Construction method of code word type EP code based on finite field resource and finite field multiple access method thereof

Abstract

The application discloses a construction method of a code word type EP code based on a finite field resource and a finite field multiple access method thereof, and belongs to the technical field of 6G communication. j The application discloses a construction method of a code word type EP code based on a finite field resource and a finite field multiple access method thereof, and belongs to the technical field of 6G communication. The application discloses a construction method of a code word type EP code based on a finite field resource and a finite field multiple access method thereof, and belongs to the technical field of 6G communication. The application discloses a construction method of a code word type EP code based on a finite field resource and a finite field multiple access method thereof, and belongs to the technical field of 6G communication. The application discloses a construction method of a code word type EP code based on a finite field resource and a finite field multiple access method thereof, and belongs to the technical field of 6G communication.

Description

Technical Field

[0001] This invention belongs to the field of 6G communication technology, specifically relating to the construction method of codeword-type EP codes and its finite field multiple access method. Background Technology

[0002] For next-generation wireless communication, VMI (Very Large Machine Communication) is a very promising application. VMI is one of the five typical scenarios of 6G, and its two key characteristics are small packet transmission and random user access. In VMI scenarios, users communicate via short packets, typically 10 bits to 100 bits. It is difficult to design coding schemes that approach the Shannon limit within a limited length. Therefore, to support short packet communication for a massive number of users and achieve an acceptable bit error rate, it is necessary to explore new multiple access methods.

[0003] Traditional multiple access methods allocate different physical resources to different users at the transmitter and use these physical resources to distinguish users at the receiver. In contrast, the FFMA multiple access method utilizes the virtual resource of finite field resources. At the transmitter, different EP codes are assigned to different users, and at the receiver, users can be distinguished in a finite field using only one detector. This effectively solves the problem of multi-user interference and provides high reliability in large-scale user communication.

[0004] However, the performance of FFMA systems depends on the EP codes used. The EP codes used in FF-TDMA only serve to distinguish users; further performance improvements require the design of new EP codes. As is well known, traditional multiple access technologies typically employ classic physical resources (such as time domain, frequency domain, code domain, and spatial domain). These physical resources are usually defined in the complex domain, such as the orthogonal spreading sequences used in CDMA, which can provide spreading gain and only require correlation operations in the complex domain to distinguish different user sequences. NOMA technology can distinguish users on the same resource block, improving spectrum utilization.

[0005] Constructing EP codes using linear block codes can not only distinguish users but also reduce the overall code rate, effectively improving the performance of FFMA systems. However, this results in fewer users being able to access the system. Furthermore, extending traditional multiple access technologies to finite fields can also construct EP codes with better performance, but this also presents significant challenges. For example, traditional NOMA can distinguish users using methods such as power, but when designing EP codes, it is necessary to consider how finite-field NOMA can distinguish users. Classical Walsh codes are generally constructed on GF(2), but Walsh codes on GF(2) cannot distinguish users in finite fields. Summary of the Invention

[0006] This invention aims to address the problem that existing EP code designs, which only consider the function of distinguishing users, negatively impact the performance of FFMA systems.

[0007] The method for constructing codeword-type EP codes based on finite field resources includes the following steps:

[0008] Assume α is GF(p) m The fundamental element of ) then Capable of representing GF(p) m All elements on GF(p) m Each element α on ) j Both can be represented as α 0 =1,...,α m-1 Linear combination:

[0009] α j =a j,0 +a j,1 α+a j,2 α 2 +...+a j,m-1 α m-1

[0010] Where j = -∞, 0, ..., p m -2 and coefficient a j,0 a j,1 ... a j,m-1 It is an element on GF(p);

[0011] α j A vector of length m on GF(p) (a j,0 ,a j,1 ,...,a j,m-1 Unique representation; when the sent information has only two cases, (0)2 and (1)2, use To represent a pair of elements, denoted as EP code, where 0 ≤ l j,0 ,l j,1 ≤p m -2 and l j,0 and l j,1 The subscript j in the text indicates that the element pair is the j-th element pair, where 0 and 1 indicate whether the message sent is (0)2 or (1)2; assume there are J distinct element pairs. Where 1≤j≤J, the Cartesian product of J pairs of elements forms the element pairs of J users. This element can represent 2 with respect to ψ. J Each codeword; [The codeword is used to extract the codeword from each element pair] Represented by a vector of length m, and... As a matrix The rows can be used to construct a matrix of size J×m. Where M represents multiplexing, and 0 represents that the information sent for each element in each row is 0;

[0012] Similarly, construct the matrix Where 1 represents that the message sent for each element in each row is 1;

[0013] Select one element from each pair and sum them. Where k j ∈{0,1},a∈GF(p m ), Indicates GF(p) m Addition on )

[0014] The total number of codewords generated by superimposing m user codes is called the codeword space, and all combinations of m codewords are called the free space; based on the above... and The EP code is designed with the codeword space being smaller than the free space.

[0015] Furthermore, in the process of designing EP codes according to the principle that the codeword space is smaller than the free space, in GF(3 m The design process involves the following steps:

[0016] Assumption It is GF(p) m A set of element pairs on ) if in, For bitwise modulo-p sum operations, p is a vector of length m, where each element is p; 0 = p in GF(p); This is called a generalized adder pair, where g stands for generalized;

[0017] The Cartesian product of J distinct pairs of generalized adder elements forms the adder element pairs for J users. in, This indicates the definition; the element is related to ψ g Capable of representing 2 J Each code character;

[0018] Constructed from generalized additive element pairs satisfy Where P is a matrix of size J×m, and each element is p;

[0019] Then, the generalized orthogonal addition method is used to construct:

[0020] Assume T o Let be an m×m matrix, where each element is an element of GF(3). If the matrix satisfies or Then T is called o It is a ternary orthogonal matrix, with the subscript "o" indicating orthogonality;

[0021] Assume T o (2,2) is a ternary orthogonal matrix of size 2×2. Using T... o (2,2) constructs in Represent the Kronecker product; and so on, constructing

[0022]

[0023] Define T o (2 κ ,2 κ The inverse matrix of ) is: T o,inv (2 κ ,2 κ ) = PT o (2 κ ,2 κ )=2·T o (2 κ ,2 κ ), where the subscript "inv" represents the inverse matrix;

[0024] The constructed T o (2 κ ,2 κ ) and T o,inv (2 κ ,2 κ It satisfies the following three properties:

[0025] (1)T o (2 κ ,2 κ The cross-correlation between any two rows is (0)3; (2)T o (2 κ ,2 κ The autocorrelation of any row is (1)3 or (2)3; (3) if So if So

[0026] Using the constructed T o (2 κ ,2 κ ) and T o,inv (2 κ ,2 κ Construct generalized addition pairs; the same rows of two matrices form a set of addition pairs, i.e.

[0027]

[0028] Thus constructing 2 κ By combining generalized addition pairs, the corresponding EP code is obtained.

[0029] or,

[0030] In designing EP codes according to the principle that the codeword space is smaller than the free space, in GF(3 m The design process involves the following steps:

[0031] Assumption It is GF(p) m A set of element pairs on ) if in, For bitwise modulo-p sum operations, p is a vector of length m, where each element is p; 0 = p in GF(p); This is called a generalized adder pair, where g stands for generalized;

[0032] The Cartesian product of J distinct pairs of generalized adder elements forms the adder element pairs for J users. in, This indicates the definition; the element is related to ψ g Capable of representing 2 J Each code character;

[0033] Constructed from generalized additive element pairs satisfy Where P is a matrix of size J×m, and each element is p;

[0034] Then, the generalized nonorthogonal addition method is used to construct:

[0035] For J generalized addition pairs k∈{0,1}, each element can be written as a vector of length m over GF(p). By using modulation, it is transformed to the complex domain to obtain If we can use the sum over the complex field Get the only Then this addition symmetry is used to construct a generalized nonorthogonal addition pair;

[0036] Assume T no (J,m) is a matrix of size J×m over GF(3):

[0037]

[0038] Among them, t j,i ∈GF(3), 1≤j≤J, 0≤i≤m and J<m; the subscript “no” indicates nonorthogonality; define T no The inverse matrix of (J,m) is Tno,inv (J,m):

[0039] T no,inv (J,m)=PT no (J,m)

[0040] T no,inv (J,m) is also a matrix of size J×m over GF(3);

[0041] Then use T no (J,m) and T no,inv Construct a generalized nonorthogonal addition pair (J,m); let the generalized nonorthogonal addition pair... and for:

[0042]

[0043] This allows us to construct generalized nonorthogonal addition pairs for J users and obtain the corresponding EP codes.

[0044] or,

[0045] In designing EP codes according to the principle that the codeword space is smaller than the free space, in GF(2 m The design process involves the following steps:

[0046] Given a finite field GF(2 m If EP code two elements and satisfy as well as That is Where 0 represents a vector of length m, such an EP code A single codeword EP code, or Single CWEP, is used, where the subscript "cw" indicates the codeword; the Cartesian product of J EP codes. Comprising J user code groups, ψ cw From 2 J It consists of individual code words; because make They satisfy a nonlinear correlation;

[0047] By constructing a Single CWEP code using linear block codes, we obtain a Single CWEP code used to distinguish J users, which is the corresponding EP code.

[0048] A finite-field multiple access method for codeword-based EP codes based on finite-field resources, including a method based on GF(p m The processing procedure of the FFMA uplink system transmitter is based on GF(p). mThe processing steps at the transmitter of the FFMA uplink system include the following:

[0049] Assume there are a total of J users, b j =(b j,0 ,b j,1 ,...,b j,k ,...,b j,K-1 ) is the binary information sequence sent by user j, where 1≤j≤J; the transmitter first uses the EP code to map the user's binary information sequence symbol by symbol from GF(2) to the non-binary field GF(p). m The encoding process represents u j,k =F B2q (b j,k ), u j,k ∈GF(p m ), thus obtaining sequence u j The EP code is an orthogonal generalized addition pair, a non-orthogonal generalized addition pair, or a Single CWEP code obtained based on the construction method of the codeword type EP code based on finite field resources.

[0050] Using EP codes, the user's binary information sequence is symbol-by-symbol mapped from GF(2) to the non-binary field GF(p). m During the process, when m≥J, EP encoding is directly performed on the bit sequences of different users; when m<J, users are first grouped into groups of m users, and EP encoding is performed on the bit sequences of different users. Different groups of users send information at different times.

[0051] After EP encoding, add (N) p ,K p Linear block code C gc Channel coding is performed to obtain sequence v j , where N p K is the code length of the linear block code. p It is the information bit length of the linear block code, and the subscript p represents C. gc It is a codeword on GF(p), a linear block code C gc The generating matrix G gc It is K p ×N p First, convert the EP code to GF(p), then convert u... j,k Write it as a vector of length m and then transform it to GF(p), u j,k =(a j,k,0 ,a j,k,1 ,...,a j,k,m-1 );

[0052] Let G be the generating matrix on GF(p). gc It is a system format:

[0053]

[0054] in, This represents the information matrix portion; The parity check matrix is ​​of size K. p ×(N p -K p A matrix of )

[0055] Using G gc,sys For the j-th user corresponding to u j,add Encode to obtain v j , by v j Determine the codeword matrix V at the transmitting end; modulate the encoded codewords to transform the finite field into the complex field; convert the modulated sequence x... j Send it.

[0056] Furthermore, in the process of directly performing EP encoding on bit sequences from different users, the mapping relationship is changed from... Determined, that is Represents a pair of elements.

[0057] or,

[0058] First, the users are grouped into m groups. The bit sequences of different users are then encoded using EP encoding as follows:

[0059]

[0060] in, Indicates rounding down; C t This represents C corresponding to each user group after grouping. j , Represents a pair of elements.

[0061] Furthermore, the users are first grouped into m groups, and the bit sequences of different users are EP encoded. The process of different groups of users sending information at different times is as follows:

[0062] J users are divided into a total of Group, This indicates rounding up. Groups within the same segment send information within the same time slot, while different groups occupy different time slots. The sending end information matrix is ​​as follows:

[0063]

[0064] in, This matrix represents the sending end information matrix, indicating that different groups of users occupy different time periods to send messages. 1≤j≤J, U h+1 Let u represent the information matrix of the (h+1)th group. j,add This means that each user adds a 0 to the codeword in a time slot that is not their own, and sends their own codeword in their own time slot; K corresponds to each user sending K codewords.

[0065] Furthermore, utilizing G gc,sys For the j-th user corresponding to u j,add Encode to obtain v j , by v j The process of determining the sender codeword matrix V includes the following steps:

[0066] Using G gc,sys For the j-th user corresponding to u j,add v obtained by encoding j =u j,add ·G gc,sys =(u j,add ,v j,red ), where the verification part v j,red =u j •Q, the subscript "red" indicates the redundant part;

[0067] The sender's codeword structure is shown below:

[0068]

[0069] V h+1,red =[v mh+1,red v mh+2,red …v mh+m,red ] T

[0070] in, V h+1,red The redundant bits represent the h+1th group of users.

[0071] Furthermore, the aforementioned finite field multiple access method for codeword-type EP codes based on finite field resources also includes a processing procedure at the FFMA uplink system receiver. This procedure, which involves transmitting sequences at the FFMA uplink system transmitter for orthogonal generalized adder pairs or non-orthogonal generalized adder pairs corresponding to the EP codes, includes the following steps:

[0072] At the receiving end, the received complex domain signal vector It is the result of the signals transmitted by J users being superimposed with noise after passing through the channel, i.e. in, It is an AWGN vector, which follows Distribution; r is the complex domain modulated signal sequence x1, x2, ..., x Jand patterns,

[0073] First, the transformation function F from the complex field to the finite field is used. C2F Transform the sum pattern over the complex field into a sum pattern over the finite field, that is, v = F C2F (r), at this time it has the following characteristics:

[0074] 1) All possible outcomes of rn are Ω r ={J,J-1,...,-J+1,-J}, where two adjacent values ​​differ by 1, the set Ωr has a total of |Ω r | = 2J + 1 elements;

[0075] 2)r n The values ​​are arranged in descending order, resulting in Ω. r The corresponding ternary set Ω v (0)3, (1)3, and (2)3 appear alternately in the text;

[0076] 3) Assume v n = (0)3, (1)3, (2)3 are equally probable. Let ι represent the number of users sending "+1" and υ represent the number of users sending "-1". Then J-ι-υ represents the number of users sending 0. The complex domain signal r received by the receiving end n =ι-υ, with a probability of in, This indicates that out of J users, ι users sent "+1". This means that if ι users send "+1", then among the remaining J-ι users, υ users send "-1", where 0≤ι,υ≤J,υ+ι≤J;

[0077] Calculate r n The probability when =J,J-1,...,-J in

[0078] Based on the above characteristics, each received signal r n The unique mapping is the sum pattern v of a finite field. n v n It is the result of J users combined, where r n ∈{J,J-1,...,-J},v n ∈{0,1,2}; then decode y by calculating the posterior probability; based on r n With y n The relationship, to obtain

[0079]

[0080] and Ωr (l) corresponds to the set and Ω r The l-th element in the matrix is ​​used to calculate v. n =The posterior probabilities corresponding to (0)3, (1)3, and (2)3 respectively;

[0081] Then, decoding is performed based on the posterior probability, and after decoding, it is used... Restore information for each user;

[0082] 1) If orthogonal generalized adders are used in EP encoding, assuming the decoded sequence is w = (w0, w1, ..., w...), k-1 ,w j,red ), where w0, w1, ..., w k-1 All are vectors of length m on GF(3);

[0083] if So there are

[0084]

[0085] in, This refers to the k-th information bit obtained from the j-th user;

[0086] if So:

[0087]

[0088] 2) If non-orthogonal generalized addition pairs are used in EP encoding, user information can be recovered by looking up a table.

[0089] The EP code design method of this invention not only considers the function of distinguishing users, but also takes into account codeword correlation. Therefore, it proposes a design method that makes the codeword space smaller than the free space, thereby improving the correlation and thus improving the performance of the FFMA system. Among them, FF-CDMA uses ternary Walsh code as EP code, which can distinguish users in a finite field through simple correlation operations; FF-NOMA can distinguish users in a finite field in most cases, and when it cannot distinguish users in a finite field, it can distinguish users from the complex field, thus improving spectral efficiency without sacrificing too much performance; FF-CCMA uses binary system form linear block code as EP code, which can distinguish users without additional operations after decoding, and using linear block code as EP code can make the system have better performance.

[0090] Based on the coding principle, this invention proposes three multiple access schemes: Finite Domain Code Division Multiple Access (FF-CDMA), Finite Domain Non-Orthogonal Multiple Access (FF-NOMA), and Finite Domain Channel Coding Multiple Access (FF-CCMA). FF-CDMA combines orthogonal sequences with channel coding to form error-correcting orthogonal sequences, providing higher reliability for CDMA networks and ultra-large-scale data communication. FF-NOMA combines non-orthogonal sequences with channel coding to form error-correcting non-orthogonal sequences, suitable for ultra-large-scale IoT connections. FF-CCMA uses linear block codes as EP codes, forming a concatenated code-like structure, suitable for ultra-large-scale machine communication scenarios. Attached Figure Description

[0091] Figure 1 This is a block diagram of the FFMA uplink system architecture.

[0092] Figure 2 This is a diagram of the transmitter structure of an FF-CDMA system.

[0093] Figure 3 This is a structural diagram of the transmitter end of an FF-NOMA system.

[0094] Figure 4 This is a structural diagram of the transmitter end of an FF-CCMA system.

[0095] Figure 5 This is a diagram showing the relationship between complex fields and patterns and finite fields and patterns.

[0096] Figure 6 This is a simulation diagram of the FFMA uplink system performance. Detailed Implementation

[0097] For scenarios involving ultra-large-scale machine communication, commonly used multiple access coding schemes, such as BCH MA codes and Polar MA codes, are two-level concatenated codes, which have high decoding complexity and cannot perfectly eliminate interference between users.

[0098] This invention first constructs a codeword-type EP code based on element-pair code (EP code), and then combines the constructed codeword to implement finite field multiple access (FFMA). Specifically, this invention is based on GF(2... mThis invention constructs a single codeword EP (SingleCWEP) code and proposes a corresponding channel codeword multiple access infinite-field (FF-CCMA) technique. This technique uses linear block codes as EP codes, forming a concatenated code structure with the overall channel coding, reducing the overall code rate and improving the performance of the original FFMA system. This invention is based on GF(3) m This invention constructs a generalized orthogonal adder pair and proposes a corresponding finite-field code division multiple access infinite-field (FF-CDMA) technology. This scheme uses the generalized orthogonal adder pair as the EP code, which, combined with channel coding, forms an error-correcting orthogonal spreading sequence that is orthogonal in both the finite and complex fields. The invention also incorporates GF(3)... 2 A generalized nonorthogonal addition pair was constructed, and a corresponding non-orthogonal multiple access in finite-field (FF-NOMA) was proposed, forming a nonorthogonal spreading sequence with error correction capability that satisfies partial orthogonality in the finite field and complete orthogonality in the complex field, thereby improving spectral efficiency. Specific implementation method one:

[0100] This implementation describes a method for constructing codeword-type EP codes based on finite field resources. It includes a ternary generalized orthogonal and non-orthogonal addition pair construction method and a Single CWEP code construction method. The construction process is based on EP code implementation to construct codeword-type EP codes. In practical applications, the ternary generalized orthogonal addition pair construction method, the ternary generalized non-orthogonal addition pair construction method, or the Single CWEP code construction method can all be used to encode the user's codewords.

[0101] Generalized addition pair concept:

[0102] Assume α is GF(p) m If α is the fundamental element, then α -∞ =0,α 0 =1,α,α 2 ,...,α pm-2 Capable of representing GF(p) m All elements on GF(p) m Each element α on ) j All can be represented as α 0 =1,...,α m-1 Linear combination:

[0103] α j =a j,0 +a j,1 α+a j,2 α 2 +...+a j,m-1 α m-1

[0104] Where j = -∞, 0, ..., p m -2 and coefficient a j,0 a j,1 ... a j,m-1 It is an element on GF(p);

[0105] From the above equation, we can see that α j It can be obtained from a vector (a) of length m on GF(p). j,0 ,a j,1 ,...,a j,m-1 (Unique representation)

[0106] When the sent information has only two cases, (0)2 and (1)2, we use To represent a pair of elements, denoted as EP code, where 0 ≤ l j,0 ,l j,1 ≤p m -2 and l j,0 and l j,1 The subscript j in the string indicates that the element pair is the j-th element pair, where 0 or 1 indicates whether the message sent is (0)2 or (1)2. Assume there are J distinct element pairs. Where 1≤j≤J, the Cartesian product of J pairs of elements forms the element pairs of J users.

[0107]

[0108] This element can be represented as 2 for ψ. J Each codeword. (The remaining codewords are used in each element pair.) Represented by a vector of length m, and... As a matrix The rows can be used to construct a matrix of size J×m.

[0109]

[0110] Where M represents multiplexing, and 0 represents that the information sent for each element in each row is 0;

[0111] Similarly, a matrix can be constructed.

[0112]

[0113] Here, 1 represents that the message sent for each element in each row is 1.

[0114] Select one element from each pair and sum them.

[0115]

[0116] Where, k j ∈{0,1},a∈GF(p m ), Indicates GF(p) m Addition on ).

[0117] If a unique value can be derived from 'a' These element pairs are said to satisfy the unique sum-pattern mapping (USPM) property.

[0118] Next, we present the EP codes for two generalized addition pairs, as well as the Single CWEP code.

[0119] (A) This embodiment provides two examples of EP codes constructed on a ternary field.

[0120] Generalized addition pair concept:

[0121] Assumption It is GF(p) m A set of element pairs on ) if

[0122]

[0123] in, For the bitwise modulo-p sum operation, p is a vector of length m, where each element is p, i.e., p = (p, p, ..., p), and 0 = p in GF(p). We will... A generalized pair of adder elements is called a generalized adder element pair, where g represents generalization. The Cartesian product of J distinct generalized adder element pairs forms the adder element pairs for J users.

[0124]

[0125] in, This element represents the definition. g It can represent 2 J Each code character.

[0126] Constructed from generalized additive element pairs Satisfy the following formula

[0127]

[0128] Where P is a matrix of size J×m, and each element is p.

[0129] Next, we will give the method for constructing ternary generalized addition pairs.

[0130] 1. Construction of the generalized orthogonal addition method:

[0131] First, construct the ternary orthogonal sequence:

[0132] Assume T o Let be an m×m matrix, where each element is an element of GF(3). If the matrix satisfies or Then we call T o It is a ternary orthogonal matrix, with the subscript "o" indicating orthogonality.

[0133] Assume T o (2,2) is a ternary orthogonal matrix of size 2×2, in the following form:

[0134]

[0135] Using T o (2,2) constructs T o (2 2 ,2 2 ):

[0136]

[0137] in, Represents Kronecker.

[0138] By analogy, T can be constructed. o (2 κ ,2 κ ):

[0139]

[0140] Next, we define T. o (2 κ ,2 κ The inverse matrix of )

[0141] T o,inv (2 κ ,2 κ ) = PT o (2 κ ,2 κ )=2·T o (2 κ ,2 κ )

[0142] The subscript "inv" represents the inverse matrix, and the latter part of the equation utilizes the properties of the finite field GF(3).

[0143] Then, the generalized orthogonal addition method is used to construct:

[0144] Based on the method for constructing the ternary orthogonal sequence, it can be found that the constructed T o (2 κ ,2 κ ) and T o,inv (2 κ ,2 κ It satisfies the following three properties:

[0145] (1)T o (2 κ ,2 κ The cross-correlation between any two rows is (0)3.

[0146] (2)T o (2 κ ,2 κ The autocorrelation of any row is (1)3 or (2)3.

[0147] (3) If So if So

[0148] The constructed T can be used o (2 κ ,2 κ ) and T o,inv (2κ,2 κ Constructing generalized addition pairs. The same rows of two matrices form a set of addition pairs, i.e.

[0149]

[0150] In this way, we can construct a total of 2 κ Groups of generalized addition pairs. Since generalized orthogonal addition pairs are based on GF(3) m The structure is constructed such that the maximum number of cases where m users are superimposed is 2. m indivual.

[0151] The codewords that can be superimposed from m users are called the codeword space, and the possible combinations of m codewords are called the free space. It can be seen that using the generalized orthogonal addition pair as the EP code, the codeword space is smaller than the free space, which improves the correlation between these m bits and thus improves the performance of the FFMA system. Therefore, using the generalized orthogonal addition pair can not only achieve orthogonality in the finite field, but also improve the performance of the FFMA system.

[0152] 2. Construction of generalized nonorthogonal addition pairs:

[0153] Suppose there are J addition pairs that do not satisfy the USPM property. k∈{0,1}, each element can be written as a vector of length m on GF(p). By using modulation, it is transformed to the complex domain to obtain If we can use the sum over the complex field Get the only This additive symmetry is then used to construct a generalized nonorthogonal additive pair. The generalized nonorthogonal additive pair does not satisfy the USPM property, but it can distinguish user information from the complex field.

[0154] Assume T no (J,m) is a matrix of size J×m over GF(3):

[0155]

[0156] Among them, t j,i ∈GF(3), 1≤j≤J, 0≤i≤m and J<m. The subscript "no" indicates nonorthogonality. Define T no The inverse matrix of (J,m) is T no,inv (J,m):

[0157] T no,inv (J,m)=PT no (J,m)

[0158] T no,inv (J,m) is also a matrix of size J×m on GF(3).

[0159] Next, we will use T no (J,m) and T no,inv (J,m) construct a generalized nonorthogonal addition pair.

[0160] Let the generalized nonorthogonal addition method pair and for:

[0161]

[0162] It is possible to construct a generalized nonorthogonal addition pair for J users.

[0163] For example: in T o By adding a set of generalized addition pairs to (2,2), T can be constructed. no (3,2):

[0164]

[0165] The subscript "no" indicates that it is not orthogonal.

[0166] Using T no The code rate at (3,2) is R q =1.5, which allows for more users compared to the generalized orthogonal addition method. no The inverse matrix T of (3,2) no,inv (3,2) can be obtained using the same method:

[0167]

[0168] Assumption This allows for the construction of a generalized addition pair that supports three users.

[0169] The table below shows all the superposition results for the three users over finite fields, as well as the superposition results for the complex field using 3ASK:

[0170] Table 1. Superposition results of nonorthogonal generalized additives

[0171]

[0172] Where b[k] is the codeword vector composed of the k-th codewords of the three users, u 1,k ,u 2,k ,u 3,k It is the codeword obtained by encoding the k-th codeword of three users using the generalized nonorthogonal addition method. FFSK is u 1,k ,u 2,k ,u 3,k The sum over a finite field, CFSP is u 1,k ,u 2,k ,u 3,k The sum in the complex domain after 3ASK modulation. Table 1 shows the case of supporting three users with two bits; the total number of possible transmissions by the three users is 2. 3 =8, while GF(3) 2 There are a total of 9 possibilities. It can be seen that the codeword space is smaller than the free space when using the generalized non-orthogonal addition pair. Therefore, even the generalized non-orthogonal addition pair can improve the performance of FFMA.

[0173] (B) Single CWEP code:

[0174] In addition to using ternary to expand the free space to meet the requirement that the codeword space is smaller than the free space, the codeword space can also be reduced in binary to meet the same requirement. In this embodiment, an EP code containing free space is constructed in the binary field.

[0175] Given a finite field GF(2 m If EP code two elements and satisfy as well as That is Where 0 represents a vector of length m, such an EP code A single codeword EP (Extended Codeword) is used, where the superscript "cw" indicates the codeword. The Cartesian product of J CWEP codes is... The code group ψ of J users cw , ψ cw From 2 J It consists of individual code words. Because Only need to meet The nonlinear correlation between them, that is

[0176]

[0177] The constructed CWEP code then satisfies USPM, ψ cw This can be used to distinguish J users. To improve the performance of the FFMA system, classic linear block codes such as polar codes, RM codes, LDPC codes, etc., can be used to construct Single CWEP codes. Assume the generator matrix G of the chosen linear block code is... lc It is a J×m matrix, a binary matrix, with the subscript "lc" used to distinguish it from the channel code after EP coding. It utilizes G... lc structure

[0178]

[0179] This construction method yields a Single CWEP code for distinguishing J users. When the EP code uses a linear block code, J ≤ m, and mJ positions are used as check bits, thus the codeword space is 2^m. J Less than 2 m This reduces the codeword space to meet the requirement that the codeword space is smaller than the free space. Compared with the original EP code, choosing the classic linear block code as the Single CWEP code can reduce the overall code rate and improve the overall performance of the FFMA system. Specific Implementation Method Two:

[0181] This implementation describes a finite-field multiple access method for codeword-type EP codes based on finite-field resources. When the user's codeword is encoded using the method corresponding to the construction process via ternary generalized orthogonal addition, the corresponding method is actually a spread spectrum multiple access method based on finite-field orthogonality. When the user's codeword is encoded using the method corresponding to the construction process via ternary generalized non-orthogonal addition, the corresponding method is actually a spread spectrum multiple access method based on finite-field non-orthogonality.

[0182] The limited-domain multiple access method described in this embodiment includes the following steps:

[0183] S201, based on GF(p) m Processing at the transmitter end of the FFMA uplink system:

[0184] Figure 1 The diagram shows the block structure of an FFMA uplink system. The transmitter first performs EP coding and channel coding on the information sequence sent by the user, then modulates the coded sequence, and finally sends the modulated sequence to the GMAC channel.

[0185] Suppose that the EP code is constructed on GF(q), where q = p m For convenience, the FFMA system uses the linear block code C. gc Based on the GF(p) construction, different EP codes are used in different FFMA systems, but the processing at the transmitter is the same, while the processing at the receiver differs. Therefore, the following section introduces the GF(p)-based... m The FFMA uplink system transmitter.

[0186] Assume there are a total of J users, b j =(b j,0 ,b j,1 ,...,b j,k ,...,b j,K-1 Let be the binary information sequence sent by user j, where 1 ≤ j ≤ J. The transmitter first uses the EP code to map the user's binary information sequence symbol by symbol from GF(2) to the non-binary field GF(p). m ), to obtain sequence u j The EP code mentioned above uses the CWEP code, orthogonal generalized adder pairs, or non-orthogonal generalized adder pairs.

[0187] When m≥J, EP encoding can be directly performed on bit sequences from different users, i.e., u j,k =F B2q (b j,k ), where u j,k ∈GF(p m This mapping relationship is... Sure

[0188]

[0189] Among them, b j,k ⊙C j It is a selection function; if the input information is 0, then it maps to... If the input information is 1, then the mapping is:

[0190] When m < J, a single EP code cannot distinguish all users. Therefore, users need to be grouped into groups of m, with different groups sending information at different times. The mapping relationship at this point is:

[0191]

[0192] in, Indicates rounding down; C t This represents the C corresponding to each user group after grouping. j That is, the EP code assigned to each user, and the corresponding C for each group. j They are the same;

[0193] J users are divided into a total of Group, This indicates rounding up. Groups within the same segment send information within the same time slot, while different groups occupy different time slots. The sending end information matrix is ​​as follows:

[0194]

[0195] in, This matrix represents the sending end information matrix, indicating that different groups of users occupy different time periods to send messages. 1≤j≤J, U h+1 Let u represent the information matrix of the (h+1)th group. j,add This indicates that each user adds a 0 to the codeword in a time slot that is not their own, and sends their own codeword in their own time slot; K corresponds to each user sending K codewords;

[0196] The following process is performed when m ≤ J.

[0197] After EP encoding, add (N) p ,K p Linear block code C gc Channel coding is performed to obtain sequence v j , where N p K is the code length of the linear block code. p It is the information bit length of the linear block code, and the subscript p represents C. gc It is a codeword on GF(p), a linear block code C gc The generating matrix G gc It is K p ×N p Dimension. Because linear block codes and EP codes are not in the same finite field, we need to first utilize F. q2p Convert the EP code to GF(p), and since q = p m Therefore, u can be j,kWrite it as a vector of length m and then transform it to GF(p).

[0198] u j,k =(a j,k,0 ,a j,k,1 ,...,a j,k,m-1 )

[0199] Let the size of GF(p) be K p ×N p The generating matrix G gc It is a system form G sys The matrix consists of two parts: the information matrix part is of size K. p ×K p The identity matrix, with the parity-check matrix denoted as Q; the systematic form of G gc Represented as

[0200]

[0201] Wherein, the verification matrix is It is of size K p ×(N p -K p A matrix of )

[0202] Using this matrix to find the u corresponding to the j-th user j,add Encode

[0203] v j =u j,add ·G gc,sys =(u j,add ,v j,red )

[0204] Among them, the verification part v j,red =u j •Q, with the subscript "red" indicating a redundant part.

[0205] The sender's codeword structure is shown below:

[0206]

[0207] V h+1,red =[v mh+1,red v mh+2,red …v mh+m,red ] T

[0208] in, V h+1,red The redundant bits represent the h+1th group of users.

[0209] The encoded codeword is modulated to transform the finite field into the complex field, denoted as x. j,n =FF2C (v j,n ), where v j,n Indicates v j The nth bit, 1≤j≤J, 0≤n≤N; the modulation scheme is determined based on the finite field variation of the channel coding. For example:

[0210] When using generalized orthogonal addition pairs and generalized non-orthogonal addition pairs, the FFMA system transmitter architecture diagram is as follows: Figure 2 as well as Figure 3 The channel coding is an LDPC code on GF(3), and the modulation scheme can use 3ASK:

[0211]

[0212] Since the modulation methods used in current multiple access simulations are mostly BPSK, 3ASK, etc., in order to make it easier to compare with existing methods and highlight the performance advantages of the present invention, 3ASK is used in this embodiment. However, other modulation methods can also be used in practice.

[0213] If a Single CWEP code is used, the structure diagram of the FFMA system transmitter is as follows: Figure 4 The channel coding is an LDPC code on GF(2), and the modulation scheme can be BPSK:

[0214]

[0215] The modulated sequence is x j =(x j,0 ,x j,1 ,...,x j,n ,…,x j,N-1 Then we send the modulated sequence to GMAC. The channel coding of the Single CWEP code is an LDPC code on GF(2), and the LDPC decoding part is the same as the existing GF(2)-based code. m The decoding part of the FFMA uplink system receiver is almost the same. It can be successfully decoded by adding CWEP constraints to the original H matrix check relationship. This implementation will not be explained further. The following only gives the FFMA uplink system receiver when using generalized orthogonal addition pairs and generalized non-orthogonal addition pairs.

[0216] S202, based on GF(3) m Processing at the receiver end of the FFMA uplink system:

[0217] At the receiving end, the received complex domain signal vector It is the result of the signals transmitted by J users being superimposed with noise after passing through the channel, i.e.

[0218]

[0219] in, It is an AWGN vector, which follows Distribution. r is a complex domain modulated signal sequence x1, x2, ..., xn. J and patterns,

[0220] The relationship between complex fields and patterns and finite fields and patterns is shown in the figure below. Figure 5 As shown.

[0221] Similar to the binary case, the first step in receiving and decoding is to use the transformation function F from the complex field to the finite field. C2F Transform the sum pattern over the complex field into a sum pattern over the finite field, that is, v = F C2F (r), Figure 4 The relationship between sums over complex fields and sums over finite fields is shown, revealing the following characteristics:

[0222] 1) All possible outcomes of rn are Ω r ={J,J-1,...,-J+1,-J}, where two adjacent values ​​differ by 1, the set Ωr has a total of |Ω r | = 2J + 1 elements;

[0223] 2) Because r n The values ​​are arranged in descending order, which gives us Ω. r The corresponding ternary set Ω v The (0)3, (1)3, and (2)3 in the formula appear alternately, that is... Where |Ω v |=|Ω r |

[0224] 3) Assume v n = (0)3, (1)3, (2)3 are equally probable. We use ι to represent the number of users sending "+1" and υ to represent the number of users sending "-1". Then J-ι-υ represents the number of users sending 0. In this case, the complex domain signal r received by the receiver is... n =ι-υ, with a probability of

[0225]

[0226] in, This indicates that out of J users, ι users sent "+1". This means that if ι users send "+1", then among the remaining J-ι users, υ users send "-1", where 0≤ι,υ≤J, andυ+ι≤J.

[0227] Therefore we can calculate r nThe probability when =J,J-1,…,-J, that is, in

[0228] Based on the above characteristics, the transformation function F is then used. C2F Each received signal r n The unique mapping is the sum pattern v of a finite field. n v n It is the result of J users combined, and the transformation function can be written as F. C2F :r n →v n Where r n ∈{J,J-1,…,-J},v n ∈{0,1,2}, therefore F C2F It is a many-to-one function.

[0229] Now we can calculate the posterior probability to decode y. Based on r n With y n The relationship can be obtained

[0230]

[0231] and Ω r (l) corresponds to the set and Ω r The l-th element in; therefore, v can be calculated. n The posterior probabilities of (0)3, (1)3, (2)3

[0232]

[0233] Decoding is based on posterior probability. If LDPC codes are used in the channel coding section, the QSPA algorithm can be used for decoding. After decoding, the [method / process] can be used... Restore the information of each user.

[0234] 1) If orthogonal generalized adders are used in EP encoding, assuming the decoded sequence is w = (w0, w1, ..., w...), k-1 ,w j,red ), where w0, w1, ..., w k-1 Both are vectors of length m on GF(3). If So there are

[0235]

[0236] in, This refers to the k-th information bit obtained from the j-th user.

[0237] if So:

[0238]

[0239] 2) If non-orthogonal generalized addition pairs are used during EP encoding, we recover user information by looking up a table. The table shows that T... no When (3,2), users cannot be distinguished by the finite field when the sum of the finite fields is (00)3, but users can be distinguished by the complex field in this case.

[0240] Example:

[0241] Example 1:

[0242] CWEP code encoding:

[0243] In GF(2) 8 Construct CWEP codes for four users on the platform.

[0244]

[0245] Generalized adder pairs ψ from 4 users cw It can represent 2 4 = 16 code characters and It is a matrix of size 4×8, where It is a zero matrix of size 4×8. for

[0246]

[0247] Example 2:

[0248] Generalized addition element pair encoding:

[0249] In GF(3) 4 Construct a generalized adder pair for 4 users on )

[0250]

[0251] Generalized adder pairs ψ from 4 users g It can represent 2 4 = 16 code characters and It is a 4×4 matrix

[0252]

[0253] Example 3:

[0254] Sparse FFMA uplink system transmitter:

[0255] Given a finite field GF(3) 4 Assume there are J = 3 users, and each user sends K = 3 bits. The bit sequences of the three users are b1 = (1,1,0), b2 = (1,0,1), and b3 = (0,0,1). The generalized adder element pairs in Example 1 are used, and the channel coding is performed using the linear block code (16,12) on GF(3).

[0256] Step 1: Encode the information using orthogonal generalized addition, based on the transformation function F. B2q We can get

[0257]

[0258] Step 2: Encode the information in the extended field into codewords for transmission, namely v. j =u j G. Here is a generator matrix G of a (16, 12) ternary linear code, in systematic form as shown below.

[0259]

[0260] After encoding, the codewords for u1, u2, and u3 are respectively

[0261] v1=u1·G eg =(1111,1111,2222,1111)

[0262] v2=u2·G eg =(2121,1212,2121,0000)

[0263] v3=u3·G eg =(1122,1122,2211,0102)

[0264] The blue part is the parity check bit. We use... This represents the summation of codewords over a finite field, where v = (v0, v1, ..., v...). n ,…,v N-1 vn is obtained by summing the codewords of each user over a finite field. For the examples given above, we have

[0265]

[0266] To compare with the single-user scenario, we used Define the summation of information bits over a finite field, where We can obtain the codeword v after τ encoding. τ :

[0267]

[0268] We can obtain v = v τ .

[0269] Step 3: Modulate the encoded codeword to map the signal from the finite domain to the complex domain. 3ASK modulation is used. The modulated signal is shown below.

[0270]

[0271] x1, x2, and x3 are then sent to GMAC.

[0272] Uplink receiver detection:

[0273] Step 1: Use the designed function F C2F This transforms the sum over the complex field into a sum over a finite field. For Example 1, the received sum *r* over the complex field is...

[0274]

[0275] When J=3, Ω can be obtained. r ={-3,-2,-1,0,+1,+2,+3}, Ω v ={0,2,1,0,2,1,0}, indicating F C2F (-3)=(0)3,F C2F (-2)=(2)3,F C2F (-1)=(1)3,F C2F (0)=(0)3,F C2F (+1)=(2)2,F C2F (+2)=(1)3,

[0276] F C2F (+3) = (0)3, therefore we can obtain the sum of Example 1 over a finite field.

[0277]

[0278] Step 2: Using the inverse function F q2B Decoding is performed. EP encoding uses orthogonal generalized addition pairs, therefore, correlation operations can be used for decoding:

[0279]

[0280] It can be seen that using orthogonal generalized addition can distinguish information from different users.

[0281] Example 4: FFMA Uplink System

[0282] Let α be a fundamental element of GF(751). Construct the following 4×8 basis matrix over GF(751):

[0283]

[0284] Then, by replacing each element in the basis matrix with a 750×750-dimensional CPM, a matrix H(4,8) of size 3000×6000 is generated. All elements in the matrix are on GF(3). This matrix is ​​used as the parity check matrix for the channel coding of the uplink system, with a code length N = 6000 and an information bit length K. Q =3001.

[0285] In the uplink, assuming each user sends K = 10 valid information bits, performance simulations are performed for two scenarios. Based on GF(3... 4 Construct orthogonal generalized adder pairs, the system can support a maximum number of users J = 300; based on GF(3 2 Construct non-orthogonal generalized adder pairs. The system supports a maximum of J = 450 users. The QSPA algorithm is used for decoding. Simulation results are as follows: Figure 6 As shown.

[0286] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for constructing codeword-type EP codes based on finite field resources, characterized in that, Includes the following steps: Assumption yes The fundamental element, then Able to represent All elements on, Each element on All can be represented as Linear combination: in, And coefficient yes Elements on; Able to be A vector of length m Unique representation; when the sent information has only one , In two cases, use To represent a pair of elements, denoted as EP code, where and , and The subscript j in the text indicates that the element pair is the j-th element pair, where 0 and 1 represent the information being sent. still Suppose there are J distinct pairs of elements. ,in The Cartesian product of J pairs of elements forms the element pairs of J users. This element is paired with Able to represent Each codeword; [The codeword is used to extract the codeword from each element pair] Represented by a vector of length m, and... As a matrix The rows can be used to construct a row of size. matrix Where M represents multiplexing, and 0 represents that the information sent for each element in each row is 0; Similarly, construct the matrix , where 1 represents that the sent information corresponding to each row element is 1; Select one element from each pair and sum them. ,in , , express Addition on top; The total number of codewords generated by superimposing m user codes is called the codeword space, and all combinations of m codewords are called the free space; based on the above... and The EP code is designed with the codeword space being smaller than the free space. The design process includes the following steps: Assumption yes A set of element pairs on, if ,in, For bitwise modulo p operations, It is a vector of length m, where each element is p; Above ;Will This is called a generalized adder pair, where g stands for generalized; The Cartesian product of J distinct pairs of generalized adder elements forms the adder element pairs for J users. ,in, This element represents a definition; Able to represent Each code character; Constructed from generalized additive element pairs , satisfy Where P is a denoted by ... A matrix, where each element is p; Then, the generalized orthogonal addition method is used to construct: Assumption It is a size of A matrix whose each element is Elements on the matrix, if the matrix satisfies or , then call It is a ternary orthogonal matrix, with the subscript "o" indicating orthogonality; Assumption It is a size of A ternary orthogonal matrix, using Construct ,in Represent the Kronecker product; and so on, constructing ; definition Inverse matrix: In this context, the subscript "inv" represents the inverse matrix; Constructed as well as Satisfy the following three properties: (1) The cross-correlation between any two rows is (2) The autocorrelation of any row is or (3) If ,So ;if ,So ; Using the constructed and Construct generalized addition pairs; the same rows of two matrices form a set of addition pairs, i.e. Thus constructing By combining generalized addition pairs, the corresponding EP code is obtained.

2. A method for constructing codeword-type EP codes based on finite field resources, characterized in that, Assumption yes The fundamental element, then Able to represent All elements on, Each element on All can be represented as Linear combination: in, And coefficient yes Elements on; Able to be A vector of length m Unique representation; when the sent information has only one , In two cases, use To represent a pair of elements, denoted as EP code, where and , and The subscript j in the text indicates that the element pair is the j-th element pair, where 0 and 1 represent the information being sent. still Suppose there are J distinct pairs of elements. ,in The Cartesian product of J pairs of elements forms the element pairs of J users. This element is paired with Able to represent Each codeword; [The codeword is used to extract the codeword from each element pair] Represented by a vector of length m, and... As a matrix The rows can be used to construct a row of size. matrix Where M represents multiplexing, and 0 represents that the information sent for each element in each row is 0; Similarly, construct the matrix , where 1 represents that the sent information corresponding to each row element is 1; Select one element from each pair and sum them. ,in , , express Addition on top; The total number of codewords generated by superimposing m user codes is called the codeword space, and all combinations of m codewords are called the free space; based on the above... and In the process of designing EP codes according to the principle that the codeword space is smaller than the free space, in The design process includes the following steps: Assumption yes A set of element pairs on, if ,in, For bitwise modulo p operations, It is a vector of length m, where each element is p; Above ;Will This is called a generalized adder pair, where g stands for generalized; The Cartesian product of J distinct pairs of generalized adder elements forms the adder element pairs for J users. ,in, This element represents a definition; Able to represent Each code character; Constructed from generalized additive element pairs , satisfy Where P is a denoted by ... A matrix, where each element is p; Then, the generalized nonorthogonal addition method is used to construct: For J generalized addition pairs , , ..., , ..., ; , Each element can be written A vector of length m By using modulation, it is transformed to the complex domain to obtain If it is possible to sum over the complex field Get the only Then this addition symmetry is used to construct a generalized nonorthogonal addition pair; Assumption yes The size of the top is The matrix: in, , , and The subscript "no" indicates non-orthogonality; definition The inverse matrix is : Too The size of the top is Matrix; Then use and Construct generalized nonorthogonal addition pairs; let the generalized nonorthogonal addition pairs be... and for: This allows us to construct generalized nonorthogonal addition pairs for J users and obtain the corresponding EP codes.

3. A method for constructing codeword-type EP codes based on finite field resources, characterized in that, Assumption yes The fundamental element, then Able to represent All elements on, Each element on All can be represented as Linear combination: in, And coefficient yes Elements on; Able to be A vector of length m Unique representation; when the sent information has only one , In two cases, use To represent a pair of elements, denoted as EP code, where and , and The subscript j in the text indicates that the element pair is the j-th element pair, where 0 and 1 represent the information being sent. still Suppose there are J distinct pairs of elements. ,in The Cartesian product of J pairs of elements forms the element pairs of J users. This element is paired with Able to represent Each codeword; [The codeword is used to extract the codeword from each element pair] Represented by a vector of length m, and... As a matrix The rows can be used to construct a row of size. matrix Where M represents multiplexing, and 0 represents that the information sent for each element in each row is 0; Similarly, construct the matrix , where 1 represents that the sent information corresponding to each row element is 1; Select one element from each pair and sum them. ,in , , express Addition on top; The total number of codewords generated by superimposing m user codes is called the codeword space, and all combinations of m codewords are called the free space; based on the above... and In the process of designing EP codes according to the principle that the codeword space is smaller than the free space, in The design process includes the following steps: Given a finite field If EP code two elements and satisfy as well as That is Where 0 represents a vector of length m, such an EP code Create a single codeword EP code, i.e., Single CWEP, where the subscript "cw" indicates the codeword; the Cartesian product of J EP codes. Form a code group for J users, Depend on It consists of individual code words; because ,make They satisfy a nonlinear correlation; By constructing a Single CWEP code using linear block codes, we obtain a Single CWEP code used to distinguish J users, which is the corresponding EP code.

4. A finite-field multiple access method for codeword-based EP codes based on finite-field resources, characterized in that, Including GF(p) m The processing procedure of the FFMA uplink system transmitter is based on GF(p). m The processing steps at the transmitter of the FFMA uplink system include the following: Assume there are a total of J users. User The transmitted binary information sequence, in which The transmitter first uses the EP code to transmit the user's binary information sequence from... Symbol-by-symbol mapping to non-binary fields The encoding process represents , Thus, the sequence is obtained. The EP code is an orthogonal generalized addition pair, a non-orthogonal generalized addition pair, or a Single CWEP code obtained based on the construction method of codeword type EP code based on finite field resources as described in any one of claims 1 to 3. Using EP codes to transmit the user's binary information sequence from Symbol-by-symbol mapping to non-binary fields During the process, when At that time, EP encoding is directly performed on the bit sequences of different users; when First, users are grouped into groups of m users. The bit sequences of different users are then EP encoded, and different groups of users send information at different times. Add after EP encoding Linear block code Channel coding is performed to obtain the sequence. , where N p K is the code length of the linear block code. p It is the information bit length of the linear block code, and the subscript p represents... yes The codeword above, linear block code Generating matrix yes First, convert the EP code to... Above, General Write it as a vector of length m and then transform it to superior, ; make Generating matrix on It is a system format: in, This represents the information matrix portion; This represents the parity check matrix, which is of size . Matrix; use For the first Each user Encode to obtain ,Depend on Determine the sender codeword matrix Modulate the encoded codewords to transform the finite field into the complex field; then, convert the modulated sequence... Send; This indicates the code text that each user adds after 0 in a time gap that does not belong to them.

5. The method for finite-field multiple access based on finite-field resources using codeword-type EP codes according to claim 4, characterized in that, In the process of directly performing EP encoding on bit sequences from different users, the mapping relationship is changed by... Determined, that is ; Represents a set of element pairs; It is a selection function; if the input information is 0, then it maps to... If the input information is 1, then the mapping is .

6. The method for finite-field multiple access based on finite-field resources using codeword-type EP codes according to claim 4, characterized in that, First, the users are grouped into m groups. The bit sequences of different users are then encoded using EP encoding as follows: in, , , Indicates rounding down; This indicates the user groups and the corresponding group for each group. , Represents a pair of elements.

7. The method for finite-field multiple access based on finite-field resources using codeword-type EP codes according to claim 6, characterized in that, First, users are grouped into groups of m users. Then, EP encoding is performed on the bit sequences of different users. The process of different groups of users sending information at different times is as follows: J users are divided into a total of Group, This indicates rounding up. Groups within the same segment send information within the same time slot, while different groups occupy different time slots. The sending end information matrix is ​​as follows: in, This matrix represents the sending end information matrix, indicating that different groups of users occupy different time periods to send messages. , , This represents the information matrix of the (h+1)th group. This means that each user adds a 0 to the codeword in a time slot that is not their own, and sends their own codeword in their own time slot; K corresponds to each user sending K codewords.

8. The method for finite-field multiple access based on finite-field resources using codeword-type EP codes according to claim 7, characterized in that, use For the first Each user Encode to obtain ,Depend on Determine the sender codeword matrix The process includes the following steps: use For the first Each user Encoding Among them, the verification part The subscript "red" indicates a redundant part; The sender's codeword structure is shown below: in, , The redundant bits represent the h+1th group of users.

9. A finite-field multiple access method for codeword-type EP codes based on finite-field resources according to any one of claims 4 to 8, characterized in that, It also includes the processing procedure at the FFMA uplink system receiver, which is the sequence transmitted during the processing of the FFMA uplink system transmitter for the EP code corresponding to orthogonal generalized adder pairs or non-orthogonal generalized adder pairs. The processing procedure at the FFMA uplink system receiver includes the following steps: At the receiving end, the received complex domain signal vector It is the result of the signals transmitted by J users being superimposed with noise after passing through the channel, i.e. ,in, It is an AWGN vector, which follows Distribution; r is a complex domain modulated signal sequence and patterns, ; First, use the transformation function from complex field to finite field. Transform the sum pattern over the complex field into the sum pattern over the finite field, that is... At this time, it has the following characteristics: 1) r n All possible outcomes are Two adjacent values ​​differ by 1, set Ω r There are a total of |Ω r | = 2J + 1 element; 2) r n The values ​​are arranged in descending order, resulting in Ω. r The corresponding ternary set Ω v (0)3, (1)3, and (2)3 appear alternately in the text; 3) Assumption It is of equal probability, using To indicate the number of users sending "+1", use This indicates the number of users who sent "-1". Indicates the number of users sending 0; the complex field signal received by the receiver. The probability is ,in, This means that among J users... If one user sends "+1", it means that if one user sends "+1", then one of the remaining users sends "-1". , ; calculate probability of time ,in ; Based on the above characteristics, each received signal r n The unique mapping is the sum pattern of a finite field. , It is the result of J users combined, where , Then, y is decoded by calculating the posterior probability; based on r n With y n The relationship, to obtain and Corresponding to a set and The l-th element in the matrix is ​​then used to calculate... Each corresponds to a posterior probability; Then, decoding is performed based on the posterior probability, and after decoding, it is used... Restore information for each user; 1) If orthogonal generalized adder pairs are used in EP encoding, assuming the decoded sequence is... ,in All A vector of length m; if So there are in, For the obtained first The kth information bit of a user; if ,So: 2) If non-orthogonal generalized addition pairs are used in EP encoding, user information can be recovered by looking up a table.

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