CN111786680A - A method and device for determining a generator matrix - Google Patents

Abstract

A method and device for determining a generator matrix are used to improve the short code performance of a control channel. The method includes: performing an iterative operation on the generator matrix one or more times until a stopping condition is satisfied, and obtaining a target generator matrix, wherein the size of the target generator matrix is K rows and N columns, and the length of the information bits to be encoded is The K, the code length is the N; the iterative operation includes: determining the minimum code distance in the code distance between any two row vectors in the generator matrix, and the minimum code distance is the first row vector and the second row vector. The code distance between the vectors; in the code word formed by the first row vector and the second row vector, any one of the (K+1)th column to the Nth column with all zero elements element is set to 1.

Description

A method and device for determining a generator matrix

technical field

The embodiments of the present application relate to the field of communication technologies, and in particular, to a method and apparatus for determining a generator matrix.

Background technique

As the most basic wireless access technology, channel coding plays a crucial role in ensuring the reliable transmission of data. In communication systems of different wireless access technologies, different coding modes are usually used to adapt to various application scenarios. In a long term evolution (LTE) system, the physical layer hybrid ARQ indicator channel (PHICH), the physical layer control format indicator channel (PCFICH), the physical layer Physical layer channels such as an uplink control channel (physical uplink control channel, PUCCH) and a physical layer uplink shared channel (physical uplink shared channel, PUSCH) will involve the application of short codes with an information vector length of 13 or less. The LTE control channel scenario is encoded using a Reed-muler (RM) code. In a new radio (NR) communication system, the coding of the control channel short code follows the RM code used for the LTE control channel.

However, the short code performance of the control channel needs to be further improved.

SUMMARY OF THE INVENTION

Embodiments of the present application provide a method and an apparatus for determining a generator matrix, so as to improve the short code performance of a control channel.

The specific technical solutions provided by the embodiments of the present application are as follows:

In a first aspect, a method for determining a generator matrix is provided, and the method can be applied to a terminal or a network device. The method includes: performing an iterative operation on the generator matrix one or more times until a stopping condition is satisfied, and obtaining a target generator matrix, wherein the size of the target generator matrix is K rows and N columns, and the length of the information bits to be encoded is The K, the code length is the N; the iterative operation includes: determining the minimum code distance in the code distance between any two row vectors in the generator matrix, where the minimum code distance is the sum of the first row vector and the second row vector In the code word formed by the first row vector and the second row vector, set any element in one of the (K+1)th columns to the Nth column with all zero elements. is 1. The performance of the linear block code is directly related to the minimum code distance. In the present application, the code words with the minimum code distance are continuously eliminated through continuous iterative operations, thereby gradually increasing the size of the minimum code distance. The generation matrix determined by this method can improve the control Short code performance of the channel.

In a possible design, the stopping condition includes that the minimum code distance reaches an upper bound, and the upper bound of the minimum code distance is determined by the K and the N. The performance of the linear block code is directly related to the minimum code distance. In the present application, the code words with the minimum code distance are continuously eliminated through continuous iterative operations, so that the minimum code distance of the linear block code is increased until the minimum code distance of the code is reached. The upper bound, the generator matrix determined by this method can improve the short code performance of the control channel.

In a possible design, the stopping condition includes that the code spectrum reaches an optimum, and the code spectrum includes the value of the minimum code distance in the generator matrix and the number of code words whose code weight is the minimum code distance. The code spectrum is directly related to the maximum likelihood performance of the code, the better the code spectrum, the better the performance of the code.

In a possible design, the stopping condition includes: on the basis that the minimum code distance reaches an upper bound, the code spectrum reaches an optimum; wherein, the upper bound of the minimum code distance is determined by the K and the N It is determined that the code spectrum includes the value of the minimum code distance in the generator matrix and the number of codewords whose code weight is the minimum code distance. In the process of continuous iterative operation, the minimum code distance is constantly being eliminated, which means that the minimum code distance is continuously increasing until it increases to the upper bound of the minimum code distance. At this time, the code spectrum can also be optimized, that is, the iterative operation can be continued, and the number of code words whose code weight is the smallest code distance can be reduced. The smaller the number, the better the code spectrum. The code spectrum is directly related to the maximum likelihood performance of the code, the better the code spectrum, the better the performance of the code. The performance of the linear block code is directly related to the minimum code distance. When the minimum code distance reaches the upper bound, the performance is directly related to the number of code words with the minimum code distance. The present application continuously performs iterative operations to make the code words with the minimum code distance continue to be used. Therefore, the minimum code distance of the linear block code becomes larger. When the upper bound of the minimum code distance of the code is reached, it continues to iterate continuously, so that the number of code words with the minimum code distance becomes less and less. The generator matrix determined by this method, The short code performance of the control channel can be improved.

In a possible design, according to different N, K, the resulting target generator matrix is as follows. N=20, K=4, and the resulting generator matrix is shown in Figure 4a.

It is also possible to save or use the generator matrix except for the first 4 rows and 4 columns of the identity matrix (ie, the sub-matrix), as shown in Fig. 4b. For the generator matrices shown in FIGS. 5 to 37 below, sub-matrices other than the unit matrix with the first K rows and K columns may be used for storage or application.

N=20, K=6, and the resulting generator matrix is shown in Figure 5.

N=20, K=7, and the resulting generator matrix is shown in Figure 6.

N=24, K=6, and the resulting generator matrix is shown in Figure 7.

N=24, K=7, and the resulting generator matrix is shown in Figure 8.

N=24, K=8, and the resulting generator matrix is shown in Figure 9.

N=24, K=9, and the resulting generator matrix is shown in Figure 10.

N=32, K=5, and the resulting generator matrix is shown in Figure 11.

N=32, K=7, and the resulting generator matrix is shown in Figure 12.

N=32, K=8, and the resulting generator matrix is shown in Figure 13.

N=32, K=9, and the resulting generator matrix is shown in Figure 14.

N=32, K=10, and the resulting generator matrix is shown in Table 15.

N=32, K=12, and the resulting generator matrix is shown in Table 16.

N=48, K=7, and the resulting generator matrix is shown in Table 17.

N=48, K=11, and the resulting generator matrix is shown in Table 18.

N=48, K=13, and the resulting generator matrix is shown in Table 19.

N=48, K=19, and the resulting generator matrix is shown in Table 20.

Compared with the golay spreading codes, LTE RM codes and codes in the Brouwer table in the prior art, the generator matrices shown in Fig. 4-a to Fig. 20 can all achieve better performance.

N=20, K=3, and the resulting generator matrix is shown in Figure 21.

N=20, K=5, and the resulting generator matrix is shown in Figure 22.

Compared with the golay spreading code and the LTE RM code in the prior art, the generator matrices shown in FIGS. 21 to 22 can achieve better performance.

N=20, K=8, and the resulting generator matrix is shown in Figure 23.

N=20, K=9, and the resulting generator matrix is shown in Figure 24.

Compared with the LTE RM codes in the prior art, the generator matrices shown in FIGS. 23 to 24 can achieve better performance.

N=20, K=10, and the resulting generator matrix is shown in Figure 25.

N=20, K=11, and the resulting generator matrix is shown in Figure 26.

N=20, K=12, and the resulting generator matrix is shown in Figure 27.

Compared with the LTE RM codes in the prior art and the codes in the Brouwer table, the generator matrices shown in FIGS. 25 to 27 can achieve better performance.

N=24, K=3, and the resulting generator matrix is shown in Figure 28.

Compared with the golay spreading code and the LTE RM code in the prior art, the generator matrix shown in FIG. 28 can achieve better performance.

N=24, K=4, and the resulting generator matrix is shown in Figure 29.

Compared with the codes in the Brouwer table and the LTE RM codes in the prior art, the generator matrix shown in FIG. 29 can achieve better performance.

N=24, K=5, and the resulting generator matrix is shown in Figure 30.

Compared with the golay spreading code and the LTE RM code in the prior art, the generator matrix shown in FIG. 30 can achieve better performance.

N=24, K=10, and the resulting generator matrix is shown in Figure 31.

N=24, K=11, and the resulting generator matrix is shown in Figure 32.

Compared with the codes in the Brouwer table and the LTE RM codes in the prior art, the generator matrices shown in FIGS. 31 to 32 can achieve better performance.

N=24, K=12, and the resulting generator matrix is shown in Figure 33.

Compared with the LTE RM code in the prior art, the generator matrix shown in FIG. 33 can achieve better performance.

N=32, K=3, and the resulting generator matrix is shown in Figure 34.

Compared with the Qualcomm golay spreading code and the LTE RM code in the prior art, the generator matrix shown in FIG. 34 can achieve better performance.

N=32, K=4, and the resulting generator matrix is shown in Figure 35.

Compared with the codes in the Brouwer table and the LTE RM codes in the prior art, the generator matrix shown in FIG. 35 can achieve better performance.

N=32, K=6, and the resulting generator matrix is shown in Figure 36.

Compared with the golay spreading code in the prior art, the generator matrix shown in FIG. 36 can achieve better performance.

N=48, K=6, and the resulting generator matrix is shown in Figure 37.

Compared with the golay spreading code and the LTE RM code in the prior art, the generator matrix shown in FIG. 37 can achieve better performance.

A second aspect provides an apparatus for determining a generator matrix, the apparatus having the function of implementing the method described in the first aspect and any possible design of the first aspect. The functions can be implemented by hardware, or can be implemented by hardware executing corresponding software. The hardware or software includes one or more modules corresponding to the above functions.

In a possible design, when part or all of the functions are implemented by hardware, the device for determining the generator matrix includes: a logic circuit, configured to execute the first aspect and any one of the possible designs of the first aspect. behavior described in.

In one possible design, the device may be a chip or an integrated circuit.

In a possible design, when some or all of the functions are implemented in software, the apparatus includes a processor and a memory, the processor is coupled to the memory, and executes a program stored in the memory, and when the program is executed, the The apparatus may execute the method described in the first aspect and any possible design of the first aspect, and the memory is used for storing the program executed by the processor.

Optionally, the above-mentioned memory may be a physically independent unit, or may be integrated with the processor.

In a possible design, when part or all of the functions are implemented in software, the decoding means includes a processor. The memory for storing the program is located outside the determining means of the generation matrix, and the processor is connected to the memory through a circuit/wire for reading and executing the program stored in the memory.

In one possible design, the device is a terminal or network device.

In a third aspect, a chip is provided, the chip is connected to a memory or the chip includes a memory for reading and executing a software program stored in the memory, so as to realize any one of the first aspect and the first aspect above methods described in possible designs.

In a fourth aspect, there is provided a computer storage medium storing a computer program, the computer program comprising instructions for performing the above aspects and any possible method in design of the aspects.

In a fifth aspect, there is provided a computer program product containing instructions that, when run on a computer, cause the computer to perform the method described in the above aspects and any possible designs of the aspects.

Description of drawings

FIG. 1a is a schematic diagram of a communication system architecture in an embodiment of the application;

FIG. 1b is a schematic diagram of a method for determining a minimum code distance in an embodiment of the present application;

2 is one of the schematic flow charts of the method for determining the generation matrix in the embodiment of the present application;

3 is the second schematic flow chart of the method for determining the generation matrix in the embodiment of the application;

Fig. 4a is one of the schematic diagrams of generating matrices of N=20 and K=4 in the embodiment of the present application;

Fig. 4b is the second schematic diagram of the generator matrix of N=20 and K=4 in the embodiment of the present application;

5 is a schematic diagram of the generator matrix of N=20 and K=6 in the embodiment of the present application;

6 is a schematic diagram of the generator matrix of N=20 and K=7 in the embodiment of the present application;

7 is a schematic diagram of the generator matrix of N=24 and K=6 in the embodiment of the present application;

8 is a schematic diagram of the generator matrix of N=24 and K=7 in the embodiment of the present application;

9 is a schematic diagram of a generator matrix of N=24 and K=8 in the embodiment of the present application;

10 is a schematic diagram of the generator matrix of N=24 and K=9 in the embodiment of the application;

11 is a schematic diagram of a generator matrix of N=32 and K=5 in the embodiment of the application;

12 is a schematic diagram of the generator matrix of N=32 and K=7 in the embodiment of the application;

13 is a schematic diagram of the generator matrix of N=32 and K=8 in the embodiment of the application;

14 is a schematic diagram of a generator matrix of N=32 and K=9 in the embodiment of the application;

15 is a schematic diagram of a generator matrix of N=32 and K=10 in the embodiment of the application;

16 is a schematic diagram of the generator matrix of N=32 and K=12 in the embodiment of the present application;

17 is a schematic diagram of the generator matrix of N=48 and K=7 in the embodiment of the application;

18 is a schematic diagram of the generator matrix of N=48 and K=11 in the embodiment of the application;

19 is a schematic diagram of the generator matrix of N=48 and K=13 in the embodiment of the application;

20 is a schematic diagram of the generator matrix of N=48 and K=19 in the embodiment of the application;

21 is a schematic diagram of the generator matrix of N=20 and K=3 in the embodiment of the application;

22 is a schematic diagram of the generator matrix of N=20 and K=5 in the embodiment of the application;

23 is a schematic diagram of a generator matrix of N=20 and K=8 in the embodiment of the application;

24 is a schematic diagram of the generator matrix of N=20 and K=9 in the embodiment of the present application;

25 is a schematic diagram of the generator matrix of N=20 and K=10 in the embodiment of the present application;

26 is a schematic diagram of the generator matrix of N=20 and K=11 in the embodiment of the present application;

27 is a schematic diagram of the generator matrix of N=20 and K=12 in the embodiment of the application;

FIG. 28 is a schematic diagram of the generator matrix of N=24 and K=3 in the embodiment of the present application;

29 is a schematic diagram of the generator matrix of N=24 and K=4 in the embodiment of the application;

30 is a schematic diagram of the generator matrix of N=24 and K=5 in the embodiment of the application;

31 is a schematic diagram of the generator matrix of N=24 and K=10 in the embodiment of the present application;

32 is a schematic diagram of the generator matrix of N=24 and K=11 in the embodiment of the application;

33 is a schematic diagram of the generator matrix of N=24 and K=12 in the embodiment of the present application;

34 is a schematic diagram of the generator matrix of N=32 and K=3 in the embodiment of the present application;

35 is a schematic diagram of the generator matrix of N=32 and K=4 in the embodiment of the application;

36 is a schematic diagram of a generator matrix of N=32 and K=6 in the embodiment of the present application;

37 is a schematic diagram of the generator matrix of N=48 and K=6 in the embodiment of the application;

FIG. 38 is a schematic diagram of performance comparison in the embodiment of the present application;

39 is one of the schematic structural diagrams of the device for determining the generation matrix in the embodiment of the present application;

FIG. 40 is the second schematic structural diagram of the apparatus for determining the generation matrix in the embodiment of the present application.

Detailed ways

The present application provides a method and apparatus for determining a generator matrix, which are used to improve the short code performance of a control channel. Among them, the method and the device are based on the same inventive concept. Since the principles of the method and the device for solving the problem are similar, the implementation of the device and the method can be referred to each other, and the repetition will not be repeated.

In the description of this application, the character "/" generally indicates that the contextual object is an "or" relationship. Words such as "first" and "second" are only used for the purpose of distinguishing and describing, and cannot be understood as indicating or implying relative importance, nor can they be understood as indicating or implying order. "And/or", which describes the association relationship of the associated objects, means that there can be three kinds of relationships, for example, A and/or B, which can mean that A exists alone, A and B exist at the same time, and B exists alone. In this application, at least one refers to one or more; multiple refers to two or more.

The embodiments of the present application will be described in detail below with reference to the accompanying drawings.

The methods and apparatuses provided in the embodiments of the present application may be applicable to various wireless communication scenarios, such as: long term evolution (long term evolution, LTE) systems, worldwide interoperability for microwave access (worldwide interoperability for microwave access, WiMAX) communication systems, future Fifth generation (5th Generation, 5G) systems, such as a new generation of radio access technology (new radio access technology, NR), and future communication systems, such as 6G systems. The method and apparatus provided by the embodiments of the present application may be, but are not limited to, applicable to enhanced mobile broadband (eMBB), massive machine type communication (mMTC), and ultra reliable low latency communication (ultra reliable low latency communication). , URLLC) scenarios.

First, the architecture of the communication system to which the embodiments of the present application are applicable is introduced.

FIG. 1a shows the architecture of a possible communication system to which the method for determining the generator matrix provided by the embodiment of the present application is applicable. Referring to FIG. 1a, the communication system 100 includes: a network device 101 and one or more terminals 102. When the communication system 100 includes a core network, the network device 101 may also be connected to the core network. The network device 101 may communicate with an IP network 103, for example, the IP network 103 may be the Internet, a private IP network, or other data networks. The network device 101 provides services for the terminals 102 within the coverage. For example, as shown in FIG. 1 a , the network device 101 provides wireless access to one or more terminals 102 within the coverage of the network device 101 . Besides, the coverage areas between network devices may have overlapping areas, for example, the coverage areas of the network device 101 and the network device 101' may have overlapping areas. The network devices can also communicate with each other, for example, the network device 101 can communicate with the network device 101'.

The network device 101 is a device that connects the terminal 102 to the wireless network in the communication system applied in this application. The network device 101 is a node in a radio access network (radio access network, RAN), which may also be referred to as a base station, and may also be referred to as a RAN node (or device). At present, examples of some network devices 101 are: general node B (gNB), new radio node B (NR-NB), transmission reception point (TRP), evolved node B ( evolved Node B (eNB), radio network controller (RNC), Node B (Node B, NB), base station controller (BSC), base transceiver station (BTS), family Base station (for example, home evolved NodeB, HeNB; or home Node B, HNB), base band unit (base band unit, BBU), or wireless fidelity (wireless fidelity, Wifi) access point (AP), or 5G A communication system or a network-side device in a possible future communication system, etc.

Terminal 102, also known as user equipment (UE), mobile station (MS), mobile terminal (MT), etc., is a device that provides voice and/or data connectivity to users . For example, the terminal 102 includes a handheld device with a wireless connection function, a vehicle-mounted device, or the like. At present, the terminal 102 may be: a mobile phone (mobile phone), a tablet computer, a notebook computer, a palmtop computer, a mobile internet device (mobile internet device, MID), a wearable device (such as a smart watch, a smart bracelet, a pedometer, etc.), In-vehicle equipment (for example, cars, bicycles, electric vehicles, airplanes, ships, trains, high-speed rails, etc.), virtual reality (VR) equipment, augmented reality (AR) equipment, industrial control (industrial control) Wireless terminals, smart home equipment (eg, refrigerators, TVs, air conditioners, electricity meters, etc.), intelligent robots, workshop equipment, wireless terminals in self-driving, wireless terminals in remote medical surgery, smart A wireless terminal in a smart grid, a wireless terminal in transportation safety, a wireless terminal in a smart city, or a wireless terminal in a smart home, flying equipment (eg, smart Robots, hot air balloons, drones, airplanes), etc.

The network architecture and service scenarios described in the embodiments of the present application are for the purpose of illustrating the technical solutions of the embodiments of the present application more clearly, and do not constitute a limitation on the technical solutions provided by the embodiments of the present application. The evolution of the architecture and the emergence of new business scenarios, the technical solutions provided in the embodiments of the present application are also applicable to similar technical problems.

The basic idea of the embodiments of the present application is to search for a generator matrix with better performance based on the method of eliminating the minimum code distance, so as to improve the performance of the control channel short code. Of course, the generator matrix provided in the embodiment of the present application can not only be applied to the control channel short code. The short code means that the length of the information vector or the length of the information bits does not exceed the set length value. The embodiments of this application can be applied to the coding of control channels in 5G NR or other systems, and can be applied to, but not limited to, the length of the information bits to be coded from 3 bits to 12 bits, or the length of the code word after coding is 20, 24, 32 bits. or a codeword of 48.

For the convenience of description, the definitions of several parameters are introduced first. K represents the length of the information bits to be encoded, and N represents the length of the encoded codeword or the length of the mother code.

The concept of code distance: any row or rows in the generator matrix can be regarded as a codeword, or in other words, any row vector or any number of row vectors can be regarded as a codeword. The distance between any two code words is the code distance. There are multiple code distances in the generator matrix, and there are two code words corresponding to the minimum code distance among the multiple code distances in a generator matrix. It can be considered that the two code words corresponding to the minimum code distance can form a new code. word, the new codeword is also a sub-matrix of the generator matrix. The code weight of the new code word is the minimum code distance. The code weight is the number of 1s in the codeword.

The process of the method for determining the generation matrix in the embodiment of the present application will be described in detail below.

First, an initial generator matrix is randomly generated, and the operation of eliminating the minimum code distance in the generator matrix is performed iteratively until the set stopping condition is met.

The initial generator matrix is used as the first input, and the generated generator matrix is output when the stopping condition is finally satisfied. The output generator matrix can also be called the target generator matrix.

The operation of eliminating the minimum code distance in the generator matrix performed iteratively between the input and the output may include steps 1 and 2.

Step 1: Transform the generator matrix, and determine the minimum code distance among the code distances between any two row vectors in the transformed generator matrix, assuming that the minimum code distance is between the first row vector and the second row vector. Yard distance.

Step 2: Set any element in one of the all-zero element columns in the (K+1)th column to the Nth column in the codeword formed by the first row vector and the second row vector to 1.

In practical applications, it is not necessary to determine the row vector, as long as the row number is determined. After step 2, return to step 1, that is, iterative execution or iterative loop execution. For ease of understanding, it is assumed that the above steps 1 and 2 are one process in the iteration, and the next process in the iteration is described below. Continue to transform the generator matrix obtained in step 2, and determine the minimum code distance in the code distance between any two row vectors in the transformed generator matrix, and the two row vectors corresponding to the minimum code distance are still recorded as the first row. vector and the second row vector, that is, the minimum code distance is the code distance between the first row vector and the second row vector. In the codeword formed by the first row vector and the second row vector, any element in one of the all-zero element columns in the (K+1)th column to the Nth column is set to 1. The operation performed by this iteration is actually the same as the first operation, except that the input generator matrix becomes the generator matrix obtained after step 2. The generator matrix is a matrix with K rows and N columns, and the submatrix formed by the 1st to Kth columns is an identity matrix.

In the multiple operations performed iteratively, the generator matrix is constantly changing. The generator matrix input for the first time is an initial generator matrix that is randomly generated. The initial generator matrix is transformed, and other operations in steps 1 and 2 above, Output a generator matrix, take the output generator matrix as input, repeat the operations of step 1 and step 2, output the next generator matrix, and iterate in this way until the stop condition is satisfied or the stop is artificially stopped.

In step 1, the input generator matrix will undergo equivalent transformation, and the equivalent transformation includes row exchange, column exchange or row operation, etc. The transformed generator matrix is the equivalent matrix of the generator matrix before the transformation, and the transformed matrix It can be regarded as the same kind of code as the matrix before transformation. The equivalent transformation may be performed one or more times. After a certain equivalent transformation, the minimum code distance in the transformed generator matrix is found. Wherein, in the transformed generator matrix, there may be more than one codeword whose code weight is the minimum code distance. Then it means that the first row vector and the second row vector may be more than one. If there are multiple code words whose code weight is the minimum code distance, in step 2, any code word is processed to eliminate the minimum code distance. Eliminating the minimum code distance means setting any element in one of the all-zero element columns in the (K+1)th column to the Nth column to 1. Since the submatrix formed by the first K rows and the first K columns of the generator matrix is a unit matrix, the unit matrix cannot be replaced. When eliminating the minimum code distance, one of the (K+1)th to Nth columns is completely Any element in the zero-element column is set to 1. For example, if the two elements in the (K+2)th column are both 0, you can set any one of the two elements to 1. For example, the (K+2)th element in the first row vector is set to 0 as 1, or set the (K+2)th element 0 in the second row vector to 1. Through the operation of setting 0 to 1, the code distance between the first row vector and the second row vector will be greater than the minimum code distance, thereby eliminating the minimum code distance.

If there are multiple codewords whose code weight is the minimum code distance, the minimum code distance can be gradually eliminated through multiple iterative operations.

Through continuous iterative operations, the found minimum code distance will become larger and larger. In this application, the upper bound of the minimum code distance of the generator matrix corresponding to (N, K) can be determined according to N and K in this application. For example, when N=20 and K=5, the upper bound of the minimum code distance of the generator matrix corresponding to (N, K) is 9. According to the steps of the above iterative operation, the iterative loop operation is performed until the minimum code distance reaches the upper bound.

When the minimum code distance reaches the upper bound, the iterative operation can be stopped, that is, the target generator matrix is output. Iterative operations can also be continued to further optimize the generator matrix.

If the iterative operation is continued, the stopping condition can be optimized for the code spectrum. The code spectrum includes the value of the minimum code distance in the generator matrix and the number of codewords whose code weight is the minimum code distance. A codeword whose code weight is the minimum code distance means that the code weight of the code word is equal to the minimum code distance. There may be multiple such code words, and the smaller the number, the better the code spectrum. In the process of continuous iterative operation, the minimum code distance is constantly being eliminated, which means that the minimum code distance is continuously increasing until it increases to the upper bound of the minimum code distance. At this time, the code spectrum can also be optimized, that is, the iterative operation can be continued, and the number of code words whose code weight is the smallest code distance can be reduced. The smaller the number, the better the code spectrum. The code spectrum is directly related to the maximum likelihood performance of the code, the better the code spectrum, the better the performance of the code.

As mentioned above, the stopping condition of the iterative operation can be that the minimum code distance reaches the upper bound; or, it can also continue to iterate on the basis that the minimum code distance reaches the upper bound, and the code spectrum can reach the optimum. Of course, the stop condition of the iterative operation can also be that the code spectrum reaches the optimum, that is, the iterative operation is stopped by taking the code spectrum as a reference.

The code spectrum in this patent can also be all possible code weights and the number of codewords corresponding to the code weights.

In practical applications, there may not be a specific standard for the code spectrum to reach the optimum. In the implementation, when the code spectrum is no longer improved by continuing to iterate n times, it can be considered that the code spectrum reaches the optimum. The value of n can be specified, and n is a positive integer. Alternatively, the iteration is continued on the basis that the minimum code distance reaches the upper bound, and the stopping timing is determined artificially.

The method for determining the minimum code distance in the above step 1 may refer to some methods in the prior art, which is not limited in this application. For example, referring to the following method, the minimum code distance and the row corresponding to the minimum code distance can be determined.

As shown in Fig. 1b, for the convenience of understanding, the generator matrix G can be divided according to Fig. 1b. Randomly select a set of information bits, and use Gaussian elimination to obtain a system generator matrix (Id _k , Z) _I , and perform the following iterations until a codeword with codeword weight w is found:

Randomly divide the information bit combination I into two parts I ₁ and I ₂ , where I ₁ = round down (k/2), I ₂ = round up (k/2), correspondingly, Z is also divided into Two parts Z ₁ and Z ₂ . A subset L of J containing x elements is randomly selected, and the p rows corresponding to Z ₁ in L are added to obtain a set M ₁ , which is put into the hash table. The p rows corresponding to Z ₂ in L are added to obtain a set M ₂ , which is put into the hash table. Find the row corresponding to the same element in M ₁ and M ₂ through the hash table, and the code weight of the code word corresponding to the corresponding row at this time is w. Randomly update the set of information bits.

Of course, other methods can also be applied to determine the minimum code distance.

Based on the above description, the method for determining the generator matrix will be described in further detail below according to the implementation process shown in FIG. 2 and FIG. 3 .

As shown in FIG. 2 , in a possible implementation manner, the method for determining the generator matrix may be implemented according to the following process.

S201, randomly generating an initial generator matrix.

S202. Determine the codeword corresponding to the minimum code distance.

Perform this step as in step 1 above.

S203, update the generator matrix.

Update as in step 2 above.

S204. Determine whether to reset the generator matrix. If so, return to S201, otherwise, execute S205.

S205. Determine whether the minimum code distance of the updated generator matrix reaches an upper bound. If so, return to S206, otherwise, execute S202.

S206. Obtain a first target generation matrix.

The first target generation matrix may be output, or subsequent steps such as S207 may be continued.

S207. Determine the code word corresponding to the minimum code distance. Same as S202.

S208, update the generator matrix. Same as S203.

S209 , judging whether the iterative operation satisfies the stop condition, if so, stop and output the second target generation matrix, otherwise return to S207 .

Since some steps in FIG. 2 are the same operation, the implementation process is simplified as the flow shown in FIG. 3 .

S301, randomly generating an initial generator matrix.

S302. Determine the codeword corresponding to the minimum code distance.

Perform this step as in step 1 above.

S303. Update the generator matrix.

Update as in step 2 above.

S304. Determine whether to reset the generator matrix. If so, return to execute S301, otherwise execute S305.

S305: Determine whether the iterative operation satisfies the stopping condition, and if so, stop and output the target generation matrix, otherwise return to S302.

The stopping condition may include that the minimum code distance reaches the upper bound, the code spectrum reaches the optimum, or the code spectrum reaches the optimum on the basis that the minimum code distance reaches the upper bound.

Based on the method for determining the generator matrix provided in this application, the target generator matrix can be obtained, and some examples of different (N, K) target generator matrices (referred to as generator matrices) are given below. Different (N, K) generator matrices can be stored and applied at encoding time. When storing, the entire generator matrix may be saved, or only the part of the generator matrix other than the identity matrix of the first K rows and K columns may be saved.

N=20, K=4, and the resulting generator matrix is shown in Figure 4a.

It is also possible to save or use the generator matrix except for the first 4 rows and 4 columns of the identity matrix (ie, the sub-matrix), as shown in Fig. 4b. For the generator matrices shown in FIGS. 5 to 37 below, sub-matrices other than the unit matrix with the first K rows and K columns may be used for storage or application.

N=20, K=6, and the resulting generator matrix is shown in Figure 5.

N=20, K=7, and the resulting generator matrix is shown in Figure 6.

N=24, K=6, and the resulting generator matrix is shown in Figure 7.

N=24, K=7, and the resulting generator matrix is shown in Figure 8.

N=24, K=8, and the resulting generator matrix is shown in Figure 9.

N=24, K=9, and the resulting generator matrix is shown in Figure 10.

N=32, K=5, and the resulting generator matrix is shown in Figure 11.

N=32, K=7, and the resulting generator matrix is shown in Figure 12.

N=32, K=8, and the resulting generator matrix is shown in Figure 13.

N=32, K=9, and the resulting generator matrix is shown in Figure 14.

N=32, K=10, and the resulting generator matrix is shown in Table 15.

N=32, K=12, and the resulting generator matrix is shown in Table 16.

N=48, K=7, and the resulting generator matrix is shown in Table 17.

N=48, K=11, and the resulting generator matrix is shown in Table 18.

N=48, K=13, and the resulting generator matrix is shown in Table 19.

N=48, K=19, and the resulting generator matrix is shown in Table 20.

Compared with the golay spreading codes, the LTE RM codes and the codes in the Brouwer table in the prior art, the generator matrices shown in FIGS. 4a to 20 can all achieve better performance.

N=20, K=3, and the resulting generator matrix is shown in Figure 21.

N=20, K=5, and the resulting generator matrix is shown in Figure 22.

Compared with the golay spreading code and the LTE RM code in the prior art, the generator matrices shown in FIGS. 21 to 22 can achieve better performance.

N=20, K=8, and the resulting generator matrix is shown in Figure 23.

N=20, K=9, and the resulting generator matrix is shown in Figure 24.

Compared with the LTE RM codes in the prior art, the generator matrices shown in FIGS. 23 to 24 can achieve better performance.

N=20, K=10, and the resulting generator matrix is shown in Figure 25.

N=20, K=11, and the resulting generator matrix is shown in Figure 26.

N=20, K=12, and the resulting generator matrix is shown in Figure 27.

Compared with the LTE RM codes in the prior art and the codes in the Brouwer table, the generator matrices shown in FIGS. 25 to 27 can achieve better performance.

N=24, K=3, and the resulting generator matrix is shown in Figure 28.

Compared with the golay spreading code and the LTE RM code in the prior art, the generator matrix shown in FIG. 28 can achieve better performance.

N=24, K=4, and the resulting generator matrix is shown in Figure 29.

Compared with the codes in the Brouwer table and the LTE RM codes in the prior art, the generator matrix shown in FIG. 29 can achieve better performance.

N=24, K=5, and the resulting generator matrix is shown in Figure 30.

Compared with the golay spreading code and the LTE RM code in the prior art, the generator matrix shown in FIG. 30 can achieve better performance.

N=24, K=10, and the resulting generator matrix is shown in Figure 31.

N=24, K=11, and the resulting generator matrix is shown in Figure 32.

Compared with the codes in the Brouwer table and the LTE RM codes in the prior art, the generator matrices shown in FIGS. 31 to 32 can achieve better performance.

N=24, K=12, and the resulting generator matrix is shown in Figure 33.

Compared with the LTE RM code in the prior art, the generator matrix shown in FIG. 33 can achieve better performance.

N=32, K=3, and the resulting generator matrix is shown in Figure 34.

Compared with the Qualcomm golay spreading code and the LTE RM code in the prior art, the generator matrix shown in FIG. 34 can achieve better performance.

N=32, K=4, and the resulting generator matrix is shown in Figure 35.

Compared with the codes in the Brouwer table and the LTE RM codes in the prior art, the generator matrix shown in FIG. 35 can achieve better performance.

N=32, K=6, and the resulting generator matrix is shown in Figure 36.

Compared with the golay spreading code in the prior art, the generator matrix shown in FIG. 36 can achieve better performance.

N=48, K=6, and the resulting generator matrix is shown in Figure 37.

Compared with the golay spreading code and the LTE RM code in the prior art, the generator matrix shown in FIG. 37 can achieve better performance.

The row transformation or column exchange of the generator matrix in this patent can be considered as equivalent codes, and the equivalent codes of the above codes are also within the protection scope of this patent.

In order to further illustrate that the generator matrix obtained according to the method of the embodiment of the present application has better performance, as shown in FIG. 38 , it is a performance comparison diagram. The performance is characterized by block error rate (BLER). It can be seen that under the same decoder and decoding complexity, the performance of the code found in the method provided by the embodiment of the present application is better than the code in the Brouwer table, the code in the LTE RM and the Qualcomm Golay spread code spectrum.

Based on the method for determining a generator matrix provided by the foregoing embodiment, as shown in FIG. 39 , an embodiment of the present application further provides an apparatus 3900 for determining a generator matrix, and the apparatus 3900 for determining a generator matrix is configured to execute the method provided by the above method embodiment, The generating matrix determination device 3900 includes a processing unit 3901 and a storage unit 3902 . The processing unit 3901 is configured to perform an iterative operation on the generator matrix one or more times until the stop condition is satisfied, and obtain a target generator matrix, wherein the size of the target generator matrix is K rows and N columns, and the length of the information bits to be encoded is is the K, and the code length is the N;

When performing the iterative operation, the processing unit 3901 is specifically configured to: determine the minimum code distance among the code distances between any two row vectors in the generator matrix, where the minimum code distance is the first row vector and the second row vector. The code distance between the vectors; in the code word formed by the first row vector and the second row vector, any one of the (K+1)th column to the Nth column with all zero elements element is set to 1. The storage unit 3902 is used to store the initial generator matrix, the target generator matrix and the generator matrix in the intermediate iterative process. Optionally, the storage unit 3902 is configured to store the partial sub-matrixes of the target generator matrix except for the identity matrix with the first K rows and K columns.

Optionally, the stopping condition includes that the minimum code distance reaches an upper bound, and the upper bound of the minimum code distance is determined by the K and the N.

Optionally, the stopping condition includes that the code spectrum reaches an optimum, and the code spectrum includes the value of the minimum code distance in the generator matrix and the number of code words whose code weight is the minimum code distance.

Optionally, the stopping condition includes: on the basis that the minimum code distance reaches an upper bound, the code spectrum reaches an optimum; wherein, the upper bound of the minimum code distance is determined by the K and the N, and the The code spectrum includes the value of the minimum code distance in the generator matrix and the number of codewords whose code weight is the minimum code distance.

The target generator matrix is the generator matrix shown in FIG. 4a to FIG. 37 .

Based on the method for determining a generator matrix provided by the foregoing embodiment, as shown in FIG. 40 , an embodiment of the present application further provides an apparatus 4000 for determining a generator matrix, and the apparatus 4000 for determining a generator matrix is configured to execute the method provided by the above method embodiment, The apparatus 4000 for determining the generator matrix includes a processor 4001 and a memory 4002 . The processor 4001 is configured to perform an iterative operation on the generator matrix one or more times until the stopping condition is satisfied, and obtain a target generator matrix, wherein the size of the target generator matrix is K rows and N columns, and the length of the information bits to be encoded is is the K, and the code length is the N;

When executing the iterative operation, the processor 4001 is specifically configured to: determine the minimum code distance among the code distances between any two row vectors in the generator matrix, where the minimum code distance is the first row vector and the second row vector. The code distance between the vectors; in the code word formed by the first row vector and the second row vector, any one of the (K+1)th column to the Nth column with all zero elements element is set to 1. The memory 4002 is used to store the initial generator matrix, the target generator matrix and the generator matrix in the intermediate iterative process. Optionally, the memory 4002 is used to store the partial sub-matrixes of the target generator matrix except the identity matrix with the first K rows and K columns.

Optionally, the stopping condition includes that the minimum code distance reaches an upper bound, and the upper bound of the minimum code distance is determined by the K and the N.

Optionally, the stopping condition includes that the code spectrum reaches an optimum, and the code spectrum includes the value of the minimum code distance in the generator matrix and the number of code words whose code weight is the minimum code distance.

Optionally, the stopping condition includes: on the basis that the minimum code distance reaches an upper bound, the code spectrum reaches an optimum; wherein, the upper bound of the minimum code distance is determined by the K and the N, and the The code spectrum includes the value of the minimum code distance in the generator matrix and the number of codewords whose code weight is the minimum code distance.

The target generator matrix is the generator matrix shown in FIG. 4a to FIG. 37 .

The processor 4001 may be a central processing unit (CPU), a network processor (NP), or a combination of CPU and NP.

The processor 4001 may further include a hardware chip. The above hardware chip may be an application-specific integrated circuit (ASIC), a programmable logic device (PLD) or a combination thereof. The above-mentioned PLD may be a complex programmable logic device (CPLD), a field-programmable gate array (FPGA), a generic array logic (GAL) or any combination thereof.

The memory 4002 may include volatile memory (volatile memory), such as random-access memory (RAM); the memory 4002 may also include non-volatile memory (non-volatile memory), such as flash memory (flash memory) ), a hard disk drive (HDD), or a solid-state drive (SSD); the memory 4002 may also include a combination of the aforementioned types of memory.

Part or all of the above method embodiments of the present application may be implemented by a chip or an integrated circuit.

In order to realize the function of the generator matrix determining apparatus described in FIG. 39 or FIG. 40 , an embodiment of the present application further provides a chip, including a processor, for supporting the implementation of the generator matrix determination apparatus 3900 or the generator matrix determination apparatus 4000 The functions of the above method embodiments. In a possible design, the chip is connected to a memory or the chip includes a memory for storing program instructions and data necessary for the means for determining the generator matrix.

An embodiment of the present application provides a computer storage medium storing a computer program, where the computer program includes instructions for executing the foregoing method embodiments.

The embodiments of the present application provide a computer program product containing instructions, which, when executed on a computer, cause the computer to execute the above method embodiments.

As will be appreciated by those skilled in the art, the embodiments of the present application may be provided as a method, a system, or a computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) having computer-usable program code embodied therein.

The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the present application. It will be understood that each flow and/or block in the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to the processor of a general purpose computer, special purpose computer, embedded processor or other programmable data processing device to produce a machine such that the instructions executed by the processor of the computer or other programmable data processing device produce Means for implementing the functions specified in a flow or flow of a flowchart and/or a block or blocks of a block diagram.

These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory result in an article of manufacture comprising instruction means, the instructions The apparatus implements the functions specified in the flow or flows of the flowcharts and/or the block or blocks of the block diagrams.

These computer program instructions can also be loaded on a computer or other programmable data processing device to cause a series of operational steps to be performed on the computer or other programmable device to produce a computer-implemented process such that The instructions provide steps for implementing the functions specified in the flow or blocks of the flowcharts and/or the block or blocks of the block diagrams.

Although the preferred embodiments of the present application have been described, additional changes and modifications to these embodiments may occur to those skilled in the art once the basic inventive concepts are known. Therefore, the appended claims are intended to be construed to include the preferred embodiment and all changes and modifications that fall within the scope of this application.

Obviously, those skilled in the art can make various changes and modifications to the embodiments of the present application without departing from the spirit and scope of the embodiments of the present application. Thus, if these modifications and variations of the embodiments of the present application fall within the scope of the claims of the present application and their equivalents, the present application is also intended to include these modifications and variations.

Claims (14)

1. A method for determining a generator matrix, comprising:

performing iteration operation on the generated matrix one or more times until a stop condition is met, and obtaining a target generated matrix, wherein the size of the target generated matrix is K rows and N columns, the length of the information bit to be coded is K, and the code length is N;

the iterative operation comprises:

determining the minimum code distance in the code distances between any two row vectors in a generated matrix, wherein the minimum code distance is the code distance between a first row vector and a second row vector;

in the code word formed by the first row vector and the second row vector, setting any element in one all-zero element column from the (K +1) th column to the Nth column as 1.

2. The method of claim 1, wherein the stop condition comprises the minimum code distance reaching an upper bound, the upper bound for the minimum code distance being determined by the K and the N.

3. The method of claim 1, wherein the stopping condition comprises a code spectrum reaching an optimum, the code spectrum comprising a value of a minimum code distance in the generator matrix and a number of codewords having code weights of the minimum code distance.

4. The method of claim 1, wherein the stop condition comprises: on the basis that the minimum code distance reaches an upper bound, the code spectrum reaches the optimum; and the code spectrum comprises the value of the minimum code distance in the generating matrix and the number of code words with code weight being the minimum code distance.

5. The method according to any one of claims 1 to 4,

the N is 20, the K is 4, and the target generation matrix is:

1 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1 1 0 1 0 0 1 0 0 1 1 1 1 0 0 1 1 0 1 0 0 1 0 0 1 0 0 1 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 1 1 1 1 1 0 0

the N is 20, the K is 6, and the target generation matrix is:

1 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 1 1 1 0 1 0 0 0 0 1 1 1 0 1 1 0 0 0 1 1 1 0 1 0 0 1 0 0 0 0 1 1 1 1 1 1 0 1 1 0 0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 1 1 1 0 0 0 1 0 0 0 0 0 1 1 1 1 0 0 1 1 1 1 0 1 0 1 0

the N is 20, the K is 7, and the target generation matrix is:

1 0 0 0 0 0 0 1 0 1 1 1 1 0 1 0 1 0 1 0 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 1 0 1 0 0 1 0 0 0 0 0 0 1 0 1 1 1 0 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 1 1 0 1 1 0 0 0 0 1 0 0 0 1 1 1 0 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 1 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 1 1 1 0

the N is 24, the K is 6, and the target generation matrix is:

1 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 1 0 1 0 1 1 1 0 1 1 1 1 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 0 1 1 1 0 0 0 1 0 0 0 0 1 1 0 0 1 1 1 0 0 0 1 1 1 1 1 0 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1 1 1 0 1 0 0 0 0 1 0 0 0 0 0 1 1 1 0 1 1 1 0 0 1 0 1 0 1 0 1 0 1 1

the N is 24, the K is 7, and the target generation matrix is:

1 0 0 0 0 0 0 1 0 1 0 1 1 1 1 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 1 1 1 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1 0 0 1 1 1 1 0 0 0 1 0 0 0 1 0 1 1 1 1 1 0 0 0 0 1 0 0 1 1 0 0 0 0 0 1 0 0 1 1 1 1 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0 1 1 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 0 1

the N is 24, the K is 8, and the target generation matrix is:

1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 1 1 1 1 0 0 1 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 1 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 0 0 1 0 0 0 0 0 1 1 0 1 1 1 1 0 1 1 0 1 0 0 1 0 0 0 0 1 0 0 0 1 1 1 0 0 1 0 0 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 1 1 1 1 0 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 1 1 1 0 0 0 1 0 1 0 0

the N is 24, the K is 9, and the target generation matrix is:

1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 1 1 0 1 1 1 0 0 0 1 0 0 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 1 1 1 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1 1 1 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 1 0 1 1 0 0 0 0

the N is 32, the K is 5, and the target generation matrix is: generating a matrix as shown in FIG. 11;

the N is 32, the K is 7, and the target generation matrix is: generating a matrix as shown in fig. 12;

the N is 32, the K is 8, and the target generation matrix is: generating a matrix as shown in fig. 13;

the N is 32, the K is 9, and the target generation matrix is: generating a matrix as shown in fig. 14;

the N is 32, the K is 10, and the target generation matrix is: generating a matrix as shown in fig. 15;

the N is 32, the K is 12, and the target generation matrix is: generating a matrix as shown in fig. 16;

the N is 48, the K is 7, and the target generation matrix is: generating a matrix as shown in fig. 17;

the N is 48, the K is 11, and the target generation matrix is: generating a matrix as shown in fig. 18;

the N is 48, the K is 13, and the target generation matrix is: generating a matrix as shown in fig. 19;

the N is 48, the K is 19, and the target generation matrix is: generating a matrix as shown in fig. 20;

the N is 20, the K is 3, and the target generation matrix is:

1 0 0 1 1 1 0 1 1 0 1 0 0 1 1 0 0 1 0 1 0 1 0 0 1 1 1 1 0 1 1 1 1 1 1 0 1 0 0 0 0 0 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 1 1 0

the N is 20, the K is 5, and the target generation matrix is:

1 0 0 0 0 1 0 0 1 0 0 1 1 0 1 0 1 1 1 1 0 1 0 0 0 0 1 1 1 1 0 1 0 0 1 1 0 0 1 1 0 0 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 1 1 0 0 0 0 1 0 1 1 1 1 1 1 0 0 0 1 0 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1 1 1 1 1 1 0 0 1 0

the N is 20, the K is 8, and the target generation matrix is:

1 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0 0 1 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 1 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 0 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 1 1 0 0

the N is 20, the K is 9, and the target generation matrix is:

1 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 0 1 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 0 0 0 1 0 0 0 0 0 1 1 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 1 1 0

the N is 20, the K is 10, and the target generation matrix is:

1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 0 1

the N is 20, the K is 11, and the target generation matrix is:

1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 1 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1

the N is 20, the K is 12, and the target generation matrix is:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1

the N is 24, the K is 3, and the target generation matrix is:

1 0 0 0 1 1 1 0 0 0 1 1 1 1 1 0 1 1 1 1 0 0 1 0 0 1 0 0 0 1 0 1 1 1 0 0 1 1 1 1 0 1 0 1 1 0 0 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 1 1 0 1 1 1 1 0 0

the N is 24, the K is 4, and the target generation matrix is:

1 0 0 0 1 1 1 0 1 1 1 0 1 0 1 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 1 0 1 1 1 1 1 1 0 0 1 0 1 1 0 1 0 0 0 1 0 0 1 1 1 1 0 1 0 1 1 1 0 1 0 0 1 0 0 0 1 0 0 0 1 1 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0

the N is 24, the K is 5, and the target generation matrix is:

1 0 0 0 0 0 1 1 0 0 0 1 1 1 0 0 1 1 0 1 1 1 0 1 0 1 0 0 0 1 1 1 0 1 1 0 0 0 0 1 0 1 0 0 1 1 1 1 0 0 1 0 0 0 1 1 0 1 1 1 1 0 1 1 1 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 1 1 0 0 0 1 1 1 1 1 0 1 1 0 0 0 0 0 1 1 0 0 1 1 0 0 1 1 1 1 1 1 0 0 1 0 0 1

the N is 24, the K is 10, and the target generation matrix is:

1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 1 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 1 0 1 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 0 1 1 1 0 0 0

the N is 24, the K is 11, and the target generation matrix is:

1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 1 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 0 1 1 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1

the N is 24, the K is 12, and the target generation matrix is:

1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 0 0 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 1 1 1 0 1

the N is 32, the K is 3, and the target generation matrix is: generating a matrix as shown in fig. 34;

the N is 32, the K is 4, and the target generation matrix is: generating a matrix as shown in FIG. 35;

the N is 32, the K is 6, and the target generation matrix is: generating a matrix as shown in fig. 36;

the N is 48, the K is 6, and the target generation matrix is: the matrix is generated as shown in fig. 37.

6. The method of any one of claims 1 to 5, further comprising:

coding the information bits to be coded according to the target generating matrix;

and transmitting the coded bit sequence.

7. An apparatus for determining a generator matrix, comprising:

the processing unit is used for executing iterative operation on the generation matrix once or for multiple times until a stop condition is met, and obtaining a target generation matrix, wherein the size of the target generation matrix is K rows and N columns, the length of the information bit to be coded is K, and the code length is N;

the processing unit, when performing the iterative operation, is specifically configured to:

determining the minimum code distance in the code distances between any two row vectors in a generated matrix, wherein the minimum code distance is the code distance between a first row vector and a second row vector;

in the code word formed by the first row vector and the second row vector, setting any element in one all-zero element column from the (K +1) th column to the Nth column as 1.

8. The apparatus of claim 7, wherein the stop condition comprises the minimum code distance reaching an upper bound, the upper bound for the minimum code distance being determined by the K and the N.

9. The apparatus of claim 7, wherein the stopping condition comprises a code spectrum reaching an optimum, the code spectrum comprising a value of a minimum code distance in the generator matrix and a number of codewords having code weights of the minimum code distance.

10. The apparatus of claim 7, wherein the stop condition comprises: on the basis that the minimum code distance reaches an upper bound, the code spectrum reaches the optimum; and the code spectrum comprises the value of the minimum code distance in the generating matrix and the number of code words with code weight being the minimum code distance.

11. The apparatus according to any one of claims 7 to 10, wherein the target generator matrix is the target generator matrix according to claim 5.

12. An apparatus for determining a generator matrix, comprising:

a memory for storing a program;

a processor for executing the program stored in the memory, the processor being configured to perform the method of any of claims 1-6 when the program is executed.

13. The apparatus of claim 12, wherein the means for generating the matrix is a chip or an integrated circuit.

14. A computer-readable storage medium having computer-readable instructions stored thereon which, when read and executed by a computer, cause the computer to perform the method of any one of claims 1-6.

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