Low-complexity multiple access channel coding and decoding method based on sparse regression code

Abstract

The invention discloses a low-complexity multiple access channel coding and decoding method based on sparse regression codes. The method comprises the following steps: determining codebook parameters and generating a dictionary matrix; wherein the codebook parameters comprise a code length, a code rate, the number of dictionary matrix regions, the number of columns in each region of a dictionary matrix and codebook power; respective to-be-transmitted information of the users is obtained through a sending end, the to-be-transmitted information is coded according to the dictionary matrix, and a coding result is obtained and transmitted through a channel; acquiring a receiving signal through a receiving end, wherein the receiving signal is the superposition of coding results of different users and channel noise; determining a decoding scheme according to the codebook power difference of different users, and decoding the received signal according to the decoding scheme to obtain a decoding result; wherein the decoding scheme comprises a joint decoding scheme and a continuous interference cancellation decoding scheme.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communication multi - access encoding and decoding, and particularly relates to a low - complexity multi - access channel encoding and decoding method based on sparse regression codes. Background Art

[0002] Multiple access technology is a key technology in wireless communication systems. Non - orthogonal multiple access (NOMA) technology supports multiple users to transmit signals in a superimposed manner on the same resources, and has technical advantages such as improving spectral efficiency and device access capabilities, reducing device power consumption and network transmission delay, and improving network transmission reliability. It has a wide range of applications in fields such as mobile communication and the Internet of Things. The uplink of NOMA is modeled by a multiple access channel (MAC). Multiple users simultaneously send data to a common receiver, and the receiver needs to correctly decode the information sent by each user from the received signal.

[0003] At the same time, non - orthogonal multiple access technology can improve system capacity and spectral efficiency without increasing spectral resources, and is suitable for scenarios such as high - density user Internet of Things in 5G and future communication systems. However, non - orthogonal multiple access technology is often implemented through relatively complex schemes. At the same time, in mobile communication, the user terminal is a small handheld device with limited available resources, and can only support communication system implementation schemes with relatively low complexity. Therefore, there is currently a lack of a multi - access channel encoding and decoding scheme with low complexity and good performance. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide a low - complexity multi - access channel encoding and decoding method based on sparse regression codes, which is used to solve the problem of lacking a multi - access channel encoding and decoding scheme with low complexity and good performance under the condition of limited available resources.

[0005] To achieve the above - mentioned purpose, the present invention provides a low - complexity multi - access channel encoding and decoding method based on sparse regression codes, including the following steps:

[0006] Determine the codebook parameters and generate a dictionary matrix; wherein, the codebook parameters include: code length, code rate, number of dictionary matrix regions, number of columns in each region of the dictionary matrix, and codebook power;

[0007] The transmitting end obtains the respective information to be transmitted by the users, encodes the information to be transmitted according to the dictionary matrix, obtains the encoding result and transmits it through the channel;

[0008] The receiving end obtains the received signal, and the received signal is the superposition of the encoding results of different users and channel noise;

[0009] Determine a decoding scheme based on the codebook power difference between two users, and decode the received signal according to the decoding scheme to obtain a decoding result;

[0010] Among them, the decoding schemes include: a joint decoding scheme and a successive interference cancellation (SIC) decoding scheme.

[0011] As an embodiment of the present invention, encoding the information to be transmitted according to a dictionary matrix, obtaining an encoding result and transmitting it through a channel, including:

[0012] Map the obtained transmission information to an information vector β, and encode the information vector through a dictionary matrix A to obtain an encoding result x, as follows:

[0013] x = Aβ

[0014] Transmit the encoding result through the channel.

[0015] As an embodiment of the present invention, obtaining a received signal through a receiving end, where the received signal is a superposition of the encoding results of different users and channel noise, including:

[0016] Obtain a received signal through a receiving end, as follows:

[0017] y = x1 + x2 + z

[0018] Among them, y is the received signal, x1 is the encoding result of the first user, x2 is the encoding result of the second user, and z is the channel noise.

[0019] As an embodiment of the present invention, determine a decoding scheme based on the codebook power difference between two users, and decode the received signal according to the decoding scheme to obtain a decoding result, including:

[0020] Judge whether the difference between the codebook powers of the two users is less than a preset value; if it is less, decode the received signal through a joint decoding scheme to obtain a decoding result;

[0021] If it is not less, decode the received signal through an SIC decoding scheme to obtain a decoding result.

[0022] As an embodiment of the present invention, decode the received signal through a joint decoding scheme to obtain a decoding result, including:

[0023] Horizontally splice the dictionary matrices of the two users into a spliced dictionary matrix;

[0024] Decode the received signal according to the spliced dictionary matrix and a decoding function to obtain the decoding results of the two users, as follows:

[0025]

[0026] Among them, is the decoding result of the first user, is the decoding result of the second user, g AMP () is the decoding function, A1 is the dictionary matrix of the first user, A2 is the dictionary matrix of the second user, info 1,2 is the signal parameter information, and y is the received signal.

[0027] As an embodiment of the present invention, the received signal is decoded by the SIC decoding scheme to obtain the decoding result, including:

[0028] Decode the received signal according to the decoding function and the dictionary matrix of the first user to obtain the decoding result of the first user As shown below:

[0029]

[0030] Among them, info1 is the signal parameter information of the first user, y is the received signal, A1 is the dictionary matrix of the first user, g AMP () is the decoding function, is the decoding result of the first user;

[0031] Encode based on the decoding result of the first user to obtain a new encoding result As shown below:

[0032]

[0033] Subtract the new encoding result from the received signal to obtain the decoded signal, and decode the decoded signal through the dictionary matrix and decoding function of the second user to obtain the decoding result of the second user As shown below:

[0034]

[0035] Among them, info2 is the signal parameter information of the second user, and A2 is the dictionary matrix of the second user.

[0036] As an embodiment of the present invention, the process of the decoding function includes:

[0037] A1: Initialization Among them, P z channel noise power, P x is the codebook power;

[0038] A2: Calculate x t+1 , x t+1The calculation formula is as follows:

[0039]

[0040] Among them, the size of U is M×L, where M is the number of columns in each area of the dictionary matrix, and L is the number of areas of the dictionary matrix;

[0041] A3: Calculate and store The calculation formula is as follows:

[0042]

[0043] A4: Let t = t + 1, and repeat the above steps A2 - A3 until τ t -τ t+1 < 0.005, and obtain the iteration number T = t + 1;

[0044] A5: Initialize t = 0, v -1 = 0, β 0 = 0;

[0045] A6: Calculate v t , v t The calculation formula is as follows:

[0046]

[0047] A7: Calculate The calculation formula is as follows:

[0048]

[0049]

[0050] Among them, j ∈ sec(l) means j ∈ {(l - 1)M + 1, …, lM};

[0051] A8: Let t = t + 1, and repeat the above steps A6 - A7 until t = T;

[0052] A9: For the L areas of β T+1 , rewrite the largest element in each area as Rewrite other elements as 0. Output β T+1 , which is the decoding result.

[0053] The beneficial effects of the present invention are as follows: The codebook design of the present invention does not depend on the channel noise distribution and has a certain robustness; the present invention maintains the advantages of sparse regression codes in the multiple access channel and can achieve good communication performance with low computational resource overhead and time resource overhead; it solves the problem of lacking a multiple access channel encoding and decoding scheme with low implementation complexity and good performance under the condition of limited available resources; at the same time, two decoding schemes are designed based on the decoding function, effectively reducing the decoding computational complexity and being applicable to different situations of the codebook power difference at the sending end.

[0054] Other advantages, objectives and features of the present invention will be described in the following specification, and to some extent, they are obvious to those skilled in the art, or those skilled in the art can obtain teachings from the practice of the present invention. The objectives and other advantages of the present invention can be achieved and obtained through the following specification. Brief Description of the Drawings

[0055] In order to make the objectives, technical solutions and beneficial effects of the present invention clearer, the present invention provides the following drawings for description:

[0056] Figure 1 It is a flow diagram of the present invention;

[0057] Figure 2 It is an algorithm flow diagram of the decoding function of the present invention;

[0058] Figure 3 It is a performance comparison of the encoding and decoding scheme of the present invention under different distributed noises;

[0059] Figure 4 It is a performance comparison of the joint decoding scheme when there are different codebook power gaps in the present invention;

[0060] Figure 5 It is a performance comparison of the SIC decoding scheme when there are different codebook power gaps in the present invention;

[0061] Figure 6 It is a performance comparison of the joint decoding scheme and the SIC decoding scheme when there are different codebook power gaps in the present invention;

[0062] Figure 7 It is a comparison between the encoding and decoding scheme of the present invention and the theoretically optimal decoding scheme. Detailed Embodiments

[0063] As Figures 1 to 2 shown, the present invention provides a low-complexity multiple access channel encoding and decoding method based on sparse regression codes, including the following steps:

[0064] Determine the codebook parameters and generate the dictionary matrix; wherein, the codebook parameters include: code length, code rate, number of dictionary matrix regions, number of columns in each region of the dictionary matrix, and codebook power.

[0065] The transmitting end obtains the information to be transmitted by each user, encodes the information to be transmitted according to the dictionary matrix, obtains the encoding result and transmits it through the channel.

[0066] The receiving end obtains the received signal, and the received signal is the superposition of the encoding results of different users and channel noise.

[0067] Determine the decoding scheme according to the codebook power difference between two users, and decode the received signal according to the decoding scheme to obtain the decoding result.

[0068] Wherein, the decoding schemes include: joint decoding scheme and SIC decoding scheme.

[0069] The working principle of the above technical solution: When performing multiple access, the transmitting end obtains the information to be transmitted by two users. The two users at the transmitting end respectively select different dictionary matrices generated according to the sparse regression code, encode the transmission information to obtain the encoding result and send it into the channel for transmission. At the same time, what the receiving end receives is the superposition of the encoding results sent by the two users and channel noise. When decoding, two decoding schemes, namely the joint decoding scheme and the SIC decoding scheme, are designed based on the decoding function. The joint decoding scheme is to horizontally splice the dictionary matrices of the two users as a new dictionary matrix, and use the decoding function to decode to obtain the decoding results of the transmission information of the two users. SIC decoding is to first regard the codeword of user 2 as noise, use the decoding function to decode to obtain the decoding result of the first user, then encode this decoding result, subtract this encoding result from the received signal, and finally use the decoding function to decode to obtain the decoding result of the second user. Among them, the codebook parameters are determined while determining the dictionary matrix for encoding; when selecting the decoding scheme, it is selected according to the codebook power in the encoding parameters.

[0070] Specifically, the codebook parameters include: code length, code rate, number of dictionary matrix regions, number of columns in each region of the dictionary matrix, and codebook power. Among them, when designing the codebook, the size of the dictionary matrix A in SPARC is n×ML, where n is the code length, and M and L satisfy M L = 2 nR , that is, the total number of codewords is M L ; the size of the information vector β is ML×1, which can be regarded as divided into L regions, each region has M elements, and only one element in each region is non-zero, and the value of the non-zero element is where P xis the codebook power of user x; each element in A independently follows a Gaussian distribution with a mean of 0 and a variance of 1 / n. The codeword x is generated by multiplying the dictionary matrix A with the information vector β, i.e., x = Aβ. The set of all codewords that can be generated by the same dictionary matrix is the codebook N corresponding to this dictionary matrix;

[0071] Advantages of the above technical solution: Through the above technical solution, the codebook design of the present invention does not depend on the channel noise distribution and has a certain robustness; the present invention maintains the advantages of sparse regression codes in the multiple access channel and can achieve good communication performance with low computational resource overhead and time resource overhead; it solves the problem of lacking a multiple access channel encoding and decoding scheme with low implementation complexity and good performance under limited available resources; at the same time, based on the decoding function, two decoding schemes are designed to effectively reduce the decoding computational complexity and are applicable to different situations of the codebook power difference at the sending end.

[0072] In one embodiment, encoding the information to be transmitted according to the dictionary matrix, obtaining the encoding result and transmitting it through the channel, including:

[0073] Mapping the obtained transmission information to the information vector β, and encoding the information vector through the dictionary matrix A to obtain the encoding result x, as follows:

[0074] x = Aβ

[0075] Transmitting the encoding result through the channel;

[0076] Obtaining the received signal at the receiving end, where the received signal is the superposition of the encoding results of different users and the channel noise, including:

[0077] Obtaining the received signal at the receiving end, as follows:

[0078] y = x1 + x2 + z

[0079] where y is the received signal, x1 is the encoding result of the first user, x2 is the encoding result of the second user, and z is the channel noise;

[0080] Working principle and advantages of the above technical solution: The first user and the second user respectively map the information to be transmitted to the information vectors β1 and β2 and perform encoding to obtain the encoding results x1 = A1β1 and x2 = A2β2; then the encoding results are sent into the channel for transmission, and the signal received at the receiving end is y = x1 + x2 + z, where z represents the channel noise.

[0081] In one embodiment, determining the decoding scheme according to the codebook power gap between two users, and decoding the received signal according to the decoding scheme to obtain the decoding result, including:

[0082] Determine whether the difference in the codebook powers of two users is less than a preset value; if it is less, decode the received signal through a joint decoding scheme to obtain a decoding result;

[0083] If it is not less, decode the received signal through a SIC decoding scheme to obtain a decoding result.

[0084] The working principle and beneficial effects of the above technical solution: After receiving the signal, select an appropriate decoding scheme according to the difference in the codebook powers of the two users; when the codebook powers of the two users are relatively close, select the joint decoding scheme, and when there is a significant difference in the codebook powers of the two users, select the SIC decoding scheme; both decoding schemes are designed based on the Approximate Message Passing (AMP) algorithm.

[0085] In one embodiment, decoding the received signal through a joint decoding scheme to obtain a decoding result includes:

[0086] Horizontally splice the dictionary matrices of the two users into a spliced dictionary matrix;

[0087] Decode the received signal according to the spliced dictionary matrix and the decoding function to obtain the decoding results of the two users, as follows:

[0088]

[0089] Among them, is the decoding result of the first user, is the decoding result of the second user, g AMP () is the decoding function, A1 is the dictionary matrix of the first user, A2 is the dictionary matrix of the second user, info 1,2 is the signal parameter information, and y is the received signal;

[0090] The working principle and beneficial effects of the above technical solution: Horizontally splice the dictionary matrices of the two users into a new dictionary matrix, that is, the spliced dictionary matrix, and directly obtain the decoding results of the two users by running the decoding function.

[0091] In one embodiment, decoding the received signal through a SIC decoding scheme to obtain a decoding result includes:

[0092] Decode the received signal according to the decoding function and the dictionary matrix of the first user to obtain the decoding result of the first user as follows:

[0093]

[0094] Among them, info1 is the signal parameter information of the first user, y is the received signal, A1 is the dictionary matrix of the first user, and g AMP () is the decoding function, is the decoding result of the first user;

[0095] Encode based on the decoding result of the first user to obtain a new encoding result as follows:

[0096]

[0097] Subtract the new encoding result from the received signal to obtain the decoded signal, and decode the decoded signal through the dictionary matrix and decoding function of the second user to obtain the decoding result of the second user as follows:

[0098]

[0099] Among them, info2 is the signal parameter information of the second user, and A2 is the dictionary matrix of the second user;

[0100] The working principle and beneficial effects of the above technical solution: First, regard the codeword of the second user in the received signal as noise, run the decoding function to obtain the decoding result of the first user; then encode the decoding result of the first user to obtain a new encoding result, subtract the new encoding result from the received signal as the decoded signal, and run the decoding function to obtain the decoding result of the second user.

[0101] In one embodiment, the process of the decoding function includes:

[0102] A1: Initialization Among them, P z channel noise power, P x is the codebook power;

[0103] A2: Calculate x t+1 , x t+1 The calculation formula of is as follows:

[0104]

[0105] Among them, the size of U is M×L, M is the number of columns in each area of the dictionary matrix, and L is the number of areas of the dictionary matrix;

[0106] A3: Calculate and store The calculation formula of is as follows:

[0107]

[0108] A4: Let t = t + 1, and repeat the above steps A2 - A3 until τ t -τt+1 <0.005, the number of iterations \(T=t + 1\) is obtained;

[0109] A5: Initialize \(t = 0\), \(v\) -1 \(= 0\), \(\beta\) 0 \(= 0\);

[0110] A6: Calculate \(v\) t , \(v\) t The calculation formula is as follows:

[0111]

[0112] A7: Calculate The calculation formula is as follows:

[0113]

[0114] where \(j\in\sec(l)\) means \(j\in\{(l - 1)M+1,\cdots,lM\}\);

[0115] A8: Let \(t=t + 1\), and repeat the above steps A6 - A7 until \(t = T\);

[0116] A9: For the \(L\) regions of \(\beta\) T+1 , rewrite the largest element in each region as Rewrite other elements as 0. Output \(\beta\) T+1 , which is the decoding result.

[0117] The working principle and beneficial effects of the above technology: The decoding function is the AMP decoding algorithm, which generates a series of sequence estimates for the received signal \(y\), and obtains the decoding result through simple calculations.

[0118] In one embodiment, as Figure 3 shown, Figure 3 shows the comparison of the error decoding probability after adding different distributions of noise using the coding method proposed in the present invention under the condition that the codebook power \(P1 = 4\), \(P2 = 2\), and the joint decoding scheme is selected. The codebook parameters are \(L1 = 64\), \(L2 = 48\), \(M = 32\), \(n = 1638\). The abscissa is the overall signal-to-noise ratio (SNR), and the calculation method is \((P1 + P2) / P\) z . The ordinate is the joint block error rate (JBLER). When It is considered as correct decoding when [condition], otherwise it is decoding error. During simulation, the number of repetitions for each point is 10,000 times, and the result shown in the graph line is the probability of decoding error among 10,000 times. Gaussian distribution noise, uniform distribution noise, and Laplace noise are respectively selected as channel noise, and other factors such as the noise mean, power, and all codebook parameters are the same during the simulation of the three channels. The results show that the JBLER hardly changes after adding different noises, and the communication performance is basically the same. Thus, it can be seen that the encoding and decoding scheme of the present invention has good robustness and has the same excellent communication performance for different channels.

[0119] As Figure 4 shown, Figure 4 shows the comparison of the incorrect decoding probability of the joint decoding scheme proposed by the present invention when keeping the sum of the two-user codebook powers P1 + P2 unchanged and changing the specific values of P1 and P2 to change their difference. The values of the codebook powers P1 and P2 are as marked in the figure. The codebook parameters are L1 = 64, L2 = 48, M = 32, n = 1638, and the channel noise is Gaussian distribution noise. The abscissa is the overall SNR, and the calculation method is (P1 + P2) / P z . The ordinate is the JBLER. When [condition] it is considered as correct decoding, otherwise it is decoding error. During simulation, the number of repetitions for each point is 10,000 times, and the result shown in the graph line is the probability of decoding error among 10,000 times. The results show that as the difference between the two-user codebook powers decreases, the JBLER gradually decreases and the communication performance improves. Therefore, the closer the two-user codebook powers are, the better the performance of the joint decoding scheme.

[0120] As Figure 5 shown, Figure 5 shows the comparison of the incorrect decoding probability of the SIC decoding scheme proposed by the present invention when keeping the sum of the two-user codebook powers P1 + P2 unchanged and changing the specific values of P1 and P2 to change their difference. The values of the codebook powers P1 and P2 are as marked in the figure. The codebook parameters are L1 = 64, L2 = 48, M = 32, n = 1638, and the channel noise is Gaussian distribution noise. The abscissa is the overall SNR, and the calculation method is (P1 + P2) / P z . The ordinate is the JBLER. When [condition] it is considered as correct decoding, otherwise it is decoding error. During simulation, the number of repetitions for each point is 10,000 times, and the result shown in the graph line is the probability of decoding error among 10,000 times. The results show that as the difference between the two-user codebook powers increases, the system BLER gradually decreases and the communication performance improves. Therefore, when the difference between the two-user codebook powers is more obvious, the SIC decoding scheme preferentially decodes the user with higher power, and the overall performance is better.

[0121] As Figure 6 shown, Figure 6 ComprehensivelyFigure 4 and Figure 5 The results show that, while keeping the sum of the powers of the two user codebooks \(P1 + P2\) unchanged and changing the specific values of \(P1\) and \(P2\) to change their difference, the comparison of the error decoding probabilities between the joint decoding scheme and the SIC decoding scheme proposed by the present invention is presented. The solid line represents joint decoding, and the dashed line represents SIC decoding. The simulation parameters and the meanings of the coordinate axes are the same as those of Figure 4 Figure 5 the same. The results show that when the powers of the two user codebooks are relatively close, as shown by curves ②⑤ or ③⑥, the performance of the joint decoding scheme is better than that of SIC decoding; when there is a significant difference in the powers of the two user codebooks, as shown by curves ①④, the performance of the SIC decoding scheme is better than that of joint decoding. In summary, when the powers of the two user codebooks are relatively close, the joint decoding scheme has better performance, and when there is a significant difference in the powers of the two user codebooks, the SIC decoding scheme has better performance.

[0122] As Figure 7 shown Figure 7 shows the comparison of the error decoding probabilities between the theoretically optimal decoding scheme and the joint decoding scheme proposed by the present invention while keeping the two-user coding design unchanged. The theoretically optimal decoding scheme traverses all combinations of codewords in the two user codebooks, and the result with the minimum Euclidean distance from the received signal is the decoding result. The expression is The codebook powers are \(P1 = 4\) and \(P2 = 2\). The codebook parameters are \(L1 = 6\), \(L2 = 4\), and \(M = 4\). The channel noise is Gaussian distributed noise with a noise power of \(P\) z = 6. The abscissa is the ratio of the total code rate to the total channel capacity \(C\), where the left ordinate is the JBLER, which is correct decoding when and incorrect decoding otherwise. The number of repetitions at each point during simulation is 10,000 times, and the results shown in the curves are the probabilities of decoding errors in 10,000 times. The right ordinate is the simulation time, representing the total running time of each point simulation. The solid line in the figure corresponds to the left ordinate, representing the communication performance; the dashed line in the figure corresponds to the right ordinate, representing the computational complexity. The results show that the JBLER of the joint decoding scheme proposed by the present invention is higher than that of the theoretically optimal decoding scheme, but the curves are relatively close and the performance difference is not significant; the running time of the joint decoding scheme proposed by the present invention is significantly lower than that of the theoretically optimal decoding scheme, with a difference of about two orders of magnitude, and the time gap will further increase when choosing larger codebook parameters. The running time of the theoretically optimal decoding scheme is too long to be applied in practical systems. In summary, the decoding scheme proposed by the present invention and the theoretically optimal decoding scheme have similar performance, but the operation overhead and time overhead are significantly reduced, and it has a low computational complexity.

[0123] Finally, it should be noted that the above preferred embodiments are only used to illustrate the technical solutions of the present invention rather than to limit them. Although the present invention has been described in detail through the above preferred embodiments, those skilled in the art should understand that various changes can be made in form and details without departing from the scope defined by the claims of the present invention.

Claims

1. A low-complexity multi-access channel encoding and decoding method based on sparse regression codes, characterized in that It includes the following steps: Determine the codebook parameters and generate a dictionary matrix; wherein, the codebook parameters include: code length, code rate, number of dictionary matrix regions, number of columns in each region of the dictionary matrix, and codebook power; The transmitting end obtains the information to be transmitted by each user, encodes the information to be transmitted according to the dictionary matrix, obtains the encoding result, and transmits it through the channel; The receiving end obtains the received signal, and the received signal is the superposition of the encoding results of different users and channel noise; Determine the decoding scheme according to the codebook power difference between two users, and decode the received signal according to the decoding scheme to obtain the decoding result; Wherein, the decoding scheme includes: joint decoding scheme and successive interference cancellation decoding scheme.

2. The low-complexity multiple access channel encoding and decoding method based on sparse regression code according to claim 1, characterized in that Encoding the information to be transmitted according to the dictionary matrix, obtaining the encoding result, and transmitting it through the channel, includes: Map the obtained transmission information to an information vector β, and encode the information vector through the dictionary matrix A to obtain the encoding result x, as follows: x = Aβ Transmit the encoding result through the channel.

3. The low-complexity multiple access channel encoding and decoding method based on sparse regression code according to claim 1, characterized in that The receiving end obtains the received signal, and the received signal is the superposition of the encoding results of different users and channel noise, includes: The receiving end obtains the received signal, as follows: y = x1 + x2 + z Wherein, y is the received signal, x1 is the encoding result of the first user, x2 is the encoding result of the second user, and z is the channel noise.

4. The low-complexity multiple access channel encoding and decoding method based on sparse regression code according to claim 1, characterized in that Determine the decoding scheme according to the codebook power difference between two users, and decode the received signal according to the decoding scheme to obtain the decoding result, includes: Judge whether the difference between the codebook powers of two users is less than a preset value; if less, decode the received signal through the joint decoding scheme to obtain the decoding result; If not less, decode the received signal through the successive interference cancellation decoding scheme to obtain the decoding result.

5. The low-complexity multiple access channel encoding and decoding method based on sparse regression code according to claim 4, characterized in that Decode the received signal through the joint decoding scheme to obtain the decoding result, includes: Horizontally splice the dictionary matrices of two users into a spliced dictionary matrix; Decode the received signal according to the spliced dictionary matrix and the decoding function to obtain the decoding results of two users, as follows: Among them, is the decoding result of the first user, is the decoding result of the second user, g AMP ( ) is the decoding function, A1 is the dictionary matrix of the first user, A2 is the dictionary matrix of the second user, info 1，2 is the signal parameter information, and y is the received signal.

6. The low-complexity multiple access channel encoding and decoding method based on sparse regression code according to claim 4, characterized in that Decode the received signal through the successive interference cancellation decoding scheme to obtain the decoding result, includes: Decode the received signal according to the decoding function and the dictionary matrix of the first user to obtain the decoding result of the first user As follows: Among them, info1 is the signal parameter information of the first user, y is the received signal, A1 is the dictionary matrix of the first user, and g AMP ( ) is the decoding function, is the decoding result of the first user; Encoding is performed based on the decoding result of the first user to obtain a new encoding result As follows: The decoded signal is obtained by subtracting the newly encoded result from the received signal, and the decoded signal is decoded through the dictionary matrix and decoding function of the second user to obtain the decoding result of the second user as follows: Wherein, info2 is the signal parameter information of the second user, and A2 is the dictionary matrix of the second user.

7. The low-complexity multiple access channel encoding and decoding method based on sparse regression code according to claim 4, characterized in that The process of the decoding function includes: A1: Initialize the iteration number \(t = 0\), the state evolution variable where \(P\) z is the channel noise power, and \(P\) x is the codebook power; A2: Calculate the intermediate variable x t+1 , x t+1 The calculation formula is as follows: Among them, the size of the estimation matrix U is M×L, denotes the element in the j-th row and the 1st column of the matrix. All elements in U independently follow a Gaussian distribution with a mean of 0 and a variance of 1; M is the number of columns in each region of the dictionary matrix, L is the number of regions of the dictionary matrix, n is the code length, and P xl represents the power allocation of the codebook in the 1st region, generally taking A3: Calculate and store The calculation formula is as follows: A4: Let \(t = t + 1\), and repeat the above steps A2 - A3 until \(\tau\) t -\(\tau\) t+1 \(< 0.005\), to obtain the number of iterations \(T=t + 1\); A5: Initialize t = 0, v -1 = 0, β 0 = 0; where v is the decoding intermediate variable, α is the decoding estimation result, and the superscript represents the number of iterative calculation rounds; A6: Calculate v t , v t The calculation formula is as follows: A7: Calculation The calculation formula is as follows: where \(j\in\sec(l)\) means \(j\in\{(l - 1)M+1,\cdots,lM\}\), \(A\) H represents the transpose of matrix \(A\), \(\eta(\cdot)\) is an estimation function, represents the \(i\)-th bit of the calculation result of the \(t\)-th round of iteration, \(s\) j is the \(j\)-th bit of the input vector \(s\) of the estimation function, A8: Let t = t + 1, and repeat the above steps A6 - A7 until t = T; A9: For the L regions of β T+1 rewrite the largest element in each region as and rewrite the other elements as 0. Output β T+1 , which is the decoding result.

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