and n is a positive integer.

The processing module 1701 is further configured to determine X Nth candidate paths according to the signal probability distribution and the first set. Each candidate path in the X Nth candidate paths indicates the value of each position in the coded sequence, one or more to-be-recovered bits of different candidate paths in the X Nth candidate paths correspond to different values, X is a positive integer greater than 1 and less than or equal to M, each to-be-recovered bit in the coded sequence corresponds to at most M candidate values, the M candidate values are values determined by the receiving device, and M is a positive integer greater than 1.

The processing module 1701 is further configured to determine a decoding result according to the X Nth candidate paths.

In one possible design, the processing module 1701 is configured to determine X Nth candidate paths according to the signal probability distribution and the first set, including:

The processing module 1701 is used to determine Yi,k i-th candidate paths according to the signal probability distribution, the first set and the k-th i-1 candidate path among Yi _-1 i-1 candidate paths when the _i- th position is a to-be-restored position; each _{i-1 candidate path among the Yi-1} i-1 candidate paths indicates the value of the first i-1 position in the coded sequence, and different _{i-1 candidate paths among the Yi-1} i-1 candidate paths have different values of one or more to-be-restored positions; each i-th candidate path among the Yi _,k i-th candidate paths indicates the value of the first i positions in the coded sequence, the value of the first i-1 position indicated by each i-th candidate path among the Yi _{,k i-th} candidate paths is the same as the value of the first i-1 position indicated by the k-th i-1 candidate path, and the values corresponding to the i-th position of different candidate paths among the Yi _{,k i} -th candidate paths are different, i is a positive integer greater than 1 and less than or equal to N, k is a positive integer less than or equal to _Yi-1 , and Y _i-1 is a positive integer less than or equal to M.

Processing module 1701 is used to determine X N _- th candidate paths according to Yi _,k th candidate paths corresponding to each i-1 th candidate path in Yi-1 th candidate paths when i is equal to N; or, when i is less than N, determine X N _- th candidate paths according to the signal probability distribution, the first set and Yi _,k th candidate paths corresponding to each i-1 th candidate path in Yi-1 th candidate paths.

In a possible design, the processing module 1701 is used to determine X N-th candidate paths according to Yi _,k i-th candidate paths corresponding to each i-1-th candidate path in Yi _-1 i-1-th candidate paths, including: when a first condition is met, determining that Yi _{,k i} -th candidate paths corresponding to each i- ₁ -th candidate path in Yi-1 i-1-th candidate paths all belong to the X N-th candidate paths. The first condition includes: the total number of i-th candidate paths is less than or equal to M.

In one possible design, the processing module 1701 is configured to determine X N-th candidate paths according to Yi _,k i-th candidate paths corresponding to each i-1-th candidate path in Yi _-1 i-1-th candidate paths, including: when the second condition is met, according to the path metric PM value of each i-th candidate path, determine X N-th candidate paths from Yi _,k i-th candidate paths corresponding to each i-1-th candidate path in Yi _-1 i-1-th candidate paths. The second condition includes: the total number of i-th candidate paths is greater than M.

PM(k+m,i)＝PM(k,i-1)+lnP(yi _,m |yi _-1,k ,…,y1 _,k )

The processing module 1701 is used to determine the pth jth candidate path according to the signal probability distribution, the first set and the pth i-1th candidate path in Y _j-1 j-1th candidate paths when the jth position is a transmission bit; each j-1th candidate path in Y _j-1 j-1th candidate paths indicates the value of the first j-1 positions in the encoded sequence, and different j-1th candidate paths in Y _j-1 j-1th candidate paths have different values of one or more to-be-recovered bits; the pth jth candidate path indicates the value of the first j positions in the encoded sequence, the value of the first j-1 position indicated by the pth j-1th candidate path is the same as the value of the first j-1 position indicated by the pth j-1th candidate path, and is the same as the value corresponding to the jth position of the jth candidate path corresponding to different p, j is a positive integer greater than 1 and less than or equal to N, p is a positive integer less than or equal to Y _j-1 , and Y _j-1 is a positive integer less than or equal to M.

The processing module 1701 is used to determine X N-th candidate paths according to the j-th candidate path corresponding to each j-1-th candidate path in Y _j-1 j-1-th candidate paths when j is equal to N; or, when j is less than N, determine X N-th candidate paths according to the signal probability distribution, the first set and the j-th candidate path corresponding to each j-1-th candidate path in Y _j- 1 j-1-th candidate paths.

In one possible design, the PM value of the p-th j-th candidate path satisfies:

PM(p,j)＝PM(p,j-1)+lnP(y _j |y _j-1,p ,…,y _1,p )

Wherein, PM(p,j) represents the PM value of the p-th j-th candidate path, PM(p,j-1) represents the PM value of the p-th j-1-th candidate path among Y _j-1 -th j-1-th candidate paths, the p-th j-1-th candidate path among Y _j-1 -th j-1-th candidate paths indicates that the values of the first i-1 positions in the encoded sequence are y _j-1,p ,…,y _1,p , lnP(y _j |y j- _1,p ,…,y _1,p ) represents the natural logarithm of (y _j |y _j-1,p ,…,y _1,p ), and P(y _j |y _j-1,p ,…,y _1,p ) represents the probability that the value of the j-th position is y j when the p-th _j -th candidate path indicates that the values of the first j-1 positions in the encoded sequence are y _j-1,p ,…,y _1,p .

In one possible design, when the encoded sequence includes at least one transmission bit, the processing module 1701 is further used to obtain a first sequence. The first sequence includes the value of each transmission bit in the at least one transmission bit. For example, the processing module 1701 obtains the first sequence from the transceiver module 1702.

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

Optionally, the communication device 1700 may further include a storage module (not shown in FIG. 17 ), which stores a program or instruction. When the processing module 1701 executes the program or instruction, the communication device 1700 may perform the function of the receiving device in the method shown in any one of FIG. 5 (or FIG. 7 , or FIG. 9 ).

In some other embodiments, the communication device 1700 may be applicable to the communication system shown in FIG. 1 to perform the functions of the receiving device in the method shown in FIG. 14 .

The processing module 1701 is used to determine L sub-blocks corresponding to the coded sequence according to the distribution of transmission bits and/or bits to be restored in the coded sequence, wherein 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= ²ⁿ , and n and L are positive integers.

The processing module 1701 is further configured to use the L _i _th matrix corresponding to the L i th sub-block among the L sub-blocks to perform a matrix operation on the L _i th sub-block to obtain a decoding sequence of the L _i th sub-block. Wherein, i is a positive integer less than or equal to L, the number of rows and columns of the L _{i th} matrix is determined according to the number of positions in the encoded sequence corresponding to the L _i th sub-block, and the elements of the L _{i th} matrix are determined according to the butterfly operation corresponding to the L _i th sub-block.

The processing module 1701 is further configured to determine a decoding result according to a decoding sequence of each sub-block in the L sub-blocks.

In one possible design, the L _{i th} matrix is an M×M matrix, where M is the number of positions in the encoded sequence corresponding to the L _i th sub-block.

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

Optionally, the communication device 1700 may further include a storage module (not shown in FIG. 17 ) storing a program or instruction. When the processing module 1701 executes the program or instruction, the communication device 1700 may perform the function of the receiving device in the method shown in FIG. 14 .

Optionally, the transceiver module 1702 may include a receiving module and a sending module (not shown in FIG. 17 ). The transceiver module 1702 is used to implement the sending function and the receiving function of the communication device 1700 .

It should be understood that the processing module 1701 involved in the communication device 1700 can be implemented by a processor or a processor-related circuit component, which can be a processor or a processing unit; the transceiver module 1702 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 1700 can be a receiving device, or a chip (system) or other parts or components that can be set in the receiving device, or a device that includes a receiving device, which is not limited in the present application.

In addition, the technical effects of the communication device 1700 can refer to the technical effects of the method shown in any one of Figures 5, 7, 9, or 14, and will not be repeated here.

Exemplarily, FIG18 is a second schematic diagram of the structure 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 can be set in the receiving device. As shown in FIG18, the communication device 1800 may include a processor 1801. Optionally, the communication device 1800 may also include a memory 1802 and/or a transceiver 1803. The processor 1801 is coupled to the memory 1802 and the transceiver 1803, such as being connected via a communication bus.

Next, the components of the communication device 1800 are specifically described in conjunction with FIG. 18 :

The processor 1801 is the control center of the communication device 1800, which can be a processor or a general term for multiple processing elements. For example, the processor 1801 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 1801 may perform various functions of the communication device 1800 by running or executing a software program stored in the memory 1802 , and calling data stored in the memory 1802 .

In a specific implementation, as an embodiment, the processor 1801 may include one or more CPUs, such as CPU0 and CPU1 shown in FIG. 18 .

In a specific implementation, as an embodiment, the communication device 1800 may also include multiple processors, such as the processor 1801 and the processor 1804 shown in FIG. 18. 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 1802 is used to store the software program for executing the solution of the present application, and the execution is controlled by the processor 1801. The specific implementation method can refer to the above method embodiment and will not be repeated here.

Optionally, the memory 1802 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 1802 may be integrated with the processor 1801, or may exist independently and be coupled to the processor 1801 through an interface circuit (not shown in FIG. 18 ) of the communication device 1800, which is not specifically limited in the embodiments of the present application.

The transceiver 1803 is used for communication with other communication devices. For example, the communication device 1800 is a receiving device, and the transceiver 1803 can be used to communicate with a transmitting device. For another example, the communication device 1800 is a transmitting device, and the transceiver 1803 can be used to communicate with a receiving device.

Optionally, the transceiver 1803 may include a receiver and a transmitter (not shown separately in FIG. 18 ), wherein the receiver is used to implement a receiving function, and the transmitter is used to implement a sending function.

Optionally, the transceiver 1803 may be integrated with the processor 1801, or may exist independently and be coupled to the processor 1801 via an interface circuit (not shown in FIG. 18 ) of the communication device 1800 , which is not specifically limited in the embodiments of the present application.

It is easy to understand that the structure of the communication device 1800 shown in FIG. 18 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 1800 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 "more than one" 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:

Acquire a signal probability distribution and a first set; the first set is used to determine the position of each to-be-recovered bit in the coded sequence, the coded sequence is a sequence after the to-be-coded sequence is coded, the length of the to-be-coded sequence is N, N=2 n , and n is a positive integer;

Determine X Nth candidate paths according to the signal probability distribution and the first set; each candidate path in the X Nth candidate paths indicates a value of each position in the encoded sequence, one or more to-be-recovered bits of different candidate paths in the X Nth candidate paths correspond to different values, X is a positive integer greater than 1 and less than or equal to M, each to-be-recovered bit in the encoded sequence corresponds to at most M candidate values, the M candidate values are values determined by the receiving device, and M is a positive integer greater than 1;

A decoding result is determined according to the X Nth candidate paths.
The method according to claim 1, wherein determining X Nth candidate paths according to the signal probability distribution and the first set comprises:

In the case where the i-th position is a bit to be restored, Yi ,k i -th candidate paths are determined according to the signal probability distribution, the first set and the k-th i-1 candidate path among Yi -1 i-1 candidate paths; each i-1 candidate path among the Yi -1 i-1 candidate paths indicates the value of the first i-1 position in the encoded sequence, and different i-1 candidate paths among the Yi -1 i-1 candidate paths have different values of one or more bits to be restored; each i-th candidate path among the Yi ,k i -th candidate paths indicates the value of the first i positions in the encoded sequence, the value of the first i-1 position indicated by each i-th candidate path among the Yi ,k i-th candidate paths is the same as the value of the first i-1 position indicated by the k-th i-1 candidate path, and the values corresponding to the i-th position of different candidate paths among the Yi ,k i -th candidate paths are different, i is a positive integer greater than 1 and less than or equal to N, k is a positive integer less than or equal to Yi-1 , and Y i-1 is a positive integer less than or equal to M;

When i is equal to N, the X Nth candidate paths are determined according to the Yi ,k i-th candidate paths corresponding to each i-1th candidate path in the Yi- 1 i-1th candidate paths; or, when i is less than N, the X Nth candidate paths are determined according to the signal probability distribution, the first set and the Yi ,k i -th candidate paths corresponding to each i-1th candidate path in the Yi- 1 i-1th candidate paths.
The method according to claim 2, characterized in that the determining the X Nth candidate paths according to the Yi ,k i -th candidate paths corresponding to each i-1th candidate path in the Yi- 1 i-1th candidate paths comprises:

When the first condition is met, determine that the Y i,k i-th candidate paths corresponding to each i-1-th candidate path in the Y i - 1 i-1-th candidate paths all belong to the X N-th candidate paths;

The first condition includes: the total number of the i-th candidate paths is less than or equal to M.
The method according to claim 2, characterized in that the determining the X Nth candidate paths according to the Yi ,k i -th candidate paths corresponding to each i-1th candidate path in the Yi- 1 i-1th candidate paths comprises:

When the second condition is met, the X Nth candidate paths are determined from the Yi ,k i-th candidate paths corresponding to each i - 1th candidate path in the Yi-1 i-1th candidate paths according to the path metric PM value of each i-th candidate path; wherein the second condition includes: the total number of the i-th candidate paths is greater than M.
The method according to any one of claims 2 to 4, characterized in that the PM value of the mth i-th candidate path determined based on the kth i-1th candidate path satisfies:

PM(k+m,i)＝PM(k,i-1)+lnP(yi ,m |yi -1,k ,…,y1 ,k )

wherein PM(k+m,i) represents the PM value of the mth i-th candidate path determined based on the kth i-1th candidate path, PM(k,i-1) represents the PM value of the kth i-1th candidate path, the kth i-1th candidate path indicates that the values of the first i-1 positions in the encoded sequence are y i-1,k ,…,y 1,k , lnP(y i,m |y i-1,k ,…,y 1,k ) represents the natural logarithm of P(y i,m |y i-1,k ,…,y 1 ,k ), P(y i,m |y i-1,k ,…,y 1,k ) represents the probability that the value of the i-th position is y i,m when the Mth i-th candidate path indicates that the value of the first i-1 positions in the encoded sequence is y i-1,k ,…,y 1,k , and the value of the i-th position in the encoded sequence is y The probability of i,m is one of the conditional probability distributions of the i-th position, and is the m-th probability in the conditional probability distribution of the i-th position arranged in descending order.
The method according to any one of claims 2 to 5 is characterized in that the PM value of the first candidate path is determined based on the conditional probability distribution of the first position in the encoded sequence.
The method according to any one of claims 1 to 6, characterized in that

The conditional probability distribution of the s-th position in the encoded sequence is discrete, and the discrete conditional probability distribution includes K 1 values of the s-th position and the probability of occurrence of each of the K 1 values, where K 1 is a positive integer; or,

The conditional probability distribution of the s-th position in the encoded sequence is continuous, and the continuous conditional probability distribution includes K 2 peak points, each of the K 2 peak points indicates a value of the s-th position and the probability of occurrence of the value, and K 2 is a positive integer; or,

The conditional probability distribution of the s-th position in the encoded sequence is continuous, and the continuous conditional probability distribution includes K 3 reference points in the first confidence interval, each of the K 3 reference points indicates a value of the s-th position and a probability of occurrence of the value, and K 3 is a positive integer;

Wherein, s is a positive integer less than or equal to N.
The method according to any one of claims 1 to 7, characterized in that the step of determining X Nth candidate paths according to the signal probability distribution and the first set comprises:

In the case where the j-th position is a transmission bit, a p-th j-th candidate path is determined according to the signal probability distribution, the first set, and the p-th i-1-th candidate path among Y j -1 j-1-th candidate paths; each j-1-th candidate path among the Y j - 1 j-1-th candidate paths indicates the value of the first j-1 positions in the encoded sequence, and different j-1-th candidate paths among the Y j-1 j-1-th candidate paths have different values of one or more bits to be restored; the p-th j-th candidate paths indicate the values of the first j positions in the encoded sequence, the value of the first j-1 position indicated by the p-th j-th candidate path is the same as the value of the first j-1 position indicated by the p-th j-1 candidate path, and is the same as the value corresponding to the j-th position of the j-th candidate paths corresponding to different p, j is a positive integer greater than 1 and less than or equal to N, p is a positive integer less than or equal to Y j-1 , and Y j-1 is a positive integer less than or equal to M;

When j is equal to N, the X Nth candidate paths are determined according to the jth candidate path corresponding to each j-1th candidate path in the Y j-1 j-1th candidate paths; or, when j is less than N, the X Nth candidate paths are determined according to the signal probability distribution, the first set and the jth candidate path corresponding to each j-1th candidate path in the Y j-1 j-1th candidate paths.
The method according to claim 8, characterized in that the PM value of the p-th j-th candidate path satisfies:

PM(p,j)＝PM(p,j-1)+lnP(y j |y j-1,p ,…,y 1,p )

Among them, PM(p,j) represents the PM value of the p-th j-th candidate path, PM(p,j-1) represents the PM value of the p-th j-1-th candidate path among the Y j-1 -th j-1-th candidate paths, the p-th j-1-th candidate path among the Y j -1 -th j-1-th candidate paths indicates that the values of the first i-1 positions in the encoded sequence are y j-1,p ,…,y 1,p , lnP(y j |y j-1,p ,…,y 1,p ) represents the natural logarithm of (y j |y j-1,p ,…,y 1,p ), and P(y j |y j-1,p ,…,y 1,p ) represents the probability that the value of the j-th position is y j when the p-th j -th candidate path indicates that the values of the first j-1 positions in the encoded sequence are y j-1,p ,…,y 1,p .
The method according to any one of claims 1 to 9, characterized in that, when the encoded sequence includes at least one transmission bit, the method further comprises:

A first sequence is obtained; the first sequence includes a value of each transmission bit in the at least one transmission bit.
The method according to any one of claims 1 to 10, characterized in that the decoding result is a real number sequence.
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 1-11.
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 1-11.
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 1-11 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 11.