Based on GF(5) m Overload Finite Field Multiple Access Method and System for Orthogonal Additive Inverse Pair Codes

Abstract

Based on GF(5) m This invention relates to an overload finite-field multiple access method and system based on orthogonal additive inverse pairs of codes, belonging to the field of 6G communication and multiple access technology. It solves the problem of limited code length for multiple users caused by the traditional non-orthogonal multiple access method of "channel coding first, then multiple access" in overloaded multi-user access scenarios. It also addresses the limitations of bit error rate performance under high spectral efficiency conditions and the difficulty in simultaneously achieving high spectral density, high reliability, and low complexity in multi-user separation. The transmitting end of this invention uses orthogonal additive inverse pairs of GF(5) to map the bits of multiple users into finite-field symbols, which are then encoded by the system's linear block code and modulated into a 5QAM signal for transmission. The receiving end uses parity check segments to enhance the distinguishability of information segment symbols, calculates the initial posterior probability using different mapping rules, and then iteratively decodes using a base-sum algorithm, achieving signal separation under overload conditions without complex multi-user detection. This invention is applied in the field of communication.

Description

Technical Field

[0001] This invention belongs to the field of 6G communication and multiple access technology. Background Technology

[0002] In modern wireless communication systems, non-orthogonal multiple access (NOA) technology is a key means to improve spectrum efficiency and support massive connectivity. With the increasing demands of 5G-Advanced and 6G networks for ultra-high data rates, ultra-low latency, and massive connectivity, achieving efficient and reliable access for multiple users under limited spectrum resources has become a core research issue. Traditional NOA schemes, such as Power Domain NOMA (PD-NOMA), Sparse Code Multiple Access (SCMA), and Pattern Partition Multiple Access (PDMA), typically follow a "channel coding first, then multi-user multiplexing" processing architecture. In this architecture, channel coding for each user is performed independently, and then multi-user signal multiplexing is achieved through power domain or code domain superposition. However, this architecture faces an inherent limitation: the limited code length for multiple users. Since multiplexing occurs after coding, the actual effective codeword length available to each user is limited by the size of their dedicated time-frequency resource block. In short data packet transmission scenarios, the effective code length for a single user is short, resulting in insufficient error correction capability of channel coding and limited system error rate performance. This problem is particularly prominent when the number of users increases.

[0003] To overcome the aforementioned limitations, the Finite Domain Multiple Access (FFMA) framework has been proposed in recent years. FFMA reverses the traditional "coding" and "multiplexing" processing order, directly placing multi-user multiplexing within a finite domain. This allows the superimposed signals from multiple users to naturally form a structured long codeword at the physical layer, effectively solving the problem of finite code length for multi-user applications. In the FFMA architecture, element pairs (EPs) are used as virtual resources to directly separate users within the finite domain. The algebraic structure of the EPs determines the system's overload capacity and performance characteristics. Current research has focused on... and The corresponding EP code was constructed. Among them, based on... The FFMA system is a basic orthogonal multiple access system with limited improvement in spectral efficiency; based on While additive inverse pair codes achieve non-orthogonal overload transmission, their relatively simple ternary finite field algebraic structure leaves room for further improvement in terms of user overload rate and error performance. Theoretically, as the order of the finite field increases... As the number of uniquely decodable AI-EPs that satisfy the uniqueness and pattern mapping (USPM) properties increases, the number of such AI-EPs can be increased, providing richer multi-user multiplexing resources. Especially when... hour, Two AI-EPs that meet the USPM criteria are provided, which can be extended to... Available Supports more than [number] degrees of freedom Overload transmission for individual users offers significant spectral efficiency advantages.

[0004] However, based on The design of orthogonal AI-EP codes faces the following two challenges. First, the complexity of codeword construction and modulation mapping: how to... AI-EP extended to Furthermore, constructing a structured generator matrix ensures that multi-user EP allocation maintains orthogonality while achieving flexible overload. Designing the mapping function from finite field symbols to complex field constellation points, facilitating the extraction of soft information from the superimposed signals' statistical characteristics at the receiver, directly impacts system feasibility and performance upper bounds. Secondly, the design of a low-complexity decoding algorithm at the receiver is crucial: in overloaded FFMA systems, the superposition of multi-user signals leads to a sharp increase in the cardinality of the complex field and the pattern at the receiver, particularly in the parity check section where the number of superimposed constellation points reaches a significant level. Accurately calculating the posterior probability of each finite field symbol requires efficient statistical decomposition methods; furthermore, for... LDPC codewords constructed above, traditional The check node update complexity of the QSPA algorithm is as high as [missing information]. ,exist When the number of users is large or the number of users is large, it is difficult to apply in practice. Therefore, it is necessary to design an improved decoding algorithm that can significantly reduce the complexity.

[0005] In summary, how to address the limitations of finite code length for multiple users caused by the traditional non-orthogonal multiple access (NOA) approach of "channel coding first, then multiple access" in overloaded multi-user access scenarios, as well as the issues of limited error performance under high spectral efficiency conditions and the difficulty in simultaneously achieving high overload, high reliability, and low complexity multi-user separation, remains to be addressed. Summary of the Invention

[0006] The purpose of this invention is to address the limitations of traditional non-orthogonal multiple access (NOA) methods in overloaded multi-user access scenarios. These NOA methods, characterized by "channel coding first, then multiple access," suffer from finite code length constraints, limited error performance under high spectral efficiency conditions, and difficulty in simultaneously achieving high spectral density, high reliability, and low complexity in multi-user separation. This invention provides a method based on GF(5)... m An overloaded finite field multiple access method and system for orthogonal additive inverse pair codes, wherein GF(5) m ) is constructed based on the finite field GF(5). Extended domain.

[0007] Based on GF(5) m Overloaded finite field multiple access methods for orthogonal additive inverse pair codes include:

[0008] Sending end processing:

[0009] Using finite fields Orthogonal additive inverse pairs, for The original binary bit sequence of each user is encoded using multi-user access coding to obtain the finite field symbol sequence of each user.

[0010] Using the definition in a finite field The system linear block code generator matrix is ​​used to extend the finite field symbol sequences of each user to an order of [order missing]. Channel coding is used to generate codeword sequences for each user;

[0011] Perform a mapping transformation from finite field symbols to 5QAM constellation points on each finite field symbol in the codeword sequence of J users to obtain a modulated complex signal sequence, and then perform power allocation on the modulated complex signal sequence;

[0012] The modulated complex signal sequence after power allocation is accessed and transmitted through the Gaussian multiple access channel;

[0013] Receiver processing procedure:

[0014] After performing complex domain superposition on the received modulated complex signal sequence, the resulting superimposed complex signal sequence is divided into an information segment and a parity check segment.

[0015] Perform the first type of mapping from complex field pattern to finite field pattern on each superimposed complex signal in the information segment to obtain the finite field symbol corresponding to each superimposed complex signal in the information segment, and calculate the initial posterior probability of the finite field symbol corresponding to each superimposed complex signal.

[0016] Calculate the real part likelihood probability and the imaginary part likelihood probability of each superimposed complex signal within the parity check segment;

[0017] Perform a second type of mapping from complex field pattern to finite field pattern on each superimposed complex signal within the parity check segment to obtain the finite field symbol corresponding to each superimposed complex signal in the parity check segment.

[0018] Calculate the initial posterior probability of the finite field symbol based on the real and imaginary likelihood probabilities of all superimposed complex signals corresponding to the same finite field symbol within the parity check segment.

[0019] use The base-sum algorithm iteratively decodes the initial posterior probabilities of each finite field symbol to obtain the decoded finite field symbol. It is a prime number;

[0020] Recovering the sequence formed by all decoded finite field symbols The original binary bit sequence of each user.

[0021] Preferably, the orthogonal additive inverse pairs of the finite field GF(5) are used to... The implementation methods for multi-user access coding of the original binary bit sequence of each user include:

[0022] Phase for obtaining the finite field symbol subsequence for each user:

[0023] Will The users are numbered sequentially according to the access order predetermined by the sender. The number of users to the number One user, The number is even; and users are paired up according to a predetermined access order, resulting in a total of [number missing]. The first user pair, and the second The user pairs are numbered odd-numbered. User and even number are The number of users constitutes, For the user, assign a number, and ;

[0024] The two fundamental additive inverse pairs contained in the orthogonal additive inverse pairs of the finite field GF(5) are respectively and ;in, and These are the first and second basic additive inverse pairs, respectively. These represent the finite field symbols for the elements in the finite field GF(5) that take values ​​from 0 to 4;

[0025] The basic additive inverse pair Users with odd-numbered IDs are assigned using basic additive inverse pairs. The original binary bit sequences of each odd-numbered user are mapped to finite field symbol sequences, thus obtaining finite field symbol subsequences for each odd-numbered user; the mapping rule is: the binary bits in the original binary bit sequence are mapped... "Mapped to finite field symbol" The binary bits in the original binary bit sequence are " "Mapped to finite field symbol" ;

[0026] The basic additive inverse pair Assigned to users with even numbers, through basic additive inverse pairs The original binary bit sequences of even-numbered users are mapped to finite field symbol sequences, thus obtaining finite field symbol subsequences for even-numbered users; the mapping rule is: the binary bits in the original binary bit sequence are mapped... "Mapped to finite field symbol" The binary bits in the original binary bit sequence are " "Mapped to finite field symbol" ;

[0027] The stage of obtaining the finite field symbol sequence for each user:

[0028] Set the length of the original binary bit sequence for each user to be... The length of the finite field symbol subsequence for each user After expansion, the sequence length is obtained as follows: A user-defined finite field symbol sequence.

[0029] Preferably, the sequence length is The structure of each user's finite field symbol sequence is as follows:

[0030] No. The finite field symbol subsequences corresponding to each user in a pair of users are distributed in a length of The first in the sequence The segment, and the first to the second finite field symbol subsequence corresponding to the user. Each finite field symbol is located in a field of length . The first in the sequence Position 1 to 2 There are positions, with a length of . All other positions in the sequence are finite field symbols. ; where the length is The sequence is divided into The paragraphs are from paragraph 1 to paragraph 2. part.

[0031] Preferably, it is defined in a finite field System linear block code generator matrix The expression is:

[0032] ;

[0033] in, for Unit array, for Dense matrix, and Each element is a finite field Finite field notation, For the parity check sign number, For matrix The total number of columns.

[0034] Preferably, the implementation method for mapping the first complex domain pattern to the finite domain pattern for each superimposed complex signal within the information segment is as follows:

[0035] The complex domain patterns corresponding to the superimposed complex signals within the information segment constitute the set of complex domain patterns. Any complex field pattern in the diagram;

[0036] The first mapping rule from complex field patterns to finite field patterns is as follows:

[0037] ;

[0038] in, To map complex signals to finite field symbols, Let represent the finite field symbols for the elements in the finite field GF(5) that take values ​​from 0 to 4. It is the imaginary unit.

[0039] Preferably, within the information segment, the calculation of the first... The initial posterior probability of the finite field symbol corresponding to the superimposed complex signal is realized as follows:

[0040] ;

[0041] ;

[0042] ;

[0043] ;

[0044] in, The first information segment A superimposed complex signal Corresponding finite field symbol , , and The initial posterior probability at time , It is an integer. Finite field symbol The values ​​that the corresponding elements can take. , For information segment power allocation factor, The average transmit power, For noise power spectral density, For the value to be The complex field diagram corresponding to the finite field symbol. to They are finite field symbols The complex domain pattern of the corresponding superimposed complex signal; , , and , It is the imaginary unit.

[0045] Preferably, the implementation method for calculating the real part likelihood probability and imaginary part likelihood probability of each superimposed complex signal within the parity check segment is as follows:

[0046] The maximum likelihood estimation method is used to estimate the probability of the real and imaginary parts of each superimposed complex signal in the parity check segment, so as to obtain the real and imaginary part likelihood probabilities of each superimposed complex signal.

[0047] Preferably, the second mapping rule from complex field patterns to finite field patterns is as follows:

[0048] Calculate the real and imaginary parts of the superimposed complex signals within the parity check segment. The result is modulo 5, and the remainder is used as the element value of the corresponding finite field symbol in the finite field GF(5), thus obtaining the finite field symbol of the element under that value; where, and These are the real and imaginary parts of any superimposed complex signal within the parity check segment.

[0049] Preferably, the sequence formed by all decoded finite field symbols is used to recover the... The implementation of the original binary bit sequence for each user is as follows:

[0050] The decoded finite field symbol sequence is decoded using the inverse operation of multi-user access coding to recover the... The original binary bit sequence of each user.

[0051] Based on GF(5) m An overloaded finite-field multiple access system for orthogonal additive inverse pair codes, comprising a storage device, a processor, and a computer program stored in the storage device and executable on the processor, wherein the processor executes the computer program to implement the GF(5)-based system described above. m An overloaded finite field multiple access method for orthogonal additive inverse pair codes.

[0052] The beneficial effects of this invention are:

[0053] 1. This invention utilizes two fundamental additive inverse pairs in the finite field GF(5) to... Multi-user access encoding is performed on the binary bit sequences of each user, and the resulting finite field symbol subsequence is expanded to a length of... A finite-field symbol sequence is generated, allowing different users to occupy different orthogonal positions within the finite-field symbol sequence. Each user's finite-field symbol sequence can then be channel-coded to construct their own codeword sequence. This enables a process of multi-user access coding followed by channel coding. The finite-field symbol sequence used in this method for multi-user access coding typically has a length greater than or equal to the binary bit sequence, thus alleviating the limitation on finite code length caused by the short user bit sequence in traditional non-orthogonal multiple access systems.

[0054] 2. This invention will Users are sequentially numbered according to a pre-determined access order from the sender, and each pair of users is divided into user pairs according to the pre-determined access order. Within each user pair, users with odd numbers obtain a finite field symbol subsequence using a first pair of basic additive inverses, while users with even numbers obtain a finite field symbol subsequence using a second pair of basic additive inverses. Subsequently, the finite field symbol subsequences of each user are expanded into user finite field symbol sequences of length JK / 2, and the... In each user pair, the finite field symbol subsequences corresponding to each user are distributed in the sequence of length JK / 2. Segments. Therefore, each segment in an information segment corresponds to a user pair, that is, the segment corresponds to a finite field symbol subsequence of two users, rather than a finite field symbol subsequence of only one user; different user pairs are distributed in different segments. Through the above method, the present invention can... Complete in each segment Multi-user access coding for individual users enables two users to share a segment to complete the access, thereby achieving overloaded multi-user access and carrying more users' binary bit sequences under the same segment number conditions, thus improving the system's spectral efficiency.

[0055] 3. This invention alleviates the limitation of limited code length for multiple users caused by the short user bit sequence in traditional non-orthogonal multiple access, which leads to the limitation of channel coding length. Under the conditions of the same number of users, the same number of transmitted bits, and the same spectral efficiency, this scheme can use channel coding to construct a longer codeword sequence. According to coding theory, a longer codeword sequence can usually improve error performance, that is, achieve higher reliability.

[0056] 4. This invention is applicable to low-complexity applications. The base-sum algorithm iteratively decodes the initial posterior probabilities of each finite field symbol in the information segment and parity check segment to obtain the decoded finite field symbol, and then recovers it using the inverse operation of multi-user access coding. The original binary bit sequence of each user enables reliable multi-user separation. Attached Figure Description

[0057] Figure 1 This invention is based on GF(5) m A schematic diagram illustrating the principle of the overloaded finite field multiple access method for orthogonal additive inverse pair codes.

[0058] Figure 2 This is a comparison chart of the bit error rate performance of the Finite Domain Multiple Access Method (FFMA) described in this invention and the traditional Power Domain Non-Orthogonal Multiple Access Method (PD-NOMA). Figure 3 This is a comparison chart of the bit error rate performance of the Finite Field Multiple Access Method (FFMA) described in this invention and the traditional Sparse Code Field Multiple Access Method (SCMA). Here, "about" indicates approximately.

[0059] Figure 4 When the total number of users is 6, the finite field symbol subsequence mapped by each user in the information segment has a length of Expand to length A schematic diagram of the construction of a user-defined finite field symbol sequence. Detailed Implementation

[0060] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0061] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0062] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but this is not intended to limit the scope of the invention.

[0063] Specific Implementation Method 1: Combination Figure 1 This embodiment describes a method based on GF(5). m Overloaded finite field multiple access methods for orthogonal additive inverse pair codes include:

[0064] (a) Processing procedure at the sending end:

[0065] Using finite fields The orthogonal additive inverse pair of ) The original binary bit sequence of each user is encoded using multi-user access coding to obtain the finite field symbol sequence of each user.

[0066] Using the definition in a finite field The system linear block code generator matrix is ​​used to extend the finite field symbol sequences of each user to an order of [order missing]. Channel coding is used to generate codeword sequences for each user;

[0067] right Each finite field symbol in the codeword sequence of a user undergoes a mapping transformation from finite field symbol to 5QAM constellation points to obtain a modulated complex signal sequence, and power allocation is performed on the modulated complex signal sequence; specifically,

[0068] The mapping transformation rule from finite field symbols to 5QAM constellation points is as follows:

[0069] ;

[0070] in, To map a finite field to a complex signal;

[0071] The modulated complex signal sequence after power allocation is accessed and transmitted through the Gaussian multiple access channel;

[0072] (II) Receiving end processing procedure:

[0073] After performing complex domain superposition on the received modulated complex signal sequence, the resulting superimposed complex signal sequence is divided into an information segment and a parity check segment.

[0074] Perform the first type of mapping from complex field pattern to finite field pattern on each superimposed complex signal in the information segment to obtain the finite field symbol corresponding to each superimposed complex signal in the information segment, and calculate the initial posterior probability of the finite field symbol corresponding to each superimposed complex signal.

[0075] Calculate the real part likelihood probability and the imaginary part likelihood probability of each superimposed complex signal within the parity check segment;

[0076] Perform a second type of mapping from complex field pattern to finite field pattern on each superimposed complex signal within the parity check segment to obtain the finite field symbol corresponding to each superimposed complex signal in the parity check segment;

[0077] Calculate the initial posterior probability of the finite field symbol based on the real and imaginary likelihood probabilities of all superimposed complex signals corresponding to the same finite field symbol within the parity check segment.

[0078] use The base-sum algorithm iteratively decodes the initial posterior probabilities of each finite field symbol to obtain the decoded finite field symbol. It is a prime number;

[0079] Recovering the sequence formed by all decoded finite field symbols The original binary bit sequence of each user.

[0080] This invention employs a joint design of the transmitting and receiving ends. The transmitting end utilizes orthogonal additive inverse pairs of the finite field GF(5) to perform multi-user access coding on the binary bits of multiple users, mapping each user's bits to a finite field symbol. Subsequently, a systematic linear block code defined on GF(5) is used to process the symbol sequences of each user. The extended-domain channel coding generates codeword sequences for each user, which are then mapped to 5QAM constellation points and transmitted through a Gaussian multiple access channel. At the receiver, the superimposed complex signal is divided into an information segment and a parity check segment. For the information segment, the first mapping from the complex domain to the finite domain is used, and the initial posterior probability is calculated. For the parity check segment, the real and imaginary likelihood probabilities are calculated, and the second mapping rule is used to obtain the initial posterior probability of the finite domain symbols. Finally, the... The radix sum-product algorithm iteratively decodes the initial posterior probabilities of all symbols. This process utilizes the additional constraints provided by the parity check segment to enhance the probabilistic distinguishability of information segment symbols, enabling the separation of user signals without complex multi-user detection under overload conditions, thereby maintaining low complexity and high reliability with high spectral efficiency.

[0081] Furthermore, the implementation methods for multi-user access coding of the original binary bit sequences of J users using orthogonal additive inverse pairs of the finite field GF(5) include:

[0082] Phase for obtaining the finite field symbol subsequence for each user:

[0083] Will The users are numbered sequentially according to the access order predetermined by the sender. The number of users to the number One user, The number is even; and users are paired up according to a predetermined access order, resulting in a total of [number missing]. The first user pair, and the second The user pairs are numbered odd-numbered. User and even number are The number of users constitutes, For the user, assign a number, and ;

[0084] The two fundamental additive inverse pairs contained in the orthogonal additive inverse pairs of the finite field GF(5) are respectively and ;in, and These are the first and second basic additive inverse pairs, respectively. These represent the finite field symbols for the elements in the finite field GF(5) that take values ​​from 0 to 4;

[0085] The basic additive inverse pair Users with odd-numbered IDs are assigned using basic additive inverse pairs. The original binary bit sequences of each odd-numbered user are mapped to finite field symbol sequences, thus obtaining finite field symbol subsequences for each odd-numbered user; the mapping rule is: the binary bits in the original binary bit sequence are mapped... "Mapped to finite field symbol" The binary bits in the original binary bit sequence are " "Mapped to finite field symbol" ;

[0086] The basic additive inverse pair Assigned to users with even numbers, through basic additive inverse pairs The original binary bit sequences of even-numbered users are mapped to finite field symbol sequences, thus obtaining finite field symbol subsequences for even-numbered users; the mapping rule is: the binary bits in the original binary bit sequence are mapped... "Mapped to finite field symbol" The binary bits in the original binary bit sequence are " "Mapped to finite field symbol" ;

[0087] The stage of obtaining the finite field symbol sequence for each user:

[0088] Set the length of the original binary bit sequence for each user to be... The length of the finite field symbol subsequence for each user After expansion, the sequence length is obtained as follows: A user-defined finite field symbol sequence;

[0089] See Figure 4 The sequence length is The structure of each user's finite field symbol sequence is as follows:

[0090] No. The finite field symbol subsequences corresponding to each user in a pair of users are distributed in a length of The first in the sequence The segment, and the first to the second finite field symbol subsequence corresponding to the user. Each finite field symbol is located in a field of length . The first in the sequence Position 1 to 2 There are positions, with a length of . All other positions in the sequence are finite field symbols. ; where the length is The sequence is divided into The paragraphs are from paragraph 1 to paragraph 2. part.

[0091] In this preferred embodiment, a specific implementation method for multi-user access coding is specified, which will Users are numbered according to their access order and divided into user pairs. Two basic additive inverse pairs are assigned to odd-numbered users and even-numbered users, respectively. The mapping rules from binary bits to finite field symbols are defined, and the length of the finite field symbol subsequence for each user is extended to... Furthermore, it is stipulated that the finite field symbol subsequences of each user in each user pair are distributed in a length of Within the corresponding segment of the sequence, the remaining positions are filled with finite field symbols. This approach ensures that symbols from different users occupy orthogonal time-domain positions in the sequence, guaranteeing the separability of the finite-field symbol sequences for each user. At the same time, length extension provides a unified sequence structure for subsequent channel coding, thereby reducing the complexity of user separation at the receiver while supporting multi-user overload access.

[0092] Furthermore, defined in a finite field System linear block code generator matrix The expression is:

[0093] ;

[0094] in, for Unit array, for Dense matrix, and Each element is a finite field Finite field notation, For the parity check sign number, For matrix The total number of columns.

[0095] In this preferred embodiment, the generator matrix of the system linear block code is defined as a combination of an identity matrix and a dense matrix, such that the encoded codeword sequence contains an information segment and a parity check segment. This structure is effective in the finite field GF(5). m The system provides redundant check information for each user's finite field symbol sequence. The receiver can use the parity check segment to perform probability constraints and error correction on the information segment, thereby improving decoding reliability under finite code length conditions and reducing the impact of inter-user interference caused by high overload superposition on bit error rate performance.

[0096] Furthermore, the implementation method for mapping the first type of complex domain pattern to finite domain pattern for each superimposed complex signal within the information segment is as follows:

[0097] The complex domain patterns corresponding to the superimposed complex signals within the information segment constitute the set of complex domain patterns. Any complex field pattern in the diagram;

[0098] The first mapping rule from complex field patterns to finite field patterns is as follows:

[0099] ;

[0100] in, To map complex signals to finite field symbols, Let represent the finite field symbols for the elements in the finite field GF(5) that take values ​​from 0 to 4. It is the imaginary unit.

[0101] In this preferred embodiment, a one-to-one mapping rule is established between the complex field pattern corresponding to the superimposed complex signal within the specified information segment and the five finite field symbols in the finite field GF(5). This mapping relationship enables the receiver to extract the initial probability information of each symbol in the finite field from the superimposed signal in the complex field, providing accurate input posterior probabilities for subsequent iterative decoding, thereby achieving effective separation of multi-user symbols under overload conditions.

[0102] Preferably, within the information segment, the calculation of the first... The initial posterior probability of the finite field symbol corresponding to the superimposed complex signal is realized as follows:

[0103] ;

[0104] ;

[0105] ;

[0106] ;

[0107] in, The first information segment A superimposed complex signal Corresponding finite field symbol , , and The initial posterior probability at time , It is an integer. Finite field symbol The values ​​that the corresponding elements can take. , For information segment power allocation factor, The average transmit power, For noise power spectral density, For the value to be The complex field diagram corresponding to the finite field symbol. to They are finite field symbols The complex domain pattern of the corresponding superimposed complex signal, and , , and , It is the imaginary unit.

[0108] This preferred embodiment provides a formula for calculating the initial posterior probability of finite-field symbols corresponding to the superimposed complex signals within an information segment. It clarifies the specific method for calculating the posterior probability of each finite-field symbol using parameters such as the complex-field pattern, power allocation factor, average transmit power, and noise power spectral density. This calculation provides a probability measure for the values ​​of five finite-field symbols for each superimposed complex signal, enabling the receiver to quantize the observations in the complex field into soft information in the finite field, thus facilitating subsequent utilization... The hexadecimal sum-product algorithm provides a probabilistic input basis for iterative decoding, thereby supporting reliable separation of multi-user symbols under high overload superposition conditions. Number bases and product algorithms are existing technologies.

[0109] Furthermore, the implementation method for calculating the real part likelihood probability and imaginary part likelihood probability of each superimposed complex signal within the parity check segment is as follows:

[0110] The maximum likelihood estimation method is used to estimate the probability of the real and imaginary parts of each superimposed complex signal in the parity check segment, so as to obtain the real and imaginary part likelihood probabilities of each superimposed complex signal.

[0111] In this preferred embodiment, the real and imaginary likelihood probabilities of each superimposed complex signal within the parity check segment are calculated using the maximum likelihood estimation method, providing a statistical estimation-based probability acquisition method for the parity check segment. This method enables the receiver to independently extract the real and imaginary likelihood information from the complex signal of the parity check segment, providing probability input for subsequently obtaining the initial posterior probability of the finite field symbol through the second mapping rule. This enhances the decoding reliability of the information segment symbol by utilizing the redundancy constraints of the parity check segment.

[0112] Furthermore, the second mapping rule from complex field patterns to finite field patterns is as follows:

[0113] Calculate the real and imaginary parts of the superimposed complex signals within the parity check segment. The result is modulo 5, and the remainder is used as the element value of the corresponding finite field symbol in the finite field GF(5), thus obtaining the finite field symbol of the element under that value; where, and These are the real and imaginary parts of any superimposed complex signal within the parity check segment.

[0114] In this preferred embodiment, a second mapping rule for complex field patterns to finite field patterns is specified. Specifically, the remainder is obtained by adding the real and imaginary parts of the superimposed complex signal within the parity check segment, taking the modulo 5, and using this remainder as the element value of the corresponding finite field symbol in the finite field GF(5). This provides a definite mapping method from complex signals to finite field symbols for the parity check segment. This mapping allows the receiver to directly obtain the corresponding finite field symbol using the complex signal of the parity check segment, thus providing a basis for calculating the initial posterior probability of each finite field symbol within the parity check segment. Furthermore, the accuracy of iterative decoding is improved by leveraging the coding constraint relationship between the parity check segment and the information segment.

[0115] Furthermore, the sequence formed by all decoded finite field symbols is used to recover the... The implementation of the original binary bit sequence for each user is as follows:

[0116] The decoded finite field symbol sequence is decoded using the inverse operation of multi-user access coding to recover the... The original binary bit sequence of each user.

[0117] Specific Implementation Method Two: The GF(5)-based implementation method described in this embodiment m An overloaded finite-field multiple access system for orthogonal additive inverse pair codes includes a storage device, a processor, and a computer program stored in the storage device and executable on the processor. The processor executes the computer program to implement the GF(5)-based system described in Specific Embodiment 1. m An overloaded finite field multiple access method for orthogonal additive inverse pair codes.

[0118] Simulation verification and effect comparison:

[0119] This embodiment verifies the technical effectiveness of the proposed solution through simulation experiments. The verification metric is BER, or Bit Error Probability, calculated as the total number of erroneous binary bits divided by the total number of binary bits transmitted by the user. Simulation conditions are set as follows: two channel coding schemes are defined in... The non-binary LDPC codes (i.e., non-binary low-density parity-check codes) are denoted as follows: and That is, non-binary LDPC code 1 and non-binary LDPC code 2. Among them, From binary LDPC code Expand to The effective spectral efficiency is obtained. Bit / Symbol; To be directly in The design above LDPC codes have an effective spectral efficiency of Bit / symbol.

[0120] The comparison objects include the traditional sparse code domain multiple access method (SCMA), the traditional power domain non-orthogonal multiple access method (PD-NOMA), and the finite domain multiple access method (FFMA) described in this invention.

[0121] Experiment 1: Performance comparison between the Finite Domain Multiple Access Method (FFMA) described in this invention and the traditional Power Domain Non-Orthogonal Multiple Access Method (PD-NOMA).

[0122] Set the number of users Number of available time slot resources Fixed multi-user transmission bits The spectral efficiency is 1.68.

[0123] Figure 2 The figure shows a comparison curve of the bit error rate (BER) performance of FFMA and PD-NOMA of the present invention. Figure 2 As can be seen, the method of this invention outperforms PD-NOMA under all user configurations tested. Specifically, when the BER is... At that time, for The bit noise power ratio required by the method of the present invention It is about 3.0 dB lower than PD-NOMA, among which, For power per bit, This represents the noise power spectral density.

[0124] for and The gains are approximately 2.4 dB and 1.6 dB, respectively. This indicates that the solution of the present invention has significant performance advantages under overload scenarios.

[0125] Experiment 2: Performance comparison between the Finite Field Multiple Access Method (FFMA) described in this invention and the traditional Sparse Code Field Multiple Access Method (SCMA).

[0126] Set the number of users We will examine two configurations.

[0127] First configuration: Transmitted bits Number of available time slot resources Total bit load The spectral efficiency is 1.5.

[0128] Traditional sparse code domain multiple access methods (SCMA) do not employ channel coding, while the finite field multiple access method (FFMA) of this invention employs code coding. To maintain an effective spectral efficiency of 1.68. Simulation results ( Figure 3 This indicates that, at the target BER of At that time, the solution of the present invention is about 5.5dB better than the uncoded SCMA.

[0129] Second configuration: FFMA settings of this invention Number of available time slot resources With an effective spectral efficiency of 1.68, it uses LDPC codes. SCMA settings , The spectral efficiency is 1.26, and it uses binary LDPC code, i.e., binary low-density parity-check code, denoted as . That is, binary LDPC code 1, both with a code rate of 0.84. Simulation results ( Figure 3 The data shows that although the proposed solution has a loss of approximately 1.2 dB before decoding convergence, due to its fast convergence speed, the BER is significantly reduced. It immediately exhibits a gain of 0.1dB, and at a BER of The gain is increased to 0.65dB.

[0130] The above simulation results fully demonstrate the effectiveness of the GF(5)-based method proposed in this invention. m The overloaded finite field multiple access method of orthogonal additive inverse pair codes outperforms the traditional PD-NOMA and SCMA methods in terms of both spectral efficiency and bit error rate performance.

[0131] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. Based on GF(5) m The overloaded finite field multiple access method for orthogonal additive inverse pair codes is characterized by, include: Sending end processing: Using finite fields Orthogonal additive inverse pairs, for The original binary bit sequence of each user is encoded using multi-user access coding to obtain the finite field symbol sequence of each user. Using the definition in a finite field The system linear block code generator matrix is ​​used to extend the finite field symbol sequences of each user to an order of [order missing]. Channel coding is used to generate codeword sequences for each user; Perform a mapping transformation from finite field symbols to 5QAM constellation points on each finite field symbol in the codeword sequence of J users to obtain a modulated complex signal sequence, and then perform power allocation on the modulated complex signal sequence; The modulated complex signal sequence after power allocation is accessed and transmitted through the Gaussian multiple access channel; Receiver processing procedure: After performing complex domain superposition on the received modulated complex signal sequence, the resulting superimposed complex signal sequence is divided into an information segment and a parity check segment. Perform the first type of mapping from complex field pattern to finite field pattern on each superimposed complex signal in the information segment to obtain the finite field symbol corresponding to each superimposed complex signal in the information segment, and calculate the initial posterior probability of the finite field symbol corresponding to each superimposed complex signal. Calculate the real part likelihood probability and the imaginary part likelihood probability of each superimposed complex signal within the parity check segment; Perform a second type of mapping from complex field pattern to finite field pattern on each superimposed complex signal within the parity check segment to obtain the finite field symbol corresponding to each superimposed complex signal in the parity check segment. Calculate the initial posterior probability of the finite field symbol based on the real and imaginary likelihood probabilities of all superimposed complex signals corresponding to the same finite field symbol within the parity check segment. use The base-sum algorithm iteratively decodes the initial posterior probabilities of each finite field symbol to obtain the decoded finite field symbol. It is a prime number; Recovering the sequence formed by all decoded finite field symbols The original binary bit sequence of each user.

2. The GF(5)-based method according to claim 1 m The overloaded finite field multiple access method for orthogonal additive inverse pair codes is characterized by, Using the orthogonal additive inverse pairs of the finite field GF(5), for The implementation methods for multi-user access coding of the original binary bit sequence of each user include: Phase for obtaining the finite field symbol subsequence for each user: Will The users are numbered sequentially according to the access order predetermined by the sender. The number of users to the number One user, The number is even; and users are paired up according to a predetermined access order, resulting in a total of [number missing]. The first user pair, and the second The user pairs are numbered odd-numbered. User and even number are The number of users constitutes, For the user, assign a number, and ; The two fundamental additive inverse pairs contained in the orthogonal additive inverse pairs of the finite field GF(5) are respectively and ;in, and These are the first and second basic additive inverse pairs, respectively. These represent the finite field symbols for the elements in the finite field GF(5) that take values ​​from 0 to 4; The basic additive inverse pair Users with odd-numbered IDs are assigned using basic additive inverse pairs. The original binary bit sequences of each odd-numbered user are mapped to finite field symbol sequences, thus obtaining finite field symbol subsequences for each odd-numbered user; the mapping rule is: the binary bits in the original binary bit sequence are mapped... "Mapped to finite field symbol" The binary bits in the original binary bit sequence "Mapped to finite field symbol" ; The basic additive inverse pair Assigned to users with even numbers, through basic additive inverse pairs The original binary bit sequences of even-numbered users are mapped to finite field symbol sequences, thus obtaining finite field symbol subsequences for even-numbered users; the mapping rule is: the binary bits in the original binary bit sequence are mapped... "Mapped to finite field symbol" The binary bits in the original binary bit sequence "Mapped to finite field symbol" ; The stage of obtaining the finite field symbol sequence for each user: Set the length of the original binary bit sequence for each user to be... The length of the finite field symbol subsequence for each user After expansion, the sequence length is obtained as follows: A user-defined finite field symbol sequence.

3. The GF(5)-based method according to claim 2 m The overloaded finite field multiple access method for orthogonal additive inverse pair codes is characterized by, The sequence length is The structure of each user's finite field symbol sequence is as follows: No. The finite field symbol subsequences corresponding to each user in a pair of users are distributed in a length of The first in the sequence The segment, and the first to the second finite field symbol subsequence corresponding to the user. Each finite field symbol is located in a field of length . The first in the sequence Position 1 to 2 There are positions, with a length of . All other positions in the sequence are finite field symbols. ; where the length is The sequence is divided into The paragraphs are from paragraph 1 to paragraph 2. part.

4. The GF(5)-based method according to claim 1 m The overloaded finite field multiple access method for orthogonal additive inverse pair codes is characterized by, Defined in a finite field System linear block code generator matrix The expression is: ； in, for Unit array, for Dense matrix, and Each element is a finite field Finite field notation, For the parity check sign number, For matrix The total number of columns.

5. The GF(5)-based method according to claim 1 m The overloaded finite field multiple access method for orthogonal additive inverse pair codes is characterized by, The implementation method for mapping the first type of complex domain pattern to finite domain pattern for each superimposed complex signal within the information segment is as follows: The complex domain patterns corresponding to the superimposed complex signals within the information segment constitute the set of complex domain patterns. Any complex field pattern in the diagram; The first mapping rule from complex field patterns to finite field patterns is as follows: ； in, To map complex signals to finite field symbols, Let represent the finite field symbols for the elements in the finite field GF(5) that take values ​​from 0 to 4. It is the imaginary unit.

6. The GF(5)-based system according to claim 1 m The overloaded finite field multiple access method for orthogonal additive inverse pair codes is characterized by, Within the information segment, calculate the first... The initial posterior probability of the finite field symbol corresponding to the superimposed complex signal is realized as follows: ； ； ； ； in, The first information segment A superimposed complex signal Corresponding finite field symbol , , and The initial posterior probability at time , It is an integer. Finite field symbol The values ​​that the corresponding elements can take. , For information segment power allocation factor, The average transmit power, For noise power spectral density, For the value to be The complex field diagram corresponding to the finite field symbol. to They are finite field symbols The complex domain pattern of the corresponding superimposed complex signal; , , and , It is the imaginary unit.

7. The method based on claim 1 The overloaded finite field multiple access method for orthogonal additive inverse pair codes is characterized by, The implementation method for calculating the real and imaginary likelihood probabilities of the superimposed complex signals within the parity check segment is as follows: The maximum likelihood estimation method is used to estimate the probability of the real and imaginary parts of each superimposed complex signal in the parity check segment, so as to obtain the real and imaginary part likelihood probabilities of each superimposed complex signal.

8. The method based on claim 1 The overloaded finite field multiple access method for orthogonal additive inverse pair codes is characterized by, The second mapping rule from complex field patterns to finite field patterns is as follows: Calculate the real and imaginary parts of the superimposed complex signals within the parity check segment. The result is modulo 5, and the remainder is used as the element value of the corresponding finite field symbol in the finite field GF(5), thus obtaining the finite field symbol of the element under that value; where, and These are the real and imaginary parts of any superimposed complex signal within the parity check segment.

9. The GF(5)-based system according to claim 1 m The overloaded finite field multiple access method for orthogonal additive inverse pair codes is characterized by, Recovering the sequence formed by all decoded finite field symbols The implementation of the original binary bit sequence for each user is as follows: The decoded finite field symbol sequence is decoded using the inverse operation of multi-user access coding to recover the... The original binary bit sequence of each user.

10. Based on GF(5) m An overloaded finite-field multiple access system for orthogonal additive inverse pair codes, comprising a storage device, a processor, and a computer program stored in the storage device and executable on the processor, characterized in that... The processor executes a computer program to implement the GF(5) based method as described in any one of claims 1 to 9. m An overloaded finite field multiple access method for orthogonal additive inverse pair codes.

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