CN111277354B

CN111277354B - Coding and decoding method and related device of low-density parity check LDPC code

Info

Publication number: CN111277354B
Application number: CN201811473706.4A
Authority: CN
Inventors: 基多·蒙托里西; 塞吉奥·贝勒迪多; 林伟; 辛岩
Original assignee: Huawei Technologies Co Ltd
Current assignee: Huawei Technologies Co Ltd
Priority date: 2018-12-04
Filing date: 2018-12-04
Publication date: 2023-03-10
Anticipated expiration: 2038-12-04
Also published as: WO2020114337A1; CN111277354A

Abstract

The application provides a coding and decoding method and device of a parity check LDPC code. According to the scheme of the application, LDPC coding is carried out on 8064 information bits according to a parity check H matrix, the LDPC code with the code rates of R =1/2,5/8,3/4,13/16,7/8 is obtained through coding, wherein the parity check H matrix is a (n + s-k) x (n + s) parity check matrix, the H matrix is divided into a Z-dimensional sub-square matrix, the Z value is 64 or 42, the sub-square matrix is a cyclic shift or null matrix of a unit matrix, s is the number of columns corresponding to the bits to be shortened and the H matrix and is a positive integral multiple of Z.

Description

Coding and decoding method and related device of low-density parity check LDPC code

Technical Field

The present invention relates to the field of communications technologies, and in particular, to a coding and decoding method and a related apparatus for a low density parity check LDPC code.

Background

The main research goal of Wireless Local Area Network (WLAN) standard ieee802.11ad/ay is to improve the user experience in the large bandwidth scenario of 60 gigahertz (gigahz, GHz), including improving the average throughput of the user and the energy usage efficiency of the battery-powered device. The 60GHz large bandwidth scenario needs to support high-speed reliable transmission of data, video and other services on limited frequency and power resources, so a channel coding and decoding scheme with high reliability and high efficiency is required. In the field of channel coding, turbo codes and Low-density parity-check (LDPC) codes are two of the most sophisticated and widespread channel coding methods, both of which have performance close to Shannon (Shannon) limit and have been widely applied to the field of communications. Compared to Turbo codes, LDPC codes have: a good error code performance can be obtained without a deep interleaver; the frame error rate performance is better; the error leveling is greatly reduced; the parallel decoding is supported to increase the throughput, the decoding time delay is small, and the like.

Therefore, the LDPC code has become a standard channel coding scheme of a low-frequency short-range WLAN communication system such as ieee802.11n/ac/ax, and has also become a channel coding scheme of a 60GHz high-frequency short-range WLAN communication system such as ieee802.11ad/ay. Based on this, it is also considered to design a new LDPC code for the next generation 60GHz WLAN system to further improve the reliability and system performance of the next generation WLAN system.

Disclosure of Invention

In a first aspect, the present application provides a method for encoding a low density parity check LDPC code, including: performing LDPC encoding on 8064 information bits according to the parity check H matrix to obtain an encoded code word C, wherein the code length of the code word C is n, the code rate R is k/n, and n is a positive integer larger than k; the H matrix is a parity check matrix of (n + s-k) x (n + s), the H matrix is divided into a sub-square matrix with Z x Z dimension, the Z value is 64 or 42, the sub-square matrix is a cyclic shift or null matrix of a unit matrix, and s is a positive integer multiple of Z, wherein s is the number of columns corresponding to the bits to be shortened and the H matrix. Based on the scheme, a new LDPC code with longer code length can be obtained, the error rate can be reduced, the calculation complexity can be reduced, and the performance and the reliability of the system can be further improved.

In a possible implementation method, s bits to be shortened are filled before the 8064 information bits to obtain (s + k) bits to be encoded, and the values of the s bits to be shortened are 0; performing LDPC encoding on the (s + k) bits to be encoded to obtain encoded code words C ₁ Said code word C ₁ The code length of (s + n); deleting the codeword C ₁ The s bits to be shortened in the H matrix are obtained as the codeword C, where the s bits to be shortened correspond to the first s columns of the H matrix. By filling s bits to be shortened with the value of 0 before k information bits, the decoding performance can be effectively improved, and the bit error rate or the code error word rate can be reduced.

In a second aspect, the present application provides a decoding method for a low density parity check LDPC code, including: obtaining a code word C subjected to LDPC coding, filling s bits to be shortened in front of the code word C to form the code word C with the code length of (s + n) ₁ Using parity check H matrix to code word C ₁ Decoding is carried out to obtain k decoded information bits; wherein the H matrix is (n + s-k) x (n + s) parity check matrix, and the parity check matrix H is divided into square matrixes of ZxZThe square matrix is a cyclic shift of the identity matrix or a null submatrix with all zero entries. s is the number of columns corresponding to the bits to be shortened and the H matrix and is a positive integer multiple of Z.

Here, the identity matrix is denoted as P0, and the cyclic permutation matrix Pi of the identity matrix P0 is referred to as a cyclic shift matrix by cyclically shifting i elements to the right of the identity matrix P0. Optionally, Z has a value of 64 or 42.

In one possible implementation, the parity check H matrix is used to align the code words C ₁ Decoding to obtain decoded k information bits, including: using parity check H matrix to code word C ₁ And after decoding, obtaining (s + k) decoding bits, deleting the first s bits to be shortened in the (s + k) decoding bits, and obtaining decoded k information bits, wherein the values of the s bits to be shortened are 0. By filling s bits to be shortened with the value of 0 before k information bits, the decoding performance can be effectively improved, and the bit error rate or the code error word rate can be reduced.

With reference to the first aspect or the second aspect or possible implementation methods thereof, the decoding method or the encoding method may be applied in a high frequency wireless communication local area network, for example, a 60ghz wireless communication system.

With reference to the first aspect or the second aspect, in one possible implementation manner, the parity check H matrix may be any one shown in example one to example ten. The parity check H matrix can also be represented in other forms, and the order of rows and columns in any one H matrix can be interchanged, and the order of columns and columns can also be interchanged.

In a third aspect, the present application provides an encoding apparatus for a low density parity check LDPC code, the apparatus having a function of implementing the encoding side referred to in the first aspect above. The function can be realized by hardware, and can also be realized by executing corresponding software by hardware. The hardware or software includes one or more units corresponding to the above functions.

In one possible implementation, when the apparatus comprises: a processor and a memory, the processor being configured to support the encoding apparatus to perform the respective functions of the method of the first aspect described above. The memory is for coupling with the processor and holds the program instructions and data necessary for the encoding device.

In another possible implementation, the apparatus includes: the device comprises a generating module, a coding module and an input and output module; the generating module is used for generating k information bits; the coding module is used for carrying out LDPC coding on the k information bits according to the parity check H matrix to obtain a coded code word C, wherein the code length of the code word C is n, and the code rate R is k/n; an input/output module 1003, configured to output the codeword C.

In yet another possible implementation, the apparatus includes: a processor, a memory, a sending module, a receiving module, a radio frequency module, and an antenna, configured to support the encoding apparatus to perform corresponding functions in the method of the first aspect.

In a fourth aspect, the present application provides an apparatus for decoding a low density parity check LDPC code, the apparatus having a function of implementing the decoding side referred to in the second aspect above. The function can be realized by hardware, and can also be realized by executing corresponding software by hardware. The hardware or software includes one or more units corresponding to the above functions.

In one possible implementation, when the apparatus comprises: a processor and a memory, the processor being configured to support the decoding means to perform the respective functions of the second aspect described above. The memory is for coupling with the processor and holds the program instructions and data necessary for the encoding device. Optionally, the memory may be located inside the processor and is an internal memory, and may also be located outside the processor and is an external memory.

In another possible implementation, the apparatus includes: the input/output module, the filling module and the decoding module; an input/output module for obtaining a codeword C to be decoded ₁ Comprising n codeword bits; the filling module is used for filling s bits to be deleted before n code word bits to form (s + n) bits to be decoded, and the value of the s bits to be deleted is 0; and the decoding module is used for carrying out LDPC decoding on the (s + n) bits to be decoded according to the parity check H matrix to obtain k decoded bits.

In yet another possible implementation, the apparatus includes: the device comprises a processor, a memory, a sending module, a receiving module, a radio frequency module and an antenna, and is used for supporting the coding device to execute corresponding functions in the method.

The processor mentioned in any of the above mentioned embodiments may be a general-purpose Central Processing Unit (CPU), a microprocessor, an application-specific integrated circuit (ASIC), or one or more integrated circuits for controlling the execution of programs of the spatial multiplexing method in the above mentioned aspects.

In a fifth aspect, the present application provides a computer-readable storage medium having instructions stored therein, the instructions being executable by one or more processors on a processing circuit. When run on a computer, cause the computer to perform the method of the first or second aspect described above.

A sixth aspect provides a computer program product comprising instructions for implementing the method of the first or second aspect, which when run on a computer causes the computer to perform the method of the first or second aspect or any possible implementation thereof. The computer program product may be stored in whole or in part on a storage medium packaged in the processor, or may be stored in whole or in part in a storage medium packaged outside the processor.

In a seventh aspect, an embodiment of the present application provides a wireless communication system, where the system includes the encoding apparatus and the decoding apparatus related to the foregoing aspects.

In an eighth aspect, a chip is provided, which includes a processor for calling up and executing instructions stored in a memory from the memory, so that a communication device in which the chip is installed executes the method in the above aspects. In a ninth aspect, there is provided another chip comprising: the input interface, the output interface, the processor, and optionally the memory, are connected via an internal connection path, the processor is configured to execute codes in the memory, and when the codes are executed, the processor is configured to perform the method in the above aspects.

A tenth aspect provides a further chip comprising one or more processing circuits, and an input-output interface. When the chip is applied to a coding device, the one or more processing circuits can be used for coding according to a parity check H matrix, and the input and output interface can be used for outputting a coded code word C; when the chip is applied to a decoding device, the one or more processing circuits can be used for decoding according to the parity check H matrix, and the input/output interface can be used for inputting a code word C to be decoded and also used for outputting decoded information bits.

In an eleventh aspect, an apparatus is provided for implementing the method in the above embodiments.

Compared with a 5G NR LDPC code, the LDPC coding method can reduce the error code rate and the calculation complexity, and further improve the reliability and the performance of a system.

Drawings

Fig. 1 is a schematic view of an application scenario provided in an embodiment of the present application;

fig. 2 is a schematic flow chart of an LDPC encoding method provided in an embodiment of the present application;

fig. 3 is a circular shift matrix with a size of 4 × 4 provided in an embodiment of the present application;

fig. 4 is a schematic flow chart of an LDPC decoding method according to an embodiment of the present application;

fig. 5 is a 20 rows and 146 columns mother matrix corresponding to a parity check H matrix provided in the embodiment of the present application;

FIG. 6 is an example of an LDPC encoding method according to an embodiment of the present application;

fig. 7 is an example of an LDPC decoding method provided in an embodiment of the present application;

FIG. 8 is a comparison of bit error rate simulation performance of a first set of LDPC codes and a 5G NR LDPC code provided by an embodiment of the present application;

FIG. 9 is a comparison of bit error rate simulation performance of a second set of LDPC codes and a 5G NR LDPC code provided by an embodiment of the present application;

fig. 10 is a schematic diagram of an LDPC code encoding apparatus according to an embodiment of the present application;

FIG. 11 is a diagram illustrating an apparatus for encoding an LDPC code according to an embodiment of the present application;

fig. 12 is a schematic diagram of an LDPC code decoding apparatus according to an embodiment of the present application;

FIG. 13 is a schematic diagram of another LDPC decoding apparatus according to an embodiment of the present application;

fig. 14 is a schematic diagram of a communication device according to an embodiment of the present application.

Detailed Description

The terminology used in the description of the embodiments section of the present application is for the purpose of describing particular embodiments of the present application only and is not intended to be limiting of the present application.

The embodiment of the application provides a low-density parity check LDPC code coding and decoding method and a coding and decoding device. It should be understood that the technical solutions of the embodiments of the present application can be applied to various mobile communication systems, for example: universal Mobile Telecommunications System (UMTS), worldwide Interoperability for Microwave Access (WiMAX) communication system, and future 5G (5G) communication system, and the like. The technical scheme of the embodiment of the application can also be applied to a Wireless Local Area Network (WLAN), and the embodiment of the application can be applied to any one of the 802.11 series protocols of the international Institute of Electrical and Electronics Engineers (IEEE) currently adopted by the WLAN. For example, to the 802.11ay standard, or to the 802.11ay next generation standard, etc. The encoding device and the decoding device in the embodiment of the present application may be network nodes in the communication system, and may also be chips in the network nodes in the communication system.

The embodiments of the present application take a WLAN communication system as an example for description. The WLAN may include one or more Basic Service Sets (BSSs), and a network node in the BSS includes an Access Point (AP) and a Station (STA), so that the encoding apparatus and the decoding apparatus in the embodiment of the present application may be the AP or the STA in the WLAN system, and may also be a chip located in the AP or the STA. The scheme of the embodiment of the application can be applied to communication between the AP and the STA, one-to-one communication between the STA and the STA, and one-to-many and many-to-many communication. For example, communication may be between one AP and one STA (e.g., as shown in the left side of fig. 1), simultaneous communication between an AP and multiple STAs (e.g., as shown in the right side of fig. 1), simultaneous communication between multiple APs and multiple STAs, or simultaneous communication between multiple STAs and an AP.

The AP is a communication device having a wireless transceiving function, and may be a directional multi-gigabit (DMG) AP/PCP, an enhanced directional multi-gigabit (EDMG) AP/PCP, or an AP supporting 60GHz, but the embodiment of the present invention is not limited thereto. The AP may also be referred to as a base station. The STA may be a communication device having a wireless transceiving function, and for example, may be a wireless communication device supporting 60GHz communication. The STA may also be referred to as a subscriber unit, access terminal, mobile station, remote terminal, mobile device, user terminal, wireless communication device, user agent, user device, or User Equipment (UE).

The technical solutions of the embodiments of the present application will be further described in detail below with reference to more drawings.

Fig. 2 shows an encoding method of a low density parity check LDPC code provided in an embodiment of the present application, and optionally, the method may be applied to a high frequency wireless local area network communication system, for example, a 60GHz wireless local area network communication system, and the method includes:

s201, acquiring k information bits, k =8064;

optionally, the encoding device fills s bits to be shortened before the k information bits, and the values of the s bits to be shortened are 0, so as to form (s + k) bits to be encoded. Wherein s is an integer greater than or equal to 0, and s is a positive integer multiple of Z.

In one example, the k information bits may all be a payload; in yet another example, some of the k information bits may be payload bits, and the remaining bits may be padding bits, and the payload bits and the remaining bits together constitute k information bits to be encoded.

S202, according to the parity check H matrix, performing LDPC coding on the k information bits to obtain a code word C subjected to the LDPC coding, wherein the code length of the code word C is n, the code rate R is k/n, and n is a positive integer larger than k;

specifically, the H matrix is a parity check matrix of (n + s-k) × (n + s). Wherein s is the number of columns of the H matrix corresponding to the bits to be shortened. In the embodiment of the present application, the codeword may also be referred to as a coded bit sequence.

Optionally, S203, the encoding apparatus outputs the encoded codeword C.

In one example, the encoding apparatus may process the codeword C and then send the processed codeword C; in another example, the encoding apparatus may output the codeword C to the rf circuit for processing and then transmitting.

Optionally, (k + s) bits to be coded are LDPC-coded based on the parity check matrix to generate (n-k) parity check bits. The (k + s) bits to be coded and the (n-k) check bits form a code word C with the code length of (s + n) ₁ Deleting code word C ₁ The first s bits to be shortened in the sequence are obtained to obtain a code word C with the code length of n, and the code word C comprises (n-k) parity check bits and k information bits. The first s bits to be shortened correspond to the first s columns in the parity check H matrix, and the code rate R is k/n. It should be noted that, during encoding, the values of the s bits are all '0', the value of the s bits in the encoded codeword is still 0, "shorten" refers to deleting the s bits whose value to be shortened is '0', and thus the deleted bits may also be referred to as shortened bits.

The parity check matrix H may be further divided into sub-square matrices of size ZxZ. The sub-square matrix is a cyclic shift of the identity matrix or a null sub-matrix with all zero entries. The identity matrix is denoted as P0, and the cyclic permutation matrix Pi of the identity matrix P0 is referred to as a cyclic shift matrix (CPM) by shifting the identity matrix P0 by i elements cyclically to the right. The index i of the cyclic shift matrix CPM indicates the number of bits of the identity matrix cyclically shifted to the right.

Z is the size of the cyclic shift matrix CPM or the sub-square. Optionally, in this embodiment, the size of the sub-square matrix is 64 or 42. For convenience of description, taking a 4x4 CPM as an example, P0, P1, P2, and P3 may be as shown in fig. 3, and similarly, a 64x64 CPM and a 42x42 CPM may be obtained by referring to fig. 3, and are not described herein again.

The matrix form of the parity check H matrix is represented by a ZxZ order square matrix, which can be called a mother matrix, wherein the mother matrix comprises (n + s-k)/Z rows and (n + s)/Z columns, and each element of the mother matrix is a ZxZ order square matrix.

The embodiment of the application provides an LDPC coding method, which has longer code length, lower error rate and better performance, thereby effectively improving the system reliability and the transmission performance.

Fig. 4 shows a decoding method of a low density parity check LDPC code provided in an embodiment of the present application, including:

s401, obtaining a code word C subjected to LDPC coding;

the decoding apparatus receives the codeword C, wherein the codeword C has a length of n and includes k information bits and (n-k) parity bits.

The signal carrying the code word C can be processed by the radio frequency circuit part and then input into a decoding device for decoding; or the signal carrying the code word C is received by the decoding device, and is decoded after being processed by radio frequency.

S402, filling S bits to be shortened with a value of 0 in front of the code word C to obtain the code word C ₁ ；

Specifically, s bits to be shortened with a value of 0 are filled in front of the code word C to form the code word C with a code length of (s + n) ₁ ；

S403, using parity check H matrix to code word C ₁ Decoding is carried out to obtain k decoded information bits;

in particular, the parity check H matrix is used to match the code word C ₁ Decoding to obtain (s + k) decoded bits, puncturingDividing the first s bits of the (s + k) decoded bits to obtain decoded k information bits; specifically, the H matrix is an (n + s-k) × (n + s) parity check matrix, and the parity check matrix H can be further divided into sub-square matrices of size ZxZ. The sub-square matrix is a cyclic shift of the identity matrix or a null sub-matrix with all zero entries. The identity matrix is denoted as P0, and the cyclic permutation matrix Pi of the identity matrix P0 is referred to as a cyclic shift matrix by cyclically shifting the identity matrix P0 by i elements to the right. The index i of the cyclic shift matrix CPM indicates the number of bits of the identity matrix cyclically shifted to the right. And Z is the size of a sub-square matrix or a cyclic shift matrix. Optionally, in this embodiment of the present application, the value of Z is 64 or 42. The matrix form of the parity check matrix is represented by a ZxZ order square matrix, which can be called a mother matrix, wherein the mother matrix comprises (n + s-k)/Z rows and (n + s)/Z columns, and each element of the mother matrix is a ZxZ order square matrix.

Compared with the 802.11ay standard and the 802.11ad standard, the LDPC code coding method with longer code length is designed, so that the code error rate is lower, and the reliability and the system performance of a communication system are further improved. And s bits to be shortened are filled before k information bits, which is beneficial to improving the decoding performance of the decoding device and reducing the bit error rate or the code error word rate.

The following further describes two groups of LDPC code encoding schemes provided in the embodiments of the present application, specifically including the design of parity check matrix.

A first set of LDPC code coding schemes: the code rates R are respectively R =7/8, 13/16,3/4,5/8,1/2, and the CPM is 64x64;

second group of LDPC code coding schemes: the code rates R are respectively R =7/8, 13/16,3/4,5/8,1/2, and the CPM is 42x42; wherein, the information bit length of the two groups of LDPC codes is k =8064 bits.

First, a first group of LDPC code coding schemes is introduced, wherein the code rates R are R =7/8, 13/16,3/4,5/8,1/2 respectively, CPM is 64x64, and the information bit length k =8064.

Example one: the code rate is 7/8, the size of a cyclic shift matrix (CPM) is 64, and the information bit length is k =8064 bits.

Code rate R =7/8 LDPC code, whose number of columns of the total parity H matrix N1= (N + s), N1 is 9344, the number of columns of the corresponding mother matrix N0= N1/64=146, the number of rows of the total parity H matrix M1= (N + s-k), M1 is 1280, the number of rows of the corresponding mother matrix M0= M1/64=20, k =8064 information bits correspond to 8064 columns of the H matrix, and k/Z =20 columns of the mother matrix. The maximum row weight of the parity check H matrix is 23, i.e., a maximum of 231 s in each row of the H matrix.

1152 parity check bits are generated according to the parity check H matrix, and the code word C of the LDPC code with the code length of n1=9344 is obtained ₁ Code word C ₁ Comprises s bits to be shortened, 8064 information bits and 1152 parity check bits; to C ₁ Shorten, i.e. delete C ₁ The first s bits to be shortened are obtained, and a shortened code word C is obtained, wherein the code word C comprises 8064 information bits and 1152 parity check bits, the real code length of the code word C is n =9216 bits, and the required shortening bits are C ₁ Is the C corresponding to the first 2 columns of the mother matrix, the first s =128 bits ₁ The first 128 bits, the first 128 bits having a value of 0.

Below, a parity check H matrix with a code rate of 7/8 is given, and the matrix form of the parity check H matrix can be expressed as the form of the 0 th row to the 19 th row, in which the number of rows and the number of columns both start from 0. Each number in the ith row as follows represents a column position in which the value in the 64 th i row of the parity check H matrix is '1', and 0. Ltoreq. I.ltoreq.19. The position from the (64i + 1) th row to the '1' th row in the (64i + 63) th row in the H matrix is obtained by performing cyclic shift on the 64i th row in the H matrix according to a cyclic shift matrix (CPM). For example, the numeral 43 in the 0 th row indicates that the position of the 43 th column in the 0 th row of the parity H matrix takes on a value of '1', and the numeral 103 in the 0 th row indicates that the position of the 103 th column in the 0 th row of the parity H matrix takes on a value of '1'. The position of the 43 th column in the 0 th row of the H matrix is '1', and a column position of 1 in the 1 st row of the H matrix is 44 through cyclic shift according to a cyclic shift matrix (CPM), and so on, and the column position of 1 in the 21 st row of the H matrix is 0.

According to the above rule, the parity check matrix H is expressed as follows:

as mentioned above, the 128 bits corresponding to the first 128 columns of the parity check H matrix need to be shortened, i.e. the bits corresponding to the 128 columns before encoding are all '0', and the '0' bits are deleted after encoding is completed. The H matrix may also be represented in the form of a mother matrix. As shown in fig. 5. The mother matrix comprises 20 rows and 146 columns, and the rows and the columns of the mother matrix are numbered from 0, namely 0 th row to 19 th row and 0 th column to 145 th column. Each element in the mother matrix is a 64x64 order square submatrix, which is a cyclic permutation of the identity matrix or a null submatrix with all zero entries. In fig. 5, the blank part represents an all-zero matrix of 64x64, and the non-zero value represents a cyclic shift coefficient of the 64x64 cyclic shift matrix. For example, a non-zero value 43 in the 1 st row and 1 st column in the mother matrix indicates that the cyclic shift coefficient of the cyclic shift matrix is 43, that is, the number of bits of the unit matrix cyclically shifted to the right is 43, and a cyclic shift matrix P43 is obtained. The 128 bits to be shortened correspond to the first 2 columns (0 th column and 1 st column) in the mother matrix, the k information bits correspond to the 2 nd to 127 th columns of the mother matrix, and the parity bits correspond to the 128 th to 145 th columns of the mother matrix. It should be noted that there may be other variations of the H matrix, for example, the order of the rows in the 0 th row to the 19 th row in the H matrix may be interchanged, that is, the order of all the rows in the H matrix is not limited to the case given in the example one, for example, 20 rows of the H matrix may be: line 19, line 18, line 17, line …, line 0; or, line 1, line 2, …, line 19, line 0, etc. The order of the columns in the H matrix may be interchanged, and the embodiments of the present application are not particularly limited.

Example two: the code rate is 13/16, the size of a cyclic shift matrix (CPM) is 64, and the information bit length is k =8064 bits.

LDPC code with code rate R =13/16, the number of columns of the parity H matrix N1= (N + s), N1 is 10176, the number of columns corresponding to the mother matrix N0= N1/64=159, the number of rows of the parity H matrix M1= (N + s-k), M1 is 2112, the number of rows corresponding to the mother matrix M0= M1/64=33, k information bits correspond to k columns of the H matrix, corresponding to k/Z columns of the mother matrix. The maximum row weight of the parity check H matrix is 16, i.e., a maximum of 161 s in each row of the H matrix.

Generating 1920 parity check bits according to the parity check H matrix to obtain the LDPC code word C with the code length of n0=10176 ₁ To C ₁ Shortening the first s bits to obtain a shortened code word C, wherein the real code length of the code word C is n =9984 bits, and the required shortened bits are C ₁ Is the C corresponding to the first 3 columns of the mother matrix, the first s =192 bits ₁ The first 192 bits, which first 192 bits take the value 0.

Below, a parity check H matrix with a code rate of 13/16 is given, and the matrix form of the parity check H matrix can be expressed as the form of the 0 th row to the 32 th row in which the number of rows and the number of columns both start from 0. As follows, each number in the ith row represents a column position of the parity check H matrix whose value in the 64 ith row is '1', and 0 ≦ i ≦ 32. The position from the (64i + 1) th row to the '1' th row in the (64i + 63) th row in the H matrix is obtained by performing cyclic shift on the 64i th row in the H matrix according to a cyclic shift matrix (CPM). For example, the numeral 17 in the 0 th row indicates that the position of the 17 th column in the 0 th row of the parity H matrix takes on a value of '1', and the numeral 156 in the 0 th row indicates that the position of the 156 th column in the 0 th row of the parity H matrix takes on a value of '1'. The position of the 17 th column in the 0 th row of the H matrix is '1', and the position of the 1 st column in the 1 st row of the H matrix is 18 through cyclic shift according to a cyclic shift matrix (CPM), and so on, and the position of the 1 st column in the 47 th row of the H matrix is 0. In addition, the '1' at the end of a line does not mean anything and can be deleted, i.e., the 0 th line: 17 156 413 1371 2211 2561 3397 3910 4614 6070 6244 6662 7213 7430 8128.

According to the above rule, the check matrix is expressed as follows:

as described above, 192 bits corresponding to the first 192 columns of the parity check H matrix need to be shortened, 192 bits corresponding to the 192 columns are all '0' during encoding, and the '0' bits are deleted after encoding is completed. I.e. the code word C output after encoding does not comprise the 192 bits to be shortened.

It is understood that the H matrix may also be represented in the form of a mother matrix. It should be noted that other variations of the H matrix are possible, the order of rows and columns in the H matrix may be interchanged, and the order of columns and rows in the H matrix may also be interchanged, and the embodiments of the present application are not particularly limited.

Example three: the code rate is 3/4, the size of a cyclic shift matrix (CPM) is 64, and the information bit length is k =8064 bits.

Code rate R =3/4 LDPC code, whose number of columns of the parity H matrix N1= (N + s), N1 is 11008, the number of columns corresponding to the mother matrix N0= N1/64=172, the number of rows of the parity H matrix M1= (N + s-k), M1 is 2944, the number of rows corresponding to the mother matrix M0= M1/64=46, k information bits correspond to k columns in the H matrix, corresponding to k/Z columns in the mother matrix. The maximum row weight of the parity check H matrix is 13, i.e., a maximum of 131 s in each row of the H matrix.

Generating 2688 parity check bits according to the parity check H matrix to obtain the LDPC code word C with the code length n0=11008 ₁ Code word C ₁ The method comprises the following steps: s bits to be shortened, 8064 information bits, 2688 parity bits; to C ₁ Shortening the first s bits to obtain a shortened code word C, wherein the real code length of the code word C is n =10752 bits and comprises 8064 bitsInformation bits and 2688 parity bits, the required shortening bits being C ₁ Is the first 4 columns of the mother matrix corresponding to C ₁ The first 256 bits, the first 256 bits having a value of 0.

A parity H matrix with a code rate of 3/4 is given below, and the matrix form of the parity H matrix can be expressed as the form of the 0 th row to the 45 th row in which the number of rows and the number of columns both start from 0. As follows, each number in the ith row represents a column position of the parity check H matrix whose value in the 64 ith row is '1', and 0 ≦ i ≦ 45. The position of '1' in the H matrix from the (64i + 1) th row to the (64i + 63) th row is obtained by cyclic shift of the 64i th row in the H matrix according to a cyclic shift matrix (CPM). For example, the numeral 53 in the 0 th row indicates that the position of the 53 th column in the 0 th row of the parity check H matrix takes a value of '1', and the numeral 199 in the 0 th row indicates that the position of the 199 th column in the 0 th row of the parity check H matrix takes a value of '1'. The position of the 53 th column in the 0 th row of the H matrix is '1', and a column position 54 with a value of 1 in the 1 st row of the H matrix can be obtained by cyclic shift according to a cyclic shift matrix (CPM), and so on, and a column position 0 with a value of 1 in the 11 th row of the H matrix. Further, ` 1 ` at the end of a line does not mean anything, and may be deleted.

According to the above rule, the parity check H matrix is expressed as follows:

as described above, 256 bits corresponding to the first 256 columns of the parity check H matrix need to be shortened, and the values of the bits corresponding to the 256 columns are all '0' during encoding, and the '0' bits are deleted after encoding is completed.

Example four: the code rate is 5/8, the size of a cyclic shift matrix (CPM) is 64, and the information bit length is k =8064 bits.

Code rate R =5/8 LDPC code, whose number of columns of the parity H matrix N1= (N + s), N1 is 13504, the number of columns of the corresponding mother matrix N0= N1/64=211, whose number of rows of the parity H matrix M1= (N + s-k), M1 is 5440, the number of rows of the corresponding mother matrix M0= M1/64=85, k information bits correspond to k columns of the H matrix, corresponding to k/Z columns of the mother matrix. The maximum row weight of the parity check H matrix is 8, i.e., a maximum of 81 s in each row.

Generating 4864 parity check bits according to the parity check H matrix to obtain the code word C of the LDPC code with the code length n0=13504 ₁ Code word C ₁ The method comprises the following steps: s bits to be deleted, 8064 information bits and 4864 parity bits; to C ₁ Shortening the first s bits to obtain a shortened code word C, wherein the real code length of the code word C is n =12928 bits, the code word C comprises 8064 information bits and 4864 parity check bits, and the required shortening bit is C ₁ Is the C corresponding to the first 8 columns of the mother matrix, the first s =576 bits ₁ The first 576 bits, which take the value 0.

A parity H matrix with a code rate of 5/8 is given below, and the matrix form of the parity H matrix can be expressed as the form of the 0 th row to 84 th row in which the number of rows and the number of columns both start from 0. As follows, each number in the ith row represents a column position of the parity check H matrix whose value in the 64 ith row is '1', and 0. Ltoreq. I.ltoreq.84. The position from the (64i + 1) th row to the '1' th row in the (64i + 63) th row in the H matrix is obtained by performing cyclic shift on the 64i th row in the H matrix according to a cyclic shift matrix (CPM). For example, the number 430 in the 0 th row indicates that the position of the 430 th column in the 0 th row of the parity H matrix takes a value of '1', and the number 1216 in the 0 th row indicates that the position of the 1216 th column in the 0 th row of the parity H matrix takes a value of '1'. The position of the 430 th column in the 0 th row of the H matrix is '1', and a column position of 1 in the 1 st row of the H matrix is 431 after cyclic shift according to a cyclic shift matrix (CPM), and so on, and a column position of 1 in the 18 th row of the H matrix is 384. Further, ` 1 ` at the end of a line does not mean anything, and may be deleted.

According to the above rule, the parity check H matrix is expressed as follows:

as described above, 576 bits corresponding to the first 576 columns of the parity check H matrix need to be shortened, and the values of the bits corresponding to the 576 columns are all '0' during encoding, and the '0' bits are deleted after the encoding is completed.

Example five: the code rate is 1/2, the size of a cyclic shift matrix (CPM) is 64, and the information bit length is k =8064 bits.

LDPC code with code rate R =1/2, the number of columns of the parity H matrix N1= (N + s), N1 is 17088, the number of columns corresponding to the mother matrix N0= N1/64=267, the number of rows of the parity H matrix M1= (N + s-k), M1 is 9024, the number of rows corresponding to the mother matrix M0= M1/64=141, k information bits correspond to k columns in the H matrix, corresponding to k/Z columns in the mother matrix. The maximum row weight of the parity check H matrix is 7, i.e., a maximum of 71 s in each row.

Generating 8064 parity check bits according to the parity check H matrix to obtain the LDPC code word C with the code length of n0=17088 ₁ Code word C ₁ The method comprises the following steps: s bits to be shortened, 8064 information bits and 8064 parity bits; to C ₁ And shortening the first s bits to obtain a shortened code word C, wherein the real code length of the code word C is n =16128 bits and comprises 8064 information bits and 8064 parity check bits. The required shortening bit is C ₁ Is the C corresponding to the first 15 columns of the mother matrix, i.e. the first s =960 bits ₁ The first 960 bits, the first 960 bits taking the value 0.

A parity H matrix with a code rate of 1/2 is given below, and the matrix form of the parity H matrix can be expressed as the form of the 0 th row to the 140 th row in which the number of rows and the number of columns both start from 0. As follows, each number in the ith row represents a column position of the parity check H matrix whose value in the 64 ith row is '1', and 0. Ltoreq. I.ltoreq.84. The position from the (64i + 1) th row to the '1' th row in the (64i + 63) th row in the H matrix is obtained by performing cyclic shift on the 64i th row in the H matrix according to a cyclic shift matrix (CPM). For example, the numeral 384 in the 0 th row indicates that the position of the 384 th column in the 0 th row of the parity H matrix takes a value of '1', and the numeral 2304 in the 0 th row indicates that the position of the 2304 th column in the 0 th row of the parity H matrix takes a value of '1'. The position of the 384 th column in the 0 th row of the H matrix is '1', and cyclic shift is performed according to a cyclic shift matrix (CPM), so that a column position 385 with a value of 1 in the 1 st row of the H matrix can be obtained, and so on, and a column position 447 with a value of 1 in the 63 th row of the H matrix can be obtained. Further, ` 1 ` at the end of a line does not mean anything, and may be deleted.

According to the above rule, the parity check H matrix is expressed as follows:

as described above, 960 bits corresponding to the first 960 columns of the parity check H matrix need to be shortened, the values of the bits corresponding to the 960 columns are all '0' during encoding, and the '0' bits are deleted after encoding is completed.

Next, a second group of LDPC code coding schemes is introduced, the code rates R are R =7/8, 13/16,3/4,5/8,1/2, respectively, and CPM is 42x42, and the information bit length k =8064.

Example six: the code rate is 7/8, the size of a cyclic shift matrix (CPM) is Z =42, and the information bit length is k =8064 bits.

Code rate R =7/8 LDPC code, whose number of columns of the parity H matrix N1= (N + s), N1 is 9366, the number of columns corresponding to the mother matrix N0= N1/42=223, whose number of rows of the parity H matrix M1= (N + s-k), M1 is 1302, the number of rows corresponding to the mother matrix M0= M1/42=31, k information bits correspond to k columns in the H matrix, corresponding to k/Z columns in the mother matrix. The maximum row weight of the parity-check H matrix is 23, i.e., a maximum of 231 s in each row.

Generating 1176 parity check bits according to the parity check H matrix to obtain the LDPC code word C with the code length n0=9366 ₁ Code word C ₁ The method comprises the following steps: s bits to be shortened, 8064 information bits and 1176 parity bits; to C ₁ And shortening to obtain a shortened code word C, wherein the real code length of the code word C is n =9240 bits and comprises 8064 information bits and 1176 parity check bits. The required shortening bit is C ₁ The first s =126 bits, that is, the first 126 bits corresponding to the first 3 columns of the mother matrix, and the values of the first 126 bits are 0.

Below, a parity check H matrix with a code rate of 7/8 is given, and the matrix form of the parity check H matrix can be expressed as the form of the 0 th row to the 30 th row, in which the number of rows and the number of columns both start from 0. As follows, each number in the ith row represents a column position of the parity check H matrix 42 ith row whose median is '1', and 0. Ltoreq. I.ltoreq.30. The position from the (42i + 1) th row to the '1' th row in the (42i + 41) th row in the H matrix is obtained by performing cyclic shift on the 42i th row in the H matrix according to a cyclic shift matrix (CPM). For example, the numeral 27 in the 0 th row indicates that the position of the 27 th column in the 0 th row of the parity H matrix takes on a value of '1', and the numeral 42 in the 0 th row indicates that the position of the 42 th column in the 0 th row of the parity H matrix takes on a value of '1'. The position of the 27 th column in the 0 th row of the H matrix is '1', and the position of the 1 st column in the 1 st row of the H matrix is 28 through cyclic shift according to a cyclic shift matrix (CPM), and so on, and the position of the 1 st column in the 15 th row of the H matrix is 0. Note that "-1" at the end of a line does not mean anything, and can be deleted.

According to the above rule, the parity check H matrix is expressed as follows:

as mentioned above, 126 bits corresponding to the first 126 columns of the parity check H matrix need to be shortened, that is, bits corresponding to the 126 columns are all '0' during encoding, and these '0' bits are deleted after encoding is completed.

Example seven: the code rate is 13/16, the size of a cyclic shift matrix (CPM) is 42, and the information bit length is k =8064 bits.

LDPC code with code rate R =13/16, the number of columns of the parity H matrix N1= (N + s), N1 is 10164, the number of columns corresponding to the mother matrix N0= N1/42=242, the number of rows of the parity H matrix M1= (N + s-k), M1 is 2100, the number of rows corresponding to the mother matrix M0= M1/42=50, k information bits correspond to k columns in the H matrix, corresponding to k/Z columns in the mother matrix. The maximum row weight of the parity check H matrix is 15, i.e., a maximum of 151 s in each row.

Generating 1890 parity check bits according to the parity check H matrix to obtain the LDPC code word C with the code length of n0=10164 ₁ Code word C ₁ The method comprises the following steps: s bits to be shortened, 8064 information bits and 1890 parity bits; to C ₁ Shortening to obtain a shortened code word C, wherein a real code length of the code word C is n =9954 bits, and the method comprises the following steps: 8064 information bits and 1890 parity bits. The required shortening bit is C ₁ The first s =210 bits, that is, the first 210 bits corresponding to the first 5 columns of the mother matrix, and the value of the first 210 bits is 0.

Below, a parity check H matrix with a code rate of 13/16 is given, and the matrix form of the parity check H matrix can be expressed as the form of the 0 th row to the 49 th row, in which the number of rows and the number of columns both start from 0. As follows, each number in the ith row represents a column position of the parity check H matrix 42 ith row whose value is '1', and 0. Ltoreq. I.ltoreq.49. The position from row (42i + 1) to row (42i + 41) in the H matrix is obtained by cyclic shift of row 42i in the H matrix according to a cyclic shift matrix (CPM). For example, the numeral 48 in the 0 th row indicates that the position of the 48 th column in the 0 th row of the parity-check H matrix takes a value of '1', and the numeral 749 in the 0 th row indicates that the position of the 749 th column in the 0 th row of the parity-check H matrix takes a value of '1'. The position of the 48 th column in the 0 th row of the H matrix is '1', and the position of the 1 st column in the 1 st row of the H matrix is 49, and so on, and the position of the 1 st column in the 36 th row of the H matrix is 42, which can be obtained by performing cyclic shift according to a cyclic shift matrix (CPM). It should be noted that "-1" at the end of the line does not mean anything, and can be deleted.

According to the above rule, the parity check H matrix is expressed as follows:

as mentioned above, 210 bits corresponding to the first 210 columns of the parity check H matrix need to be shortened, that is, the bits corresponding to the 210 columns are all '0' during encoding, and the '0' bits are deleted after encoding is completed.

It is understood that the H matrix may also be represented in the form of a mother matrix. It should be noted that the H matrix may have other modifications, the order of rows and columns in the H matrix may be interchanged, and the order of columns and rows in the H matrix may also be interchanged, which is not specifically limited in the embodiments of the present application.

Example eight: the code rate is 3/4, the size of a cyclic shift matrix (CPM) is 42, and the information bit length is k =8064 bits.

Code rate R =3/4 LDPC code, whose number of columns of the parity H matrix N1= (N + s), N1 is 11046, the number of columns of the corresponding mother matrix N0= N1/42=263, whose number of rows of the parity H matrix M1= (N + s-k), M1 is 2982, the number of rows of the corresponding mother matrix M0= M1/42=71, k information bits correspond to k columns of the H matrix, corresponding to k/Z columns of the mother matrix. The maximum row weight of the parity check H matrix is 12, i.e., a maximum of 121 s in each row.

Generating 2688 parity check bits according to the parity check H matrix to obtain the code word C of the LDPC code with the code length n0=11046 ₁ Code word C ₁ The method comprises the following steps: s bits to be shortened, 8064 information bits and 2688 parity bits; to C ₁ And shortening to obtain a shortened code word C, wherein the real code length of the code word C is n =10752 bits and comprises 8064 information bits and 2688 parity check bits. The required shortening bit is C ₁ The first s =294 bits, that is, the first 294 bits corresponding to the first 7 columns of the mother matrix, and the first 294 bits take the value of 0.

A parity H matrix with a code rate of 3/4 is given below, and the matrix form of the parity H matrix may be expressed as the form of the 0 th row to the 70 th row in which the number of rows and the number of columns both start from 0. As follows, each number in the ith row represents a column position of the parity check H matrix whose value in the 42 ith row is '1', and 0 ≦ i ≦ 70. The position from the (42i + 1) th row to the '1' th row in the (42i + 41) th row in the H matrix is obtained by performing cyclic shift on the 42i th row in the H matrix according to a cyclic shift matrix (CPM). For example, the numeral 72 in the 0 th row indicates that the position of the 72 th column in the 0 th row of the parity H matrix takes on a value of '1', and the numeral 241 in the 0 th row indicates that the position of the 241 th column in the 0 th row of the parity H matrix takes on a value of '1'. The position of the 72 th column in the 0 th row of the H matrix is '1', and a column position 73 with a value of 1 in the 1 st row of the H matrix can be obtained by performing cyclic shift according to a cyclic shift matrix (CPM), and so on, and a column position 42 in the 1 st row of the H matrix is 12 th. Note that "-1" at the end of a line does not mean anything, and can be deleted.

According to the above rule, the parity check H matrix is expressed as follows:

as mentioned above, 294 bits corresponding to the first 294 columns of the parity check H matrix need to be shortened, that is, the 294 columns of bits are all '0' during encoding, and the '0' bits are deleted after encoding.

Example nine: the code rate is 5/8, the size of a cyclic shift matrix (CPM) is 42, and the information bit length is k =8064 bits.

Code rate R =5/8 LDPC code, whose number of columns of the parity H matrix N1= (N + s), N1 is 13440, the number of columns of the corresponding mother matrix N0= N1/42=320, whose number of rows of the parity H matrix M1= (N + s-k), M1 is 5376, the number of rows of the corresponding mother matrix M0= M1/42=128, k information bits correspond to k columns of the H matrix, corresponding to k/Z columns of the mother matrix. The maximum row weight of the parity check H matrix is 9, i.e., a maximum of 91 s in each row.

Generating 4872 parity check bits according to the parity check H matrix to obtain the LDPC code word C with the code length n0=13440 ₁ Code word C ₁ The method comprises the following steps: s bits to be shortened, 8064 information bits and 4872 parity bits; to C ₁ And shortening to obtain a shortened code word C, wherein the real code length of the code word C is n =12936 bits: 8064 information bits and 4872 parity bits. The required shortening bit is C ₁ The first s =504 bits are the first 504 bits corresponding to the first 12 columns of the mother matrix, and the values of the first 504 bits are 0.

Given below is a parity check H matrix with a code rate of 5/8, the matrix form of the parity check H matrix can be expressed as the form of the 0 th row to 127 th row, where the number of rows and the number of columns both start from 0. As follows, each number in the ith row represents a column position of the parity check H matrix 42 ith row whose value is '1', 0 ≦ i ≦ 127. The position from row (42i + 1) to row (42i + 41) in the H matrix is obtained by cyclic shift of row 42i in the H matrix according to a cyclic shift matrix (CPM). For example, a numeral 11 in the 0 th row indicates that the position of the 11 th column in the 0 th row of the parity H matrix takes a value of '1', and a numeral 239 in the 0 th row indicates that the position of the 239 th column in the 42i th row of the parity H matrix takes a value of '1'. The position of the 11 th column in the 0 th row of the H matrix is '1', and the position of the 1 st column in the 1 st row of the H matrix is 12 through cyclic shift according to a cyclic shift matrix (CPM), and so on, and the position of the 1 st column in the 31 th row of the H matrix is 0. Note that "-1" at the end of a line does not mean anything, and can be deleted.

According to the above rule, the parity check H matrix is expressed as follows:

as mentioned above, 504 bits corresponding to the first 504 columns of the parity check H matrix need to be shortened, that is, the bits corresponding to the 504 columns are all '0' during encoding, and the '0' bits are deleted after encoding is completed.

It is understood that the H matrix can also be represented in the form of a mother matrix. It should be noted that other variations of the H matrix are possible, the order of rows and columns in the H matrix may be interchanged, and the order of columns and rows in the H matrix may also be interchanged, and the embodiments of the present application are not particularly limited.

Example ten: the code rate is 1/2, the size of a cyclic shift matrix (CPM) is 42, and the information bit length is k =8064 bits.

Code rate R =1/2 LDPC code, whose number of columns of the parity H matrix N1= (N + s), N1 is 17052, number of columns corresponding to the mother matrix N0= N1/42=406, number of rows of the parity H matrix M1= (N + s-k), M1 is 8988, number of rows corresponding to the mother matrix M0= M1/42=214, k information bits correspond to k columns of the H matrix, corresponding to k/Z columns of the mother matrix. The maximum row weight of the parity check H matrix is 7, i.e., a maximum of 71 s in each row.

Generating 8064 parity check bits according to the parity check H matrix to obtain the code word C of the LDPC code with the code length of n0=17052 ₁ Code word C ₁ The method comprises the following steps: s bits to be shortened, 8064 information bits and 8064 parity bits; to C ₁ Shortening to obtain a shortened code word C, wherein the real code length of the code word C is n =16128 bits, and the method comprises the following steps: 8064 information bits and 4872 parity bits. The required shortening bit is C ₁ The first s =924 bits are the first 924 bits corresponding to the first 22 columns of the mother matrix, and the values of the first 924 bits are 0.

A parity H matrix with a code rate of 1/2 is given below, and the matrix form of the parity H matrix can be expressed as the form of the 0 th row to 213 th row in which the number of rows and the number of columns both start from 0. As follows, each number in the ith row represents a column position of the parity check H matrix with a value of '1' in the 42 ith row, and 0. Ltoreq. I.ltoreq.213. The position from the (42i + 1) th row to the '1' th row in the (42i + 41) th row in the H matrix is obtained by performing cyclic shift on the 42i th row in the H matrix according to a cyclic shift matrix (CPM). For example, the number 289 in the 0 th row indicates that the position of the 289 column in the 0 th row of the parity check H matrix takes a value of '1', and the number 924 in the 0 th row indicates that the position of the 924 column in the 0 th row of the parity check H matrix takes a value of '1'. The position of the 289 column in the 0 th row of the H matrix is '1', and a column position 290 of 1 in the 1 st row of the H matrix, and so on can be obtained through cyclic shift according to a cyclic shift matrix (CPM), and a column position 252 of 1 in the 5 th row of the H matrix. Note that "-1" at the end of a line does not mean anything, and can be deleted.

According to the above rule, the parity check H matrix is expressed as follows:

as mentioned above, the 924 bits corresponding to the first 924 columns of the parity check H matrix need to be shortened, that is, the 924 columns of bits are all '0' during encoding, and the '0' bits are deleted after encoding.

Fig. 6 shows an example of an encoding flow. After the encoding device produces k information bits, s bits to be shortened with the value of 0 can be filled in front of the k information bits to obtain (k + s) bits to be encoded. Further, according to any one of the H matrices provided in the foregoing embodiments, (k + s) bits to be coded are coded to obtain a codeword C ₁ The code length is n + s. Finally, the encoding device may delete the filled s bits to be shortened whose values are 0 to obtain the final codeword C with the code length n, and output the codeword C.

Fig. 7 shows an example of the decoding flow. The decoding device receives the signal of the code word C after channel transmission, and obtains the likelihood values of n bits through likelihood estimation, wherein the likelihood values may be probabilities or log-likelihood ratios. The likelihood values for the n bits include likelihood values for k information bits and likelihood values for (n-k) parity bits. Furthermore, the decoding device fills the likelihood values corresponding to the bits to be shortened with s values of 0 in front of the n-bit likelihood values to form (s + n) bits. Decoding likelihood values corresponding to (n + s) bits according to an H matrix used in encoding to obtain (k + s) bits; and finally, the decoding device carries out shortening processing to delete the first s bits to obtain k information bits.

In the embodiment of the application, the performance comparison analysis of the code error rate and the operation complexity is performed by taking a 5G new air interface (5G new radio,5G NR) LDPC code as a reference.

Fig. 8 shows a comparison of simulation performance of codeword error rates of the first group of LDPC codes and the 5G NR LDPC codes provided in the embodiments of the present application. Fig. 9 shows a comparison of simulation performance of codeword error rates of the second group LDPC codes and the 5G NR LDPC codes provided in the embodiments of the present application. The result curves shown in fig. 8 and fig. 9 are obtained by simulation under the same code rate and code length, wherein the information bit length is fixed to 8064, the cpm size is 64, and the maximum number of iterations is 50 by using a Min-Sum-Offset (Min-Sum-Offset) decoding algorithm of layered decoding, wherein an abscissa represents a Signal-to-noise ratio (SNR), an ordinate represents a codeword error rate, a black solid line is a simulation result curve of the codeword error rate of the LDPC coding scheme of the embodiment of the present application, a black circled solid line is a simulation result curve of the codeword error rate of the 5G NR LDPC, and a black line dotted line is the reference performance of the non-fast coding matrix. For example, as shown in three curves with a code rate R of 1/2 in fig. 8, when the signal-to-noise ratio SNR is equal, the code error rate of the LDPC code coding scheme proposed in the embodiment of the present application is significantly lower than that of the 5G NR LDPC. As can be seen from fig. 8 and 9, the code error rate performance of the first group of coding schemes and the second group of coding schemes in the embodiment of the present application is better than that of the 5G NR LDPC code rate performance under each code rate, and the lower the code rate is, the more significant the performance advantage is.

Table 1 shows a simulation performance comparison of the operation complexity of the first group LDPC code and the 5G NR LDPC code provided in the embodiment of the present application. Table 2 shows a simulation performance comparison of the operation complexity of the second group LDPC code and the 5G NR LDPC code provided in the embodiment of the present application. Wherein the first row in table 1 sequentially represents: a code Rate R (Rate), a column number K0 (K0 = K/Z) of K information bits of the LDPC code at the code Rate in the mother matrix, a column number C0 (C0 = n/Z) of a codeword C corresponding to S bits to be shortened in the mother matrix, a column number S0 (S0 = S/Z) of a check matrix to be punctured in the mother matrix corresponding to S bits to be shortened, a size Z of a cyclic shift matrix, and a column degree distribution d of the check matrix _v (i.e., the percentage of each column in all columns), the degree of parallelism distribution d _c (i.e., the percentage of each row weight in all rows), performance Gain (Gain), and Computational complexity percentage (ratio). Wherein: the Gain in performance (Gain) is referred to when the codeword error rate is 10 ^-3 Compared with the performance gain of the 5G NR LDPC scheme, the computation complexity percentage of the LDPC scheme of the embodiment of the application represents the percentage of the computation times required by the LDPC coding of the embodiment of the application and the computation times required by the 5G NR LDPC coding under the same parameters; the three numbers in the column degree distribution represent in sequence: column weight, total number of columns, and the ratio of the number of columns to the total number of columns, e.g., the first set of numbers in the first row in table 1: 2 7488.438202, which shows 7488 columns with a column weight of 2 and 0.438202. The calculation complexity represents the calculation times required by LDPC coding under the same parameters, and the advantage of the scheme of the embodiment of the application in the aspect of complexity compared with the 5G NR LDPC can be embodied by the calculation complexity percentage.

As can be seen from tables 1 and 2, the percentage of the computation complexity of the first group of coding schemes and the computation complexity of the 5G NR LDPC is less than 100%, that is, the computation complexity of the LDPC coding of the first group of coding schemes is lower than the computation complexity of the 5G NR LDPC coding; the percentage of the computation complexity of the second group of coding schemes and the computation complexity of the 5G NR LDPC is less than 100%, that is to say, the computation complexity of the LDPC coding of the second group of coding schemes is lower than the computation complexity of the 5G NR LDPC coding; therefore, the complexity of decoding operation of the first group of coding schemes and the second group of coding schemes in the embodiments of the present application is lower than that of the 5G NR LDPC code under the same parameter under various code rates, and the lower the code rate is, the more obvious the complexity advantage of the LDPC coding scheme provided in the embodiments of the present application is.

Therefore, the LDPC code provided by the embodiment of the application can effectively improve the performance and reliability of the system.

TABLE 1

TABLE 2

Referring to fig. 10, a schematic diagram of an LDPC code encoding apparatus 1000 according to an embodiment of the present application, where the LDPC code encoding apparatus 1000 may execute the method according to any one of the above aspects, may be a complete device, and may also be a chip or an integrated circuit in the device, and the LDPC code encoding apparatus 1000 includes: a generating module 1001, an encoding module 1002, and an outputting module 1003.

A generating module 1001 configured to obtain k information bits, where k =8064; the encoding module 1002 is configured to perform LDPC encoding on the k information bits according to the parity check H matrix to obtain an encoded codeword C, where a code length of the codeword C is n and a code rate R is k/n; the H matrix is a parity check matrix of (n + s-k) x (n + s) order, the H matrix is divided into a sub-square matrix of Z x Z order, Z is 64 or 42, and the sub-square matrix is an identity matrix P ₀ S is the number of bits to be shortened and is a positive integer multiple of Z; an input/output module 1003, configured to output the codeword C. In one example, the generating module 1001, the encoding module 1002, and the outputting module 1003 may be integrated in a processing unit, and the outputting module 1003 may be an interface circuit of the processing unit, and is used to input and output signaling or data for the processing unit to interact with other units.

Optionally, the apparatus further comprises: a filling module 1004, configured to fill s bits to be shortened before the k information bits to obtain k + s bits to be coded, where a value of the s bits to be shortened is 0; the encoding module is configured to perform LDPC encoding on the (s + k) bits to be encoded to obtain an encoded codeword C ₁ Said code word C ₁ The code length of (b) is n + s; a deletion module 1005: for deleting the code word C ₁ The s bits to be shortened in the H matrix are obtained as the codeword C, where the s bits to be shortened correspond to the first s columns of the H matrix.

It should be noted that, for different code rates, the parity check H matrix may refer to the foregoing examples one to ten or their modified forms, which are not described herein again.

Referring to fig. 11, an embodiment of the present application provides an LDPC code encoding apparatus 1100. The encoding apparatus 1100 includes: the processor 1101, optionally, also includes a memory 1102. Memory 1102 may be used to store a parity check H matrix. Processor 1101 may be configured to LDPC-encode the k information bits according to a parity-check H matrix to obtain an LDPC-encoded codeword c. Optionally, the processor may be further configured to determine an H matrix from the H matrices stored in the memory 1102 for LDPC encoding. Specifically, how to determine the H matrix, the processor may be selected according to a code rate or a service requirement, and the embodiment of the present application is not particularly limited.

Referring to fig. 12, an LDPC code decoding apparatus 1200 provided in an embodiment of the present application is a schematic diagram of an LDPC code decoding apparatus 1200, where the LDPC code decoding apparatus 1200 may execute the method in any one of the above aspects, may be a complete device, and may also be a chip or an integrated circuit in the device, and the LDPC code decoding apparatus 1200 includes: an input/output module 1201, a filling module 1202, and a decoding module 1203.

The input and output module 1201 acquires the code word C subjected to LDPC coding, wherein the code length is n; a padding module 1202, configured to pad s bits to be shortened with a value of 0 at the forefront of the codeword C to obtain the codeword C ₁ And the values of the s bits to be shortened are 0. A decoding module 1203, configured to decode the codeword C according to the parity check H matrix ₁ And performing LDPC decoding to obtain (s + k) decoded bits, and deleting the bits to be shortened with the first s values of 0 to obtain k information bits. The H matrix is a parity check matrix of (n + s-k) x (n + s) order, the H matrix is divided into a sub-square matrix of Z x Z order, Z is 64 or 42, and the sub-square matrix is an identity matrix P ₀ S is the number of bits to be shortened and is a positive integer multiple of Z;

in one example, the input/output module 1201, the padding module 1202, and the decoding module 1203 may be integrated in a processing unit, and the input/output module 1003 may be an interface circuit of the processing unit, and is used for inputting and outputting signaling or data for the processing unit to interact with other units.

It should be noted that, for different code rates, the parity check H matrix may refer to the foregoing examples one to ten, and details are not repeated here.

Referring to fig. 13, an embodiment of the present application provides an LDPC code decoding apparatus 1300. The decoding apparatus 1300 comprises: the processor 1301, optionally, also includes a memory 1302. A memory 1302 may be used to store a parity check H matrix. The processor 1301 may be configured to perform LDPC decoding on the codeword bits according to the parity check H matrix, so as to obtain information bits after LDPC decoding. Optionally, the processor may be further configured to determine an H matrix from the H matrices stored in the memory 1302, for performing LDPC decoding. Specifically, how to determine the H matrix, the processor may be selected according to a code rate or a service requirement, and the embodiment of the present application is not particularly limited. Optionally, the memory 1302 may be an internal memory integrated with the processor 1301, or an external memory coupled to the processor.

Fig. 14 shows a wireless communication apparatus 1400 in a wireless communication system, the apparatus 1400 comprising: processor 1401, transmitting module 1403, receiving module 1404, radio frequency module 1405, antenna 1406. Rf module 1405 and receive module 1404 may filter, amplify, demodulate, downconvert, digitize, and decode, etc. a signal received via antenna 1406) and provide input samples, and rf module 1405 and transmit module 1403 may encode, analog convert, filter, amplify, modulate, and upconvert a signal to be transmitted and transmit via antenna 1406. Optionally, the apparatus 1400 further comprises a memory 1402.

In one example, the apparatus 1400 may be configured as an encoding apparatus that performs LDPC encoding, and may perform any of the above-described aspects related to the method of encoding. Apparatus 1400 may be, for example, an access point AP (based on AP111 in fig. 1), a station (e.g., station 112 in fig. 1), etc., and may also be a chip within the access point AP and the station.

LDPC code encoder may also be included in the transmit module 1403 of apparatus 1400. The encoder may be configured to encode information bits to be transmitted to generate a codeword. In one example, the encoder may obtain k information bits, and perform LDPC encoding on the k information bits according to a parity check H matrix, thereby obtaining an LDPC encoded codeword c. For the parity check H matrix, reference may be made to the first to tenth examples, and one or more parity check H matrices may be selected according to the code rate for encoding, which is not described herein again. Codeword C is further processed by other circuits in transmit module 1403 and rf module 1405 and then output to antenna 1406 for transmission.

In another example, the apparatus 1400 may be configured as a decoding apparatus for performing LDPC encoding, and may perform any of the above-described aspects related to a method of decoding. Apparatus 1400 may be, for example, an access point AP (based on AP111 in fig. 1), a station (e.g., station 112 in fig. 1), etc., and may also be a chip within the access point AP and the station.

The receiving module 1404 of the apparatus 1400 may include an LDPC code decoder. The decoder may be configured to perform decoding processing on information bits to be transmitted to generate a codeword. In one example, the decoder may obtain codeword bits, and perform LDPC decoding on the codeword bits according to a parity-check H matrix, thereby obtaining LDPC decoded information bits. For the parity check H matrix, reference may be made to the first to tenth examples, and one or more parity check H matrices may be selected according to the code rate for decoding, which is not described herein again.

An embodiment of the present application further provides a computer program product, where the computer program product includes: computer program code which, when run by a computer, causes the computer to perform the method in the examples described above.

Embodiments of the present application further provide a computer-readable medium for storing a computer program, where the computer program includes instructions for executing the method in each of the above examples.

The embodiment of the present application further provides a chip, which includes a processor, configured to call and execute the instructions stored in the memory from the memory, so that a communication device in which the chip is installed executes the method in each of the above examples.

The embodiment of the present application further provides another chip, including: the system comprises an input interface, an output interface, a processor and a memory, wherein the input interface, the output interface, the processor and the memory are connected through an internal connection path, the processor is used for executing codes in the memory, and when the codes are executed, the processor is used for executing the method in each example.

The embodiment of the present application further provides another chip, which includes one or more processing circuits and an input/output interface. When the chip is applied to a coding device, the one or more processing circuits can be used for coding according to a parity check H matrix, and the input and output interface can be used for outputting a coded code word C; when the chip is applied to a decoding device, the one or more processing circuits can be used for decoding according to the parity check H matrix, and the input/output interface can be used for inputting a code word C to be decoded and also used for outputting decoded information bits.

The embodiment of the application also provides a device for realizing the method in the embodiments.

In the above embodiments, all or part of the implementation may be realized by software, hardware, firmware, or any combination thereof. When implemented in software, may be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the procedures or functions described in accordance with the present application are generated, in whole or in part. The computer may be a general purpose computer, a special purpose computer, a network of computers, or other programmable device. The computer instructions may be stored in a computer readable storage medium or transmitted from one computer readable storage medium to another computer readable storage medium, for example, the computer instructions may be transmitted from one website, computer, server, or data center to another website, computer, server, or data center by wire (e.g., coaxial cable, fiber optic, digital subscriber line) or wirelessly (e.g., infrared, wireless, microwave, etc.). The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device, such as a server, a data center, etc., that incorporates one or more of the available media. The usable medium may be a magnetic medium (e.g., floppy Disk, hard Disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid State Disk).

Claims

1. A method for encoding a Low Density Parity Check (LDPC) code, comprising:

acquiring k information bits, wherein k =8064;

performing LDPC coding on the k information bits according to the parity check H matrix to obtain a coded codeword C, wherein the code length of the codeword C is n, the code rate R is k/n, and n is a positive integer greater than k;

the H matrix is a parity check matrix of (n + s-k) x (n + s), the H matrix is divided into a sub-square matrix with the size of Z x Z, the value of Z is 64 or 42, the sub-square matrix is a cyclic shift or null matrix of a unit matrix, and s is a positive integer multiple of Z, wherein the number of columns corresponding to bits to be shortened and the H matrix is s;

the obtaining, according to the parity check H matrix, a codeword C obtained by LDPC encoding of the k information bits specifically includes:

filling s bits to be shortened before the k information bits to obtain (s + k) bits to be coded, wherein the values of the s bits to be shortened are 0;

performing LDPC encoding on the (s + k) bits to be encoded to obtain encoded code words C ₁ Said code word C ₁ Has a code length of (s + n), said code word C ₁ Comprising the s bits to be shortened, k information bits and (n-k) parity bits;

deleting the codeword C ₁ The s bits to be shortened in the H matrix are obtained as the codeword C, where the s bits to be shortened correspond to the first s columns of the H matrix.

2. The method of claim 1, wherein the method is applied in a wireless local area network communication system with 60 gigahertz (GHz).

3. The method of claim 1, wherein the code length n =9216, the code rate is R =7/8, the Z =64, and the H matrix is represented as:

line 0: 43 103 292 985 1077 1885 2266 2378 3195 3618 3740 4088 4595 5133 5301 6091 6297 6593 7029 7542 7841 7949 8128

Line 1: 5790 410 781 1235 1556 1958 2541 2823 3307 3845 4145 4716 5353 5509 6023 6191 6995 7122 7393 7666 8176 8192

Line 2: 22 115 195 875 1308 1800 2333 2372 2875 3265 3981 4099 4756 5111 5617 5792 6367 6673 7043 7635 7811 7960 8256

Line 3: 2779 374 897 1267 1766 2159 2655 3048 3395 3657 4053 4910 4964 5501 6184 6629 6719 7292 7445 8213 8277 8320 line 4: 61 102 448 832 1389 1728 2112 2809 3008 3456 3840 4288 4893 5120 5568 5952 6550 6848 7104 7336 7680 8064 8384

Line 5: 12 123 477 703 1458 1535 2032 2592 3024 3263 3647 4137 4479 5123 5409 6053 6222 6956 7563 7691 8328 8388 8448

Line 6: 36 125 345 704 1180 1567 1920 2528 2752 3462 3648 4466 4480 4928 5376 5760 6272 6656 7309 7759 8122 8448 8512

Line 7: 109 142 632 678 1130 1503 2202 2316 2746 2919 3476 3669 4226 4485 4955 5649 6116 6289 6989 7390 8117 8575 8576

Line 8: 43 83 397 895 1293 1677 2061 2573 3102 3405 3959 4237 4685 5255 5681 6193 6413 6859 7245 7704 7885 8420 8640

Line 9: 465 595 670 1420 1769 2019 2663 3140 3431 3855 4377 4706 5451 5579 5953 6371 6810 7091 7465 8526 8671 8704

Line 10: 2088 404 1080 1328 1601 1923 2398 2974 3294 3829 4343 4823 5042 5756 5984 6417 6730 7177 7582 8016 87348768

Line 11: 569 517 901 1349 1797 2181 2629 2693 3077 3578 3909 4608 4741 5189 5637 6021 6469 7098 7301 7749 8773 8832

Line 12: 48 188 320 768 1216 1600 2129 2496 3090 3570 3776 4160 4608 5244 5504 5888 6551 6942 7168 7616 7908 8865 8896

Line 13: 30 255 534 942 1206 1703 1984 2463 2816 3375 3719 4174 4544 4992 5727 5847 6443 6823 7483 8016 8631 8775 8960

Line 14: 30 96 230 722 1101 1657 2364 2487 2908 3252 3794 4266 4584 4901 5348 5834 6261 6629 7204 7582 8919 8996 9024

Line 15: 22 107 295 751 1127 1794 2108 2579 2967 3343 4010 4170 4517 5247 5430 5790 6247 6750 7247 7527 8359 8679 9088

Line 16: 4088 471 1027 1508 1884 2095 2432 2944 3589 3963 4405 4748 5056 5440 5824 6336 6784 8128 8910 9071 9088 9152

Line 17: 35 98 265 1016 1348 1706 2294 2775 3250 4032 4303 4816 5118 5330 5920 6480 6855 7504 7863 8268 9042 9176 9216

Line 18: 113 128 576 960 1408 1856 2240 3136 3520 3968 4352 4800 5302 5696 6080 6528 6912 7360 7936 8576 8832 9216 9280

Line 19: 38 65 561 819 1164 1548 2204 2892 3340 3724 4439 4658 5004 5550 6478 6732 7757 8012 8244 9199 9271 9280;

wherein, the number in the ith row represents the column position with the median value of 1 in the 64 th i row in the H matrix, and the column position with the median value of 1 in the 64 th row to 64i +63 row in the H matrix is obtained by cyclic shift according to the cyclic shift matrix.

4. The method of claim 1, wherein the code length n =9984, the code rate is R =13/16, the Z =64, and the H matrix is represented as:

line 0: 17 156 413 1371 2211 2561 3397 3910 4614 6070 6244 6662 7213 7430 8128

Line 1: 29 103 179 758 1203 1907 3000 3591 4505 4927 5363 6400 7000 7603 8179 8192

Line 2: 19 155 800 1344 2112 2688 3936 4160 4992 5504 6860 7168 7334 7973 8256

Line 3: 48 135 999 1628 2045 2709 3763 4032 5153 5591 6272 6912 7959 8309 8320

Line 4: 489 376 939 1303 1936 2829 3232 4458 4612 5953 6685 6824 7484 8354 8384

Line 5: 96 180 862 1675 2317 3045 3599 3968 5146 5561 6331 7090 8069 8384 8448

Line 6: 43 148 705 1146 1849 2901 3887 4300 4931 5987 6343 7160 7789 8488 8512

Line 7: 2 130 576 2010 2335 2705 3782 4163 5097 5832 6208 6848 8192 8512 8576

Line 8: 90 263 510 1630 1821 2670 3390 4148 4734 5385 6384 7354 8089 8637 8640

Line 9: 61 114 581 1337 2389 2533 3223 3946 4716 5565 6061 7606 7788 8698 8704

Line 10: 296 376 534 1507 1974 2550 3318 4014 4700 5750 6150 6724 7542 8158 8768

Line 11: 26 99 169 512 1428 1792 2771 3868 4024 4993 5741 6080 6720 8640 8768 8832

Line 12: 6 186 384 1088 2556 2560 3514 4584 4888 5368 6107 7148 7627 7680 8896

Line 13: 119 150 883 1230 2059 2926 3313 4130 5262 5383 6270 6899 7738 8935 8960

Line 14: 116 192 960 1674 2434 3008 3712 4593 5213 5824 6768 7546 8061 8960 9024

Line 15: 19 115 131 450 1197 2280 3078 3699 4460 4657 5766 6540 7254 7520 9080 9088

Line 16: 57 170 889 1759 2297 2937 3715 4409 5113 5753 6642 7161 8050 9145 9152

Line 17: 35 115 136 904 1544 2312 2952 3656 4424 5128 5768 6472 7944 8712 9160 9216

Line 18: 98 256 1243 1600 2368 3072 3776 4480 5184 5888 6528 7232 8000 9216 9280

Line 19: 108 227 988 1106 2055 3109 3291 4943 5104 5631 6031 6946 8202 9331 9344

Line 20: 72 149 788 1730 2443 2671 3449 4500 4793 5433 6463 6841 7673 9401 9408

Line 21: 1 168 768 1472 2176 2816 3584 4288 5210 5632 6400 7292 7872 9408 9472

Line 22: 30 102 145 444 1399 2407 3192 3330 4083 4845 5493 6309 7385 8878 9523 9536

Line 23: 110 264 680 1557 1989 3033 3461 4335 4869 5665 6341 6981 7749 9541 9600

Line 24: 48 110 148 1079 1209 2164 2953 3444 4415 4778 5472 6631 6800 7369 7707 9664

Line 25: 122 154 704 1408 2249 2752 3520 4224 5328 5568 6691 7464 7808 9664 9728

Line 26: 172 497 639 1456 2175 2617 3341 4055 4863 5920 6173 6924 7864 9736 9792

Line 27: 898 138 1060 1216 1920 3155 3479 4221 4800 5650 6144 7002 7907 9815 9856

Line 28: 20 65 214 574 1556 1891 2826 3703 4265 5053 5765 6132 7398 7629 9911 9920

Line 29: 19 171 959 1280 2048 2624 3582 4096 5295 5902 6485 7040 7911 9920 9984

Line 30: 5594 684 1480 1758 2756 3814 4265 4754 5834 6531 8740 8848 9994 10048

Line 31: 73 320 1024 1664 2432 3136 3840 4544 5248 5952 6592 7296 8064 10048 10112

Line 32: 58 167 688 1864 2182 3237 3562 4401 4976 5488 6483 7053 7830 9648 10112;

5. The method of claim 1, wherein the code length n =10752, the code rate is R =3/4, the Z =64, and the H matrix is represented as:

line 0: 53 199 1356 1994 3149 3624 4661 6453 7300 7458 7839 8128

Line 1: 8 234 1096 1992 3080 3976 6024 7432 7870 8072 8136 8192

Line 2: 113 234 1495 1914 3270 3613 5526 6582 7061 8067 8233 8256

Line 3: 89 168 533 896 1792 3025 4354 4861 5824 6848 7945 8256 8320

Line 4: 5238 1087 1600 2624 3520 5075 6239 6968 7558 8359 8384

Line 5: 29 224 830 1550 2590 4015 4693 5504 6500 7884 8390 8448

Line 6: 18 255 1147 1630 2738 4041 5187 5441 7002 7767 8504 8512

Line 7: 69 194 1154 2114 3138 4098 4994 6082 7282 7405 8514 8576

Line 8: 243 789 1709 2557 3491 4541 5812 6692 7580 8447 8640

Line 9: 55 155 1212 1537 2543 4231 5031 5577 6739 8577 8641 8704

Line 10: 78 485 1398 2254 3439 4238 5134 6222 7118 7374 8595 8768

Line 11: 126 320 1280 2304 3264 4288 5184 6272 7168 8704 8768 8832

Line 12: 127 197 551 2358 2632 3733 5191 5563 7039 7660 8868 8896

Line 13: 0 235 686 3069 3819 3952 4756 4982 5590 6625 8918 8960

Line 14: 72 187 1427 2159 2730 3863 4586 5882 6506 7937 9002 9024

Line 15: 49 217 704 1949 3135 3648 3776 4785 5917 6801 9024 9088

Line 16: 21 191 863 1970 2659 3579 4544 5479 7129 7525 9115 9152

Line 17: 40 177 562 2203 2710 4109 5070 5912 6892 7527 9063 9216

Line 18: 41 246 640 1895 3493 3886 5124 5747 6528 7488 9216 9280

Line 19: 26 250 695 2205 2858 3543 4522 6342 6956 9195 9299 9344

Line 20: 80 138 1116 1821 2816 4132 4608 5632 6656 7680 9344 9408

Line 21: 78 220 1429 2450 2557 3727 3801 5053 5665 6461 7869 9472

Line 22: 112 174 989 1729 2960 4672 4946 6227 6720 8736 9472 9536

Line 23: 121 128 576 1624 2560 3690 5434 6004 7108 8192 9573 9600

Line 24: 106 154 455 1013 1597 2810 3959 5293 5823 6478 7935 9627 9664

Line 25: 114 197 1244 1704 3256 4318 4454 6162 6407 7786 9431 9728

Line 26: 64 384 1344 2368 3328 4413 5248 6360 7232 9664 9728 9792

Line 27: 131 280 1179 2490 2970 4178 4880 5839 7276 7643 8319 9856

Line 28: 67 228 1343 2048 3166 4032 6004 6284 6976 8000 9856 9920

Line 29: 147 400 1064 2158 2930 4427 4635 5455 7349 8062 9980 9984

Line 30: 24 128 960 1728 1856 3374 4800 5888 6912 9818 9984 10048

Line 31: 21 201 1233 2080 2944 3840 4864 6305 7040 7168 8033 10112

Line 32: 6 225 950 1835 2609 4279 5299 5644 6672 9804 10146 10176

Line 33: 159 361 633 2296 3255 3696 6085 7696 8088 10095 10232 10240

Line 34: 43 137 1309 2397 2752 4329 4676 6207 6865 7616 10048 10304

Line 35: 49 215 710 2100 2870 4204 4914 5618 6811 7727 10367 10368

Line 36: 117 131 901 2002 3446 4079 5138 6125 6603 7563 9562 10432

Line 37: 125 256 1216 2176 3200 4160 5056 6144 10240 10368 10432 10496

Line 38: 69 345 834 2396 3335 4013 5410 5738 6577 9439 10551 10560

Line 39: 112 162 730 1711 2912 3631 4841 5743 7194 7791 10607 10624

Line 40: 57 188 832 2346 3088 3712 4736 5760 6784 10514 10624 10688

Line 41: 34 243 599 1485 3310 3518 4486 5389 6777 9335 10694 10752

Line 42: 92 317 1534 1745 2290 2775 4590 6022 6654 8932 10766 10816

Line 43: 189 420 1058 1954 3042 3938 5367 5986 7970 10269 10850 10880

Line 44: 140 448 1408 2432 3392 4352 5312 6336 7296 9184 10880 10944

Line 45: 1146 788 2900 4434 4948 5355 6040 7892 10628 10810 10944;

6. The method of claim 1, wherein the code length n =12928, the code rate is R =5/8, the Z =64, and the H matrix when s =576 is represented as:

line 0: 430 1216 3550 3802 5326 6769 8128

Line 1: 492 1119 2525 4253 6761 8187 8192

Line 2: 98 366 1938 3708 5707 7296 8192 8256

Line 3: 42 625 2493 2900 4718 6574 8271 8320

Line 4: 363 2091 3883 6105 7659 8363 8384

Line 5: 111 512 2240 3776 3968 5888 8384 8448

Line 6: 471 1728 3520 5376 7168 8000 8512

Line 7: 18 440 2144 4169 5184 7040 8569 8576

Line 8: 58 482 1324 2794 4922 6387 8629 8640

Line 9: 129 2334 3969 4394 7654 8645 8704

Line 10: 103 247 1424 3909 5268 6188 8748 8768

Line 11: 66 217 1676 3261 5511 6582 8768 8832

Line 12: 428 2332 2946 4510 7232 8849 8896

Line 13: 465 2296 5859 7552 8064 8896 8960

Line 14: 570 1049 2612 5834 7876 9022 9024

Line 15: 427 1159 3167 5594 7081 9063 9088

Line 16: 34 311 1344 5125 7054 8084 9088 9152

Line 17: 262 1280 3846 4928 6784 9171 9216

Line 18: 415 1882 2880 4736 7606 9257 9280

Line 19: 224 1809 2562 5315 6814 9293 9344

Line 20: 472 768 4141 5918 6808 9363 9408

Line 21: 701 905 3352 5385 7157 9451 9472

Line 22: 159 2188 3593 4863 6463 9479 9536

Line 23: 29 342 1979 3328 5430 7939 9536 9600

Line 24: 46 426 872 4397 6046 7360 9659 9664

Line 25: 48 405 1655 4228 4330 7761 8048 9728

Line 26: 138 223 960 2913 5241 6895 9728 9792

Line 27: 267 892 4134 4521 6322 9828 9856

Line 28: 256 1984 3712 5696 7488 9856 9920

Line 29: 442 2369 2877 4879 7784 9954 9984

Line 30: 4317 2289 3392 5686 7489 9984 10048

Line 31: 28 549 1472 3990 6159 7490 10056 10112

Line 32: 275 2084 3327 4309 6680 10116 10176

Line 33: 122 278 1266 2688 5217 6400 10176 10240

Line 34: 25 138 1228 3057 5042 7277 10247 10304

Line 35: 86 136 1733 2760 4969 6560 10312 10368

Line 36: 64 656 2304 4032 5952 7872 10368 10432

Line 37: 327 2417 3713 4396 6940 10441 10496

Line 38: 28 380 1088 3055 5137 6615 10496 10560

Line 39: 340 1503 3459 4733 6621 10604 10624

Line 40: 518 1819 2676 5453 8479 10632 10688

Line 41: 319 896 2624 5962 6272 10688 10752

Line 42: 34 183 1560 4266 4779 7230 10793 10816

Line 43: 521 1748 3200 4992 6848 10816 10880

Line 44: 40 242 1989 2944 5951 6592 10908 10944

Line 45: 125 269 1325 2688 4288 7719 10992 11008

Line 46: 0 310 829 3129 5081 6517 11017 11072

Line 47: 570 2004 3648 5632 7424 11072 11136

Line 48: 44 310 994 3475 4544 7683 11191 11200

Line 49: 193 2064 2954 4735 7026 11256 11264

Line 50: 24 217 793 2727 6128 7363 9668 11328

Line 51: 148 576 2368 4096 6016 7936 11328 11392

Line 52: 187 720 1153 3009 4837 6657 11396 11456

Line 53: 0 448 2176 4033 5824 7744 11456 11520

Line 54: 9 394 1459 4477 5111 6270 11558 11584

Line 55: 320 1600 3456 5120 6976 11584 11648

Line 56: 97 454 2114 4665 6022 7204 11654 11712

Line 57: 191 938 1566 2816 4608 6464 11712 11776

Line 58: 46 489 1708 3097 4419 6211 11827 11840

Line 59: 143 592 2549 4602 5312 7104 11840 11904

Line 60: 94 330 1029 2560 4741 7624 11907 11968

Line 61: 436 2187 2856 4491 6276 12008 12032

Line 62: 2394 1792 3584 5440 7331 12032 12096

Line 63: 108 366 1664 3607 5248 7348 12124 12160

Line 64: 552 1024 3701 5595 6978 12199 12224

Line 65: 20 368 1161 3526 4625 6701 12244 12288

Line 66: 2 232 1359 3841 4958 6922 12288 12352

Line 67: 33 518 1490 5443 5819 6235 11321 12416

Line 68: 503 1536 5056 7592 8072 12416 12480

Line 69: 36 233 832 3439 5551 6479 12513 12544

Line 70: 114 490 1631 3328 5302 12359 12580 12608

Line 71: 498 747 3245 5658 6418 7844 12672

Line 72: 139 530 2523 3136 4864 7112 12672 12736

Line 73: 1515 3167 4047 6007 6861 12799 12800

Line 74: 3 284 2465 3120 4848 6768 12836 12864

Line 75: 384 2112 3904 5760 7680 12864 12928

Line 76: 57 559 986 3924 4560 6148 12990 12992

Line 77: 10 221 1112 3408 6356 7473 12993 13056

Line 78: 343 1920 3750 5568 7360 13056 13120

Line 79: 234 727 2678 4417 7468 13142 13184

Line 80: 47 365 1902 3269 5008 6341 13189 13248

Line 81: 478 1346 2779 5752 7822 8459 13312

Line 82: 228 1892 4212 5540 7268 13348 13376

Line 83: 176 640 2432 4160 6080 12608 13376 13440

Line 84: 22 533 1471 3327 5767 6975 13311 13440;

7. The method of claim 1, wherein the code length n =16128, the code rate is R =1/2, the Z =64, and the H matrix is represented as:

line 0: 384 2304 5312 7680 7936 8128

Line 1: 96 798 7691 7940 8156 8192

Line 2: 83 739 3123 5976 7552 8256

Line 3: 91 728 2696 7105 8298 8320

Line 4: 101 851 3881 6331 7612 8384

Line 5: 328 738 3762 6261 8381 8448

Line 6: 5 416 1809 3325 8404 8475 8512

Line 7: 436 1188 4860 7405 7523 8576

Line 8: 144 832 6891 8244 8597 8640

Line 9: 94 991 3257 6667 7855 8704

Line 10: 331 871 4668 7847 8743 8768

Line 11: 2638 1917 3520 7340 8640 8832

Line 12: 43 343 1805 5174 8775 8882 8896

Line 13: 114 911 4419 6607 8898 8960

Line 14: 77 890 2624 6352 8960 9024

Line 15: 49 206 653 3342 6953 9037 9088

Line 16: 104 906 3705 6408 9096 9152

Line 17: 546 714 3472 8080 9168 9216

Line 18: 62 161 1051 5039 5828 6303 9280

Line 19: 32 338 1984 5056 9216 9280 9344

Line 20: 103 698 2196 3243 7449 8114 9408

Line 21: 39 459 687 2646 5585 9430 9472

Line 22: 33 368 1303 4329 6553 9505 9536

Line 23: 83 786 4697 6788 9392 9600

Line 24: 64 864 3852 5589 9573 9664

Line 25: 91 247 709 2497 5863 9655 9728

Line 26: 41 77 2387 2901 9685 9749 9792

Line 27: 212 942 2807 5715 8971 9856

Line 28: 57 550 1683 4165 8561 9856 9920

Line 29: 58 259 682 4136 6144 9977 9984

Line 30: 58 144 2272 5358 9255 10002 10048

Line 31: 191 754 4009 6995 10098 10112

Line 32: 116 822 3702 9802 10166 10176

Line 33: 595 1157 4332 7237 10181 10240

Line 34: 102 313 1344 5307 7424 10240 10304

Line 35: 305 681 4395 6063 10306 10368

Line 36: 565 2747 4612 8048 10368 10432

Line 37: 160 846 3529 8024 10478 10496

Line 38: 8 602 1239 2969 6278 10502 10560

Line 39: 481 743 3912 5669 9122 10624

Line 40: 28 475 896 3904 7657 10624 10688

Line 41: 95 525 2437 4691 5808 10727 10752

Line 42: 58 207 1620 3008 6935 10752 10816

Line 43: 95 755 5271 7778 10841 10880

Line 44: 31 214 953 2776 5984 10912 10944

Line 45: 95 670 3502 6622 10974 11008

Line 46: 583 2176 5184 10560 11008 11072

Line 47: 29 280 1302 3542 5658 9657 11136

Line 48: 526 1728 4800 7744 11136 11200

Line 49: 62 912 1460 4352 7894 11215 11264

Line 50: 117 628 2623 5631 11294 11328

Line 51: 120 1469 3806 6503 11387 11392

Line 52: 67 959 2867 6169 11392 11456

Line 53: 81 626 2846 7657 11509 11520

Line 54: 501 757 4250 6341 11520 11584

Line 55: 21 385 2174 4595 7511 11584 11648

Line 56: 36 403 927 4777 6511 11649 11712

Line 57: 23 461 1739 4421 11124 11712 11776

Line 58: 18 173 1146 2977 11077 11810 11840

Line 59: 76 875 3392 6995 11840 11904

Line 60: 98 731 2816 6208 11904 11968

Line 61: 57 323 2376 3095 6369 10817 12032

Line 62: 229 721 4354 6687 12063 12096

Line 63: 58 165 1581 3776 7188 12096 12160

Line 64: 368 815 3832 5766 12027 12224

Line 65: 40 128 1046 3840 6976 12224 12288

Line 66: 94 811 5504 12201 12294 12352

Line 67: 313 1206 4917 5464 6109 12416

Line 68: 56 273 2464 3366 5478 6566 12480

Line 69: 10 518 1792 5342 9792 12480 12544

Line 70: 617 1140 3200 12416 12590 12608

Line 71: 16 432 1216 4288 4992 7296 12672

Line 72: 89 690 4089 7909 12680 12736

Line 73: 61 448 2368 5376 12608 12736 12800

Line 74: 29 545 2328 3017 5733 12825 12864

Line 75: 59 407 912 2499 7121 11490 12928

Line 76: 569 890 3145 5824 12928 12992

Line 77: 106 778 4122 6685 13014 13056

Line 78: 21 575 1642 4714 7658 12906 13120

Line 79: 360 2112 5120 13056 13120 13184

Line 80: 88 781 2587 5518 8363 13248

Line 81: 202 2002 5186 6735 13248 13312

Line 82: 5372 2129 5239 13214 13330 13376

Line 83: 95 938 3338 6079 13439 13440

Line 84: 113 886 3448 5950 13441 13504

Line 85: 327 775 3712 6789 9495 13568

Line 86: 124 719 3032 6541 13576 13632

Line 87: 17 256 2048 5911 13504 13632 13696

Line 88: 779 1011 2635 5680 13031 13760

Line 89: 11 192 1856 4928 12352 13760 13824

Line 90: 9 119 775 3304 6762 13831 13888

Line 91: 25 508 2090 3493 13711 13888 13952

Line 92: 31 144 1368 5087 7250 11968 14016

Line 93: 43 495 1586 4526 5986 14010 14080

Line 94: 461 1896 3968 7040 14080 14144

Line 95: 73487 805 4909 12655 14186 14208

Line 96: 48 143 1626 4520 6401 14214 14272

Line 97: 26 497 1024 4160 7168 14016 14336

Line 98: 63 627 2005 4227 12391 14272 14400

Line 99: 64 776 5432 14370 14449 14464

Line 100: 78 667 3618 13195 13498 14528

Line 101: 295 1536 4608 8512 14528 14592

Line 102: 549 1514 4966 14509 14592 14656

Line 103: 214 878 3620 6054 14696 14720

Line 104: 405 1513 3584 7221 14720 14784

Line 105: 64 806 2881 6080 14814 14848

Line 106: 117 935 5406 5519 14881 14912

Row 107: 32 129 620 2752 7044 14912 14976

Line 108: 436 576 3448 6464 14976 15040

Line 109: 33 398 1922 2736 5921 15081 15104

Line 110: 257 1408 4480 7360 7789 15168

Line 111: 5 280 661 4089 6114 15207 15232

Line 112: 294 928 5152 13721 15252 15296

Line 113: 229 2503 2905 6263 15129 15360

Line 114: 20 304 1664 4736 14464 15360 15424

Line 115: 52 701 1472 4544 7488 15454 15488

Line 116: 15 222 883 3176 6856 15493 15552

Line 117: 24 553 2268 3287 7346 15319 15616

Line 118: 1457 1742 6869 15573 15637 15680

Line 119: 33 540 1666 3656 7255 14866 15744

Line 120: 43 223 891 4773 7431 15760 15808

Line 121: 333 637 3143 5817 11340 15872

Line 122: 24 196 1280 4416 15808 15872 15936

Line 123: 102 671 3973 6427 14980 16000

Line 124: 64 2071 3939 6912 16000 16064

Line 125: 68 852 2944 8148 15104 16128

Line 126: 178 760 5058 16102 16170 16192

Line 127: 108 813 4956 9673 15963 16256

Line 128: 7 261 2618 4601 6204 16313 16320

Line 129: 122 687 5755 7566 15740 16384

Line 130: 1350 2234 4864 7872 16384 16448

Line 131: 641 2365 4172 6767 16454 16512

Line 132: 496 1088 4224 15985 16512 16576

Line 133: 24 621 1930 4096 16236 16627 16640

Line 134: 21 406 1015 4087 7159 16663 16704

Line 135: 614 1958 15718 16230 16742 16768

Line 136: 57 320 2240 5248 8000 16768 16832

Line 137: 21 174 899 4832 7040 16320 16896

Line 138: 38 404 1360 3118 6634 16946 16960

Line 139: 0 512 2432 8192 8768 16960 17024

Line 140: 33 384 1261 3732 6804 16837 17024;

8. The method of claim 1, wherein the code length n =9240, the code rate is R =7/8, the Z =42, and the H matrix is represented as:

line 0: 27 42 378 913 1260 1680 2100 2562 2982 3150 3402 3864 4242 4704 5124 5586 6006 6426 6846 7308 7728 8020 8106

Line 1: 120 435 580 1345 1654 2069 2330 2910 3091 4307 4426 4867 5472 5868 6196 6618 6988 7627 7996 8098 8128 8148

Line 2: 85 170 683 1014 1544 1914 2226 2870 3382 3920 4183 4368 4830 5519 6040 6306 6558 6888 7393 7686 7854 8190

Line 3: 13 80 110 840 1253 1780 2195 2528 2873 3465 3621 4082 4607 5195 5267 5901 6164 6691 6888 7169 7889 8211 8232

Line 4: 28 54 502 672 1176 1512 2058 2560 2856 3276 3738 4337 4785 4998 5557 5945 6462 6678 7224 7604 8022 8232 8274

Line 5: 4491 502 1036 1349 2011 2277 3017 3422 3580 4156 4492 5197 5501 5894 6600 6700 7319 7488 8051 8304 8316

Line 6: 34 119 322 497 927 1392 2017 2452 2853 3289 3561 4260 4648 5014 5233 5854 6115 6863 7118 7782 7949 8350 8358

Line 7: 51 246 666 1304 1506 2052 2430 2850 3270 3732 4152 4659 4992 5496 6051 6294 6769 7357 7596 8265 8394 8400

Line 8: 4099 618 1097 1434 2083 2961 3152 3196 3511 3892 4110 4398 4854 5597 5972 6404 7036 7149 7432 7880 8442

Line 9: 1348 270 804 1098 1392 1993 2358 2628 2778 3198 3660 4038 4771 5299 5382 6089 6222 6959 7285 7780 8448 8484

Line 10: 13 84 241 546 1000 1284 1932 2310 2730 3482 3803 4180 4536 4914 5334 5796 6295 6636 7140 7907 8316 8420 8526

Line 11: 44 120 876 1084 1555 1794 2400 2646 3328 3643 4237 4356 4813 5657 5763 6266 6785 6999 7601 7842 8563 8568

Line 12: 108 286 748 1268 1588 2158 2470 2638 2932 3338 3861 4192 4654 5120 5633 5956 6334 6754 7450 7636 8518 8610

Line 13: 60 294 756 1218 1596 2104 2478 2969 3318 3780 4200 4662 5040 5502 6022 6342 6762 7375 7644 8568 8610 8652

Line 14: 59 343 758 1140 1396 1946 2334 2605 2725 3110 3601 4056 4427 5037 5312 6109 6308 6666 6912 7250 7542 8694

Line 15: 2069 431 659 1523 1646 2036 2510 2931 3568 3988 4450 4908 5363 5710 6369 6550 7283 7531 8104 8681 8734 8736

Line 16: 24 56 163 661 1072 1756 1896 2515 3056 3081 3925 4457 4613 5113 5355 5713 6147 6806 7029 7696 7949 8764 8778

Line 17: 3961 208 544 1008 1640 1689 1848 2268 2688 3689 3990 4494 4872 5292 5754 6237 6877 7056 7845 7896 8778 8820

Line 18: 88 146 786 1172 1481 1878 2306 2646 3108 3716 4226 4718 5156 5409 5985 6442 6969 7069 7650 8661 8820 8862

Line 19: 6125 312 627 956 1759 2209 3069 3401 3512 3737 4297 4533 4884 5285 5944 6212 6642 7184 7466 8856 8877 8904

Line 20: 12 46 371 723 1134 1428 1974 2593 3026 3259 3801 4074 4578 5051 5418 5880 6482 6753 7182 7728 8148 8904 8946

Line 21: 23 70 109 586 1208 1711 1843 2239 2695 3296 3562 4015 4539 5220 5450 5798 6394 6990 7246 7743 8912 8973 8988

Line 22: 58 266 718 933 1575 1828 2471 2658 3160 3211 3877 3951 4372 4812 5222 5798 6256 6729 7135 7395 9001 9030

Line 23: 1076 338 800 968 1319 2183 2522 2942 3362 3824 4664 4959 5084 5546 5966 6386 6806 7268 7688 8402 9032 9072

Line 24: 1356 238 895 1107 1495 1964 2184 2995 3428 3764 3950 4720 5151 5516 5746 6489 6585 7347 7598 7831 8573 9114

Line 25: 791 411 518 905 1452 1844 2392 2788 3122 3693 4362 4522 4966 5396 5790 6525 6841 7038 7457 8154 9083 9156

Line 26: 34 102 159 537 1238 1377 1923 2393 2771 3603 4050 4679 4917 5699 6110 6378 6627 7131 7509 7996 9134 9189 9198

Line 27: 7184 681 1182 1603 1870 2416 2739 3840 4117 4559 5046 5432 5712 6174 6552 7089 7492 7924 9142 9207 9240

Line 28: 24 84 407 806 1602 1783 2245 2811 3256 3745 4024 4483 4793 5551 5673 6172 6951 7659 8056 8101 8484 92629282

Line 29: 86 420 840 1302 1722 2142 3024 3444 3486 3906 4284 4746 5166 5628 6048 6468 7350 7770 8988 9072 9282 9324

Line 30: 121 176 596 985 1058 2125 2594 2820 3620 4249 4920 5276 5598 5846 6530 727526 7946 8744 9206 9290 9324;

wherein, the number in the ith row represents the column position of which the median is 1 in the 42 ith row in the H matrix, and the column position of which the median is 1 in the 42 ith to 42i +41 rows in the H matrix is obtained by cyclic shift according to the cyclic shift matrix.

9. The method of claim 1, wherein the code length n =9954, the code rate is R =13/16, the Z =42, and the H matrix when s =210 is represented as:

line 0: 48 749 1801 2039 2142 2856 3612 4242 4956 5628 6426 7056 7812 8022 8106

Line 1: 14 141 410 1080 2350 2536 3310 4312 4923 5279 6078 6898 7923 8137 8148

Line 2: 40 184 459 1581 1953 2727 3399 4029 4827 5945 6462 6843 7515 8187 8190

Line 3: 47 150 714 1428 2100 2968 3849 4564 4914 5792 6384 7225 7770 8190 8232

Line 4: 186 344 1069 2282 2578 3154 3935 5013 5370 5972 6686 7358 8237 8274

Line 5: 7 114 399 1113 2510 2583 3852 4341 5047 5803 6111 7252 7664 8295 8316

Line 6: 19 177 776 1450 1864 2656 3311 4478 5263 5759 6390 6776 7935 8330 8358

Line 7: 161 462 1218 1806 2730 3645 4166 4994 5857 6174 6989 7537 8358 8400

Line 8: 5186 459 1617 2115 3121 3568 3903 4783 5515 6633 6672 7514 8420 8442

Line 9: 167 334 1653 2011 2712 3500 4317 4610 5695 6267 7138 7737 8482 8484

Line 10: 151 861 1717 2058 2932 3570 4398 4872 5586 6342 7346 7953 8484 8526

Line 11: 59 108 491 1451 2152 3133 3779 4171 4705 5558 6012 6679 7532 8549 8568

Line 12: 52 267 590 1264 1683 2481 3656 4440 4581 5920 6242 6955 7951 8571 8610

Line 13: 51 122 750 1155 1818 2754 3255 4241 4683 5313 6222 6830 7425 8631 8652

Line 14: 0 126 798 1470 2226 2940 3713 4326 4998 5712 6513 7140 7854 8652 8694

Line 15: 1177 992 1259 2417 2887 3329 4137 5245 5412 6271 7069 7874 8735 8736

Line 16: 112 544 924 1344 1974 2916 3600 4158 5082 5544 6258 6972 7686 8736 8778

Line 17: 154 803 1222 1895 2774 3180 4105 5235 5851 5994 6732 7889 8813 8820

Line 18: 42 210 882 1554 2268 3024 3696 4410 5082 5796 6510 7224 7938 8820 8862

Line 19: 186 518 1734 2248 3437 4094 4606 5357 6172 7216 7571 8102 8892 8904

Line 20: 66 133 559 1273 1903 2986 3457 4087 4843 5528 6344 6859 7573 8917 8946

Line 21: 91 355 588 1479 2403 3034 3749 4247 4988 5460 6216 6888 7602 8946 8988

Line 22: 14 181 299 1159 1983 3035 3240 3978 4729 5671 5922 7120 7823 9005 9030

Line 23: 45 156 479 986 2053 3785 3842 5164 5630 64737169 7468 8025 8080 9072

Line 24: 125 187 672 1386 2016 2814 3528 4200 5073 5668 6300 7014 7728 9072 9114

Line 25: 115 250 692 1133 2168 2671 3203 3872 4836 5744 6339 6870 7436 9114 9156

Line 26: 195 992 1008 1856 2721 3726 4490 4698 5470 6094 7142 7512 9156 9198

Line 27: 43 131 366 1355 1945 2436 3245 4070 4536 5613 6076 6947 7786 9219 9240

Line 28: 4122 646 1661 2320 2586 3497 4041 5155 5496 5981 7284 7415 9037 9282

Line 29: 52 184 857 1273 2387 2814 3333 4201 4853 5388 6496 6774 7624 9316 9324

Line 30: 57 192 560 1551 1794 3104 3651 3978 4682 5457 6200 7223 7735 9354 9366

Line 31: 138 630 1302 1932 2857 3486 4116 5092 5502 6415 6930 7644 9366 9408

Line 32: 165 909 1176 2075 2646 3318 4419 4746 5418 6211 6814 7999 9421 9450

Line 33: 27 207 950 1426 1754 3099 3461 3910 4925 5434 6137 6720 7703 9485 9492

Line 34: 148 300 1073 1721 2559 3373 4012 5181 5315 6427 6735 7997 9263 9534

Line 35: 38 96 700 1375 2184 3276 4359 4890 5334 6132 7284 7392 8064 9534 9576

Line 36: 6130 550 1101 1722 2520 3393 3906 4620 5549 6697 6780 7606 9612 9618

Line 37: 4 199 603 1023 2241 2808 3224 4006 4824 5926 6043 6658 7824 9645 9660

Line 38: 36 133 761 1891 2096 2394 3414 3864 4789 5728 6083 7022 7566 9496 9702

Line 39: 35 261 428 1549 2102 2510 3594 3973 4544 5314 6368 7034 7387 9739 9744

Line 40: 65 168 840 1512 2454 2982 3654 4368 5040 5754 6583 7182 7896 9744 9786

Line 41: 8384 826 1396 2203 2752 3532 4375 4704 5376 6527 6997 7434 9660 9828

Line 42: 88 248 1021 1486 1766 2999 3151 4141 4620 5906 6007 6917 7646 9861 9870

Line 43: 38 185 773 1557 2201 2915 3800 4301 5037 5687 6485 7115 9825 9887 9912

Line 44: 71 149 393 1197 1678 2606 2976 3693 4501 4771 5812 6318 6674 7376 9954

Line 45: 81 208 887 1145 2286 2848 3203 4523 4634 5261 6587 7061 7687 9965 9996

Line 46: 41 114 631 1209 2355 2477 2634 3471 4274 5183 5238 6095 6885 7786 10038

Line 47: 108 1315 1611 1834 2321 3077 3749 4463 5135 5849 6563 7277 7991 10049 10080

Line 48: 98 252 924 1596 2352 3108 3780 4494 5166 5880 6594 7308 9912 10080 10122

Line 49: 109 199 521 1313 1865 2789 3419 4049 5616 6617 7318 7535 10013 10122;

10. The method of claim 1, wherein the code length n =10752, wherein the code rate is R =3/4, wherein Z =42, and wherein the H matrix represents, when s = 294:

line 0: 72 241 462 1386 3402 4452 5749 6504 7571 7812 8096 8106

Line 1: 33 89 439 1253 2965 3161 4248 5697 6830 7833 8140 8148

Line 2: 201 786 1893 2541 3251 4341 5663 6589 7787 8165 8190

Line 3: 146 672 1512 2520 3712 4578 5628 6678 7518 8190 8232

Line 4: 93 280 2121 2213 3550 4579 5512 6328 7274 7801 8274

Line 5: 106 672 1998 2903 3620 4410 5418 6342 7573 8274 8316

Line 6: 150 544 1372 2290 3138 4559 6029 6831 7223 8347 8358

Line 7: 99 630 2038 2883 3858 4521 5886 6607 8241 8386 8400

Line 8: 38 227 978 1896 2177 3278 4668 5203 6859 7112 8022 8442

Line 9: 204 429 1353 2319 3369 4654 5469 6393 7531 8451 8484

Line 10: 272 840 1764 2856 3780 4830 5796 6893 7854 8484 8526

Line 11: 169 600 1218 2246 3192 4421 5166 6333 7411 8566 8568

Line 12: 73 177 1130 1215 2181 3441 4789 5425 6697 7888 8598 8610

Line 13: 22 87 961 1602 2402 3577 4820 5765 6644 7406 8610 8652

Line 14: 59 150 411 1428 2438 3711 4281 6087 6452 7140 8670 8694

Line 15: 121 282 1562 2196 2639 3224 4779 5326 6452 8717 8736

Line 16: 189 645 1422 2512 3143 4303 5924 6532 7340 8025 8778

Line 17: 99 592 2128 3369 3532 4991 5506 6556 7671 8782 8820

Line 18: 206 882 1848 2940 3864 4914 5880 6888 7896 8820 8862

Line 19: 47 185 496 1987 2701 3163 4934 5171 6275 7479 8864 8904

Line 20: 203 449 1941 2346 3609 4284 5511 6659 7292 8904 8946

Line 21: 261 363 2175 2398 3258 4475 5355 6406 7527 8975 8988

Line 22: 20 43 261 1528 2531 3990 4159 5351 6095 7103 8756 9030

Line 23: 84 295 1629 2671 3263 4664 6201 6756 7381 9041 9072

Line 24: 4 290 1018 1596 2646 3807 4620 5876 6762 7644 9072 9114

Line 25: 55 153 331 1301 2633 2914 3230 5066 5590 6368 9152 9156

Line 26: 173 546 1452 2978 3444 4546 5805 6468 7350 9156 9198

Line 27: 223 545 1709 2593 3983 4168 5464 6895 7682 9210 9240

Line 28: 2129 732 1319 2809 3986 5000 5753 6220 7903 9244 9282

Line 29: 277 350 1489 2577 3290 4382 6150 7015 7280 9296 9324

Line 30: 244 682 1302 2383 3661 4898 5686 6300 7310 9324 9366

Line 31: 93 852 1260 2268 3325 4242 5292 6856 7712 9366 9408

Line 32: 39 213 897 1193 2702 3108 4926 5921 7137 8414 9434 9450

Line 33: 37 244 756 1779 2688 3612 4662 5712 6804 7686 9477 9492

Line 34: 164 317 1339 2388 4054 4349 5357 6288 7955 9524 9534

Line 35: 41 135 470 2093 2795 3939 4908 5967 6414 7380 9551 9576

Line 36: 262 924 1890 2982 3906 4956 6028 6930 7938 9576 9618

Line 37: 150 802 1501 2663 4062 4410 5290 6242 7719 9627 9660

Line 38: 239 798 1680 2772 3696 4746 5754 7060 8400 9660 9702

Line 39: 54 134 256 1735 2230 4155 4762 5960 6726 7497 9708 9744

Line 40: 286 1077 2073 2488 3580 4546 5596 6646 7486 9754 9786

Line 41: 3 134 935 1814 2906 3830 4880 5846 6854 7991 9794 9828

Line 42: 21 188 966 1932 3024 3948 4998 5922 6972 8004 9828 9870

Line 43: 42 847 1810 2562 4130 4960 5670 6720 7560 9891 9912

Line 44: 79 249 578 1160 2126 3456 4192 5132 6589 7617 9937 9954

Line 45: 70 163 714 1554 4112 4842 5758 6969 7602 8064 9954 9996

Line 46: 151 1159 1640 3094 3334 4341 5568 6515 7263 10027 10038

Line 47: 75 285 1832 2870 3903 5110 5389 6132 7887 10038 10080

Line 48: 70 267 1781 3037 3670 4607 5407 6946 7957 10114 10122

Line 49: 98 571 1358 2184 3545 4200 5298 6363 7453 10122 10164

Line 50: 114 973 1881 2346 4098 4399 5556 6153 7231 10205 10206

Line 51: 141 620 1186 3398 5073 5424 6503 7735 8069 10232 10248

Line 52: 39 245 405 2234 3494 3873 4386 5223 6189 8049 10263 10290

Line 53: 64 154 630 1470 2436 3842 5036 5544 6594 7434 10290 10332

Line 54: 197 765 1664 3017 3415 4625 5254 6990 7926 10370 10374

Line 55: 110 1164 1638 2730 3654 4704 5810 7054 7728 10374 10416

Line 56: 99 1099 1422 2748 4024 4294 5286 6798 7766 10457 10458

Line 57: 204 731 1428 2846 3751 5211 5992 6510 7626 10458 10500

Line 58: 168 504 1541 2352 3910 4842 5866 6426 7308 10528 10542

Line 59: 1669 809 1861 3047 3150 4498 5636 6604 7182 10560 10584

Line 60: 95 266 1274 2306 3456 4122 5226 6111 9007 10592 10626

Line 61: 202 372 1717 2831 3306 4213 5130 6981 7240 9007 10668

Line 62: 82 229 1008 1974 3087 3990 5040 5964 7058 7980 10668 10710

Line 63: 224 378 1591 2740 3318 4745 5376 6258 10649 10715 10752

Line 64: 236 1023 1218 2452 3522 4204 5468 6130 7179 10758 10794

Line 65: 143 280 2057 2999 3753 4455 5138 6796 7436 10808 10836

Line 66: 84 882 1722 2814 3738 4788 6256 7162 10626 10836 10878

Line 67: 230 254 1745 2499 3792 4734 5609 6179 7188 8741 10920

Line 68: 7 201 1083 2049 3099 4065 5100 6039 7047 8181 10953 10962

Line 69: 0 210 1092 2058 2604 3627 4074 5082 6048 7056 10962 11004

Line 70: 213 1077 1946 2400 3492 4500 6074 6698 7398 10899 11004;

11. The method of claim 1, wherein the code length n =12936, the code rate is R =5/8, the Z =42, and the H matrix is represented as:

line 0: 11 239 1276 1605 4020 5316 7189 7320 8106

Line 1: 72 1042 2455 3948 5796 7644 8106 8148

Line 2: 121 399 3219 3290 5455 6902 8174 8190

Line 3: 284 450 1800 4067 5565 6725 8221 8232

Line 4: 34 212 1153 1801 3435 6530 6963 7354 8274

Line 5: 51 849 2571 4523 6015 7905 8283 8316

Line 6: 35 261 939 3041 4176 5940 7911 8356 8358

Line 7: 205 795 3331 4200 6170 7350 8358 8400

Line 8: 36 258 644 2338 5003 5923 6730 7125 8442

Line 9: 53 498 1696 2630 4694 6605 8482 8484

Line 10: 19 377 1870 4168 5482 7246 8484 8526

Line 11: 3289 359 2099 3708 5598 7404 8538 8568

Line 12: 76 294 1680 4353 5469 7555 7938 8610

Line 13: 52 503 3132 3713 5178 6877 8614 8652

Line 14: 26 473 1669 3524 5654 6943 7195 8694

Line 15: 130 1387 2254 3510 6893 8658 8718 8736

Line 16: 334 826 2268 4794 5754 7602 8568 8778

Line 17: 241 1036 2566 5163 5673 8751 8792 8820

Line 18: 3577 434 2583 3320 5130 7741 8849 8862

Line 19: 8192 836 3370 4490 6200 7766 8900 8904

Line 20: 32 230 966 2772 4750 6258 8736 8904 8946

Line 21: 53 717 2685 3866 6485 7891 8983 8988

Line 22: 0 229 1134 2898 5082 6342 7879 8988 9030

Line 23: 59 490 2939 4258 5847 7656 9064 9072

Line 24: 21 100 434 1574 3960 5106 7712 9093 9114

Line 25: 3493 1193 2117 3797 6057 7493 9131 9156

Line 26: 1310 1295 2604 4494 6048 8064 9156 9198

Line 27: 14 213 714 2855 4368 6365 7930 9216 9240

Line 28: 40 336 2142 3822 5904 7518 7595 9282

Line 29: 170 487 2170 4229 5293 7279 9296 9324

Line 30: 1394 1184 2394 4074 6284 6720 8232 9366

Line 31: 201 443 2118 3563 5124 9351 9374 9408

Line 32: 10 340 1006 2399 4451 5930 8182 9271 9450

Line 33: 185 681 1848 4205 5347 7111 9463 9492

Line 34: 69 350 1994 4297 5288 7810 9500 9534

Line 35: 141 1075 2700 5167 6554 7452 9571 9576

Line 36: 104 423 2445 4334 6337 7191 7420 9618

Line 37: 171 467 2788 4991 5563 9595 9637 9660

Line 38: 44 460 1919 4029 6575 9596 9685 9702

Line 39: 295 517 2310 4678 5864 7770 9702 9744

Line 40: 15 314 1350 1617 3509 5260 7982 9765 9786

Line 41: 52 874 2494 3316 5541 7259 9786 9828

Line 42: 70 460 1932 5034 5622 7308 9156 9870

Line 43: 21 347 1643 3449 6824 7659 9878 9912

Line 44: 40 195 446 3071 3612 6027 8030 9912 9954

Line 45: 145 434 1639 4833 5977 8045 9982 9996

Line 46: 9 251 1302 3066 4746 6510 9861 9996 10038

Line 47: 62 480 2790 4390 5236 8427 10043 10080

Line 48: 73 387 1974 3769 6193 7495 10080 10122

Line 49: 136 638 3082 4323 5573 7154 10149 10164

Line 50: 50 400 1826 4599 6092 7433 9945 10206

Line 51: 37 312 1024 2830 4636 6335 10180 10222 10248

Line 52: 2393 837 2436 4284 6542 7980 9324 10290

Line 53: 5 201 1511 2226 3864 5670 10284 10309 10332

Line 54: 160 630 2837 4242 5964 7938 10332 10374

Line 55: 125 1349 1940 3649 5058 6822 10415 10416

Line 56: 285 615 2071 5062 5801 9264 10451 10458

Line 57: 216 898 3168 3685 5513 7010 10496 10500

Line 58: 74 458 2058 4989 6035 7434 10534 10542

Line 59: 147 339 2158 3570 5418 7619 10551 10584

Line 60: 265 504 3413 4539 5838 9432 10500 10626

Line 61: 66 400 2138 3407 6433 8259 10654 10668

Line 62: 80 492 2199 3603 6358 7250 10702 10710

Line 63: 57 1328 2427 4405 5218 10621 10745 10752

Line 64: 81 356 3016 3597 6229 7951 8606 10794

Line 65: 0 348 546 2352 4032 6488 7812 10794 10836

Line 66: 165 321 1825 4104 5180 7049 10838 10878

Line 67: 357 1231 2364 4954 6651 8014 9853 10920

Line 68: 55 348 1956 5109 5768 7498 10961 10962

Line 69: 168 1260 3024 5634 6468 10878 10962 11004

Line 70: 59 450 4576 5512 8071 10868 11026 11046

Line 71: 216 954 3342 3906 5712 7560 11046 11088

Line 72: 72 480 1722 3552 5250 7056 10088 11130

Line 73: 281 405 2291 3905 6669 11102 11130 11172

Line 74: 33 296 1228 2740 4621 6114 7140 9768 11214

Line 75: 49 1131 1562 4644 6892 10785 11254 11256

Line 76: 26 215 1103 2646 4536 6090 11173 11256 11298

Line 77: 169 392 2921 3752 6384 7828 11324 11340

Line 78: 104 414 2023 3270 5696 7032 10614 11382

Line 79: 0 462 2321 3990 6958 7686 11382 11424

Line 80: 38 147 1077 1891 3392 6448 7703 11340 11466

Line 81: 49 407 1977 4450 5415 7178 11505 11508

Line 82: 66 410 2745 4487 5418 6868 11424 11550

Line 83: 123 1455 1754 4752 6998 11509 11581 11592

Line 84: 57 404 2210 4179 5830 7584 8510 11634

Line 85: 148 434 2253 5057 5642 7823 11648 11676

Line 86: 0 126 1050 2975 4838 6300 11597 11676 11718

Line 87: 218 1552 1564 3671 5345 10431 11755 11760

Line 88: 64 703 2882 3712 7118 7267 8670 11802

Line 89: 52 381 2269 4874 5909 9492 11802 11844

Line 90: 8 252 588 2612 2675 4116 5880 7353 11886

Line 91: 43 441 1699 3360 5340 7014 11922 11928

Line 92: 221 477 3267 4107 5214 11794 11941 11970

Line 93: 18 316 1344 3111 4788 6552 9660 11970 12012

Line 94: 118 672 2478 4326 6224 8022 10668 12054

Line 95: 4 277 519 3055 3811 5379 11852 12095 12096

Line 96: 26 264 1404 3108 4830 6594 11592 12096 12138

Line 97: 169 868 3763 5725 8081 12045 12155 12180

Line 98: 56 380 2885 3640 5741 7070 7541 12222

Line 99: 177 403 1734 4245 6763 12201 12252 12264

Line 100: 85 399 2055 3918 6608 11379 11799 12306

Line 101: 274 1092 2856 4662 6860 10248 12306 12348

Line 102: 48 895 2199 4585 6770 7334 12376 12390

Line 103: 37 257 1430 3152 4916 6680 12188 12392 12432

Line 104: 190 331 3202 4063 5974 11952 12286 12474

Line 105: 7252 1470 3192 4956 7854 12432 12474 12516

Line 106: 166 756 2520 4410 6418 10752 11508 12558

Row 107: 85 577 2553 4928 6683 7619 12562 12600

Line 108: 21 341 882 3187 4578 6174 8316 12600 12642

Line 109: 370 731 1905 3679 6070 7291 12683 12684

Line 110: 299 575 2026 4120 6821 7075 8860 12726

Line 111: 20 328 773 3258 4505 6684 7779 12740 12768

Line 112: 54 429 2516 3977 5795 11885 12725 12810

Line 113: 22 254 1176 2940 4874 6384 12768 12810 12852

Line 114: 15 160 1338 1629 3459 5414 11447 12852 12894

Line 115: 21 234 1466 3014 4132 6151 12852 12931 12936

Line 116: 344 1493 2688 4807 6132 11172 12936 12978

Line 117: 74 1171 1806 3528 9072 12516 12999 13020

Line 118: 159 996 1764 3848 5491 8423 11112 13062

Line 119: 165 473 2530 3841 5324 13032 13074 13104

Line 120: 54 490 2727 3811 5626 10361 13023 13146

Line 121: 33 84 924 2730 4719 6216 9408 13146 13188

Line 122: 68 468 1881 4704 6984 7744 13198 13230

Line 123: 9 200 602 2392 3937 7448 12532 13242 13272

Line 124: 6 264 1224 2988 4710 6432 11045 13278 13314

Line 125: 33 218 1394 3481 4880 6644 13145 13322 13356

Line 126: 313 1512 3301 4998 6762 13140 13356 13398

Line 127: 6 298 1520 2942 4473 6279 12296 12716 13398;

12. The method of claim 1, wherein the code length n =16128, the code rate is R =1/2, the Z =42, and the H matrix is represented as:

line 0: 289 924 4942 5554 7862 8106

Line 1: 348 803 4359 6838 8132 8148

Line 2: 86 767 2716 7099 7872 8190

Line 3: 37 473 1999 4817 7799 8190 8232

Line 4: 8 555 2727 3888 6453 8273 8274

Line 5: 194 882 4507 7182 8274 8316

Line 6: 31 520 1088 5226 7966 8329 8358

Line 7: 7 312 1561 3451 7943 8373 8400

Line 8: 19 357 1050 4580 7266 8400 8442

Line 9: 288 859 5461 6111 8477 8484

Line 10: 21 494 1974 5040 8022 8484 8526

Line 11: 25 454 675 2568 6392 8566 8568

Line 12: 5 205 1551 4410 8025 8568 8610

Line 13: 120 616 2680 6841 8620 8652

Line 14: 122 794 3357 6300 8148 8694

Line 15: 136 835 2842 7922 8699 8736

Line 16: 246 1846 3098 6645 8656 8778

Line 17: 563 1019 4017 6362 8818 8820

Line 18: 42 530 1554 4751 7825 8820 8862

Line 19: 262 736 2811 5592 8888 8904

Line 20: 447 1277 2688 6977 8768 8946

Line 21: 80 752 3344 5760 8973 8988

Line 22: 24 394 1764 4788 7933 8988 9030

Line 23: 109 2294 5028 6372 9049 9072

Line 24: 18 150 943 2892 7832 8940 9114

Line 25: 54 431 853 5006 7158 9114 9156

Line 26: 50 246 1615 5310 6427 9177 9198

Line 27: 36 563 1596 4214 7077 9213 9240

Line 28: 32 344 1424 3311 5650 9247 9282

Line 29: 79 183 1344 4494 7476 9282 9324

Line 30: 69 684 2856 6973 9072 9366

Line 31: 40 339 707 3569 9328 9403 9408

Line 32: 35 430 627 4083 6034 7879 9450

Line 33: 513 585 3116 5877 9489 9492

Line 34: 3289 814 2522 7558 9505 9534

Line 35: 101 859 3799 6991 9553 9576

Line 36: 126 1134 4974 8000 9576 9618

Line 37: 72 304 1329 3741 6891 9654 9660

Line 38: 36 210 2118 4830 9408 9660 9702

Line 39: 76 441 1379 4160 6135 9740 9744

Line 40: 57 870 3234 7028 9744 9786

Line 41: 54 855 4202 6243 9819 9828

Line 42: 65 191 1944 4185 5968 9244 9870

Line 43: 73 612 3570 6174 9870 9912

Line 44: 545 2251 3669 6390 9917 9954

Line 45: 0 629 2159 3005 7400 9977 9996

Line 46: 38 413 1932 4998 7980 9996 10038

Line 47: 426 1339 2924 5874 10078 10080

Line 48: 33 467 1103 2606 6935 9865 10122

Line 49: 13 352 1592 4700 7682 10160 10164

Line 50: 97 679 3181 6336 10111 10206

Line 51: 70 586 1848 4914 10164 10206 10248

Line 52: 85 779 3381 5895 8763 10290

Line 53: 504 1553 3753 6370 10318 10332

Line 54: 110 646 5493 6048 9492 10374

Line 55: 269 1149 4448 7790 10359 10416

Line 56: 24 487 1092 4242 7308 10416 10458

Line 57: 81 326 2126 4139 10384 10494 10500

Line 58: 125 785 2922 7164 9930 10542

Line 59: 0 380 1596 5132 7686 10542 10584

Line 60: 233 833 3095 8080 10586 10626

Line 61: 3 567 1442 4530 7098 10626 10668

Line 62: 580 1436 4617 7260 10690 10710

Line 63: 108 828 2771 6471 10751 10752

Line 64: 227 2326 3519 5922 10752 10794

Line 65: 78 571 3383 6797 10825 10836

Line 66: 37 334 720 4623 5931 8928 10878

Line 67: 84 844 2976 6881 10919 10920

Line 68: 124 599 3035 5659 10864 10962

Line 69: 14 462 2394 5376 10920 10962 11004

Line 70: 51 817 4344 5700 9078 11046

Line 71: 102 693 2562 6201 11046 11088

Line 72: 101 647 3458 6922 11104 11130

Line 73: 19 214 1033 2607 7742 11133 11172

Line 74: 482 610 3042 5898 11190 11214

Line 75: 102 1389 3910 7380 11218 11256

Line 76: 36 384 2058 5082 7896 11256 11298

Line 77: 523 2288 3727 6552 11307 11340

Line 78: 415 670 5084 7449 11370 11382

Line 79: 107 973 2940 6685 11382 11424

Line 80: 77 920 3972 11040 11424 11466

Line 81: 37 475 1007 6059 11014 11489 11508

Line 82: 607 1680 4809 7770 11508 11550

Line 83: 164 1482 4243 6475 11586 11592

Line 84: 24 554 1722 4746 7812 11592 11634

Line 85: 2559 1428 5380 7560 11636 11676

Line 86: 550 2188 3723 10261 11693 11718

Line 87: 65 410 2448 3330 10260 11730 11760

Line 88: 57 816 5378 6384 11760 11802

Line 89: 53 795 3297 7220 11804 11844

Line 90: 230 750 2786 5642 8666 11886

Line 91: 71 736 3549 7132 11924 11928

Line 92: 193 852 5217 6594 11928 11970

Line 93: 74 220 2229 4910 7570 12001 12012

Line 94: 291 785 2965 5578 11880 12054

Line 95: 304 2014 3784 6905 12079 12096

Line 96: 53 607 3379 6487 12031 12138

Line 97: 61 292 720 3442 12136 12178 12180

Line 98: 39 226 716 2637 6281 12203 12222

Line 99: 348 1765 4077 6029 12236 12264

Line 100: 75 763 4053 5718 11199 12306

Line 101: 88 2391 5334 7498 12264 12348

Line 102: 92 918 3627 6777 12384 12390

Line 103: 69 524 2268 5250 12306 12390 12432

Line 104: 514 696 3492 5712 10785 12474

Line 105: 94 612 3166 8100 12512 12516

Line 106: 120 342 1470 4578 7602 12516 12558

Line 107: 72 807 2991 5531 12579 12600

Line 108: 209 713 2531 5689 11097 12642

Line 109: 352 1176 4326 7686 12642 12684

Line 110: 464 1173 4542 6510 12724 12726

Line 111: 336 677 4026 10514 12735 12768

Line 112: 123 835 3444 7453 12768 12810

Line 113: 74 489 2550 5256 6286 12828 12852

Line 114: 259 1269 2680 5714 12619 12894

Line 115: 388 2396 4885 7350 12894 12936

Line 116: 7 731 1726 3121 7658 12936 12978

Line 117: 110 901 4032 7056 12978 13020

Line 118: 478 1129 4863 7055 12893 13062

Line 119: 7552 1512 4620 7995 13062 13104

Line 120: 3431 1914 3948 7202 13035 13146

Line 121: 272 1663 4706 13116 13154 13188

Line 122: 338 740 3265 5796 8177 13230

Line 123: 63 398 918 4980 6662 13255 13272

Line 124: 95 920 3822 7607 13272 13314

Line 125: 15 161 1816 3663 5820 13326 13356

Line 126: 303 1853 4953 5605 13361 13398

Line 127: 109 650 3276 6216 13398 13440

Line 128: 59 691 2767 5611 9828 13482

Line 129: 172 2788 5057 6679 13499 13524

Line 130: 551 2436 5418 13188 13524 13566

Line 131: 310 858 2648 6120 13573 13608

Line 132: 444 701 3883 7375 13637 13650

Line 133: 72 883 4104 7170 13680 13692

Line 134: 22 378 2184 5166 10500 13692 13734

Line 135: 517 638 3631 5868 13745 13776

Line 136: 84 1008 4200 7398 13776 13818

Line 137: 106 644 2571 5502 13443 13860

Line 138: 15 334 892 4299 6587 13881 13902

Line 139: 73 206 1774 4656 7702 13940 13944

Line 140: 212 798 5328 6846 13819 13986

Line 141: 154 761 3652 12437 14003 14028

Line 142: 21 152 1900 3486 7298 14028 14070

Line 143: 37 666 2030 5533 6526 14090 14112

Line 144: 8 433 2387 4284 12449 14112 14154

Line 145: 127 750 5207 7618 14161 14196

Line 146: 13 252 1890 4956 8044 14196 14238

Row 147: 130 841 3439 7513 14254 14280

Line 148: 391 1260 5145 7392 14280 14322

Line 149: 3 266 1386 4536 7518 13944 14364

Line 150: 118 1058 3221 6064 14324 14406

Line 151: 21 67 843 2842 14404 14410 14448

Line 152: 141 2071 2909 6274 9747 14490

Line 153: 296 2351 4692 5761 14497 14532

Line 154: 92 920 6235 9435 13458 14574

Line 155: 108 740 4417 6772 14574 14616

Line 156: 36 409 1936 2744 5965 14651 14658

Line 157: 16 336 2142 5199 8064 14658 14700

Line 158: 282 645 4043 6655 14735 14742

Line 159: 72 414 1218 5767 6731 14742 14784

Line 160: 437 1376 3571 7259 14804 14826

Line 161: 49 508 2310 5292 6720 14826 14868

Line 162: 19 149 823 3103 6752 14889 14910

Line 163: 96 2481 5351 6930 14910 14952

Line 164: 374 774 5046 7667 14984 14994

Line 165: 110 1642 4138 6129 15035 15036

Line 166: 93 744 3776 6520 14539 15078

Line 167: 28 420 2226 5208 7938 15078 15120

Line 168: 200 877 4676 6187 15152 15162

Line 169: 29 470 1227 3796 6964 15200 15204

Line 170: 67 760 3700 14475 15208 15246

Line 171: 9316 1700 4116 7224 15246 15288

Line 172: 432 2088 3528 6678 15036 15330

Line 173: 23 243 771 4466 15325 15330 15372

Line 174: 97 683 3212 7043 10869 15414

Line 175: 5 196 2408 4461 6887 12638 15456

Line 176: 8 248 650 3936 6171 15481 15498

Line 177: 536 2100 5124 15414 15498 15540

Line 178: 17 382 2197 3192 7317 14532 15582

Line 179: 521 1236 3242 5834 15598 15624

Line 180: 56 257 966 4291 7588 15624 15666

Line 181: 627 2446 5100 6635 15701 15708

Line 182: 13 623 1203 5259 15544 15713 15750

Line 183: 61 589 1806 4872 15372 15750 15792

Line 184: 62 754 3694 6844 15815 15834

Line 185: 86 897 5434 15564 15834 15876

Line 186: 2 468 893 3437 6142 15905 15918

Line 187: 30 314 1748 2884 7275 15947 15960

Line 188: 134 608 3018 6627 11853 16002

Row 189: 67 652 1669 4735 7759 16033 16044

Row 190: 16 639 2352 5334 12194 16044 16086

Line 191: 261 2490 3846 5670 15960 16128

Line 192: 365 768 4400 5889 16129 16170

Line 193: 294 2016 5421 16124 16170 16212

Line 194: 120 900 3065 7325 13371 16254

Line 195: 56 816 3108 6006 16254 16296

Line 196: 80 631 4376 6464 16303 16338

Line 197: 208 2039 3990 16249 16338 16380

Line 198: 88 694 4255 6577 16384 16422

Line 199: 10 187 2161 4767 7769 16422 16464

Line 200: 117 779 3849 5561 10083 16506

Line 201: 23 454 1302 4452 13194 16506 16548

Line 202: 143 879 3160 6005 16487 16590

Line 203: 34 309 1878 3928 16578 16625 16632

Line 204: 85 863 2852 7086 16330 16674

Line 205: 210 1504 4368 7434 16674 16716

Line 206: 14 472 1209 3864 16247 16730 16758

Line 207: 121 908 4836 5928 16777 16800

Line 208: 112 924 4158 15402 16800 16842

Line 209: 73 634 3574 16636 16845 16884

Line 210: 97 819 4567 15990 16663 16926

Line 211: 92 691 4706 6309 16952 16968

Line 212: 0 504 2478 5460 14448 16968 17010

Line 213: 36 202 1712 3961 7532 16896 17010;

wherein, the number of the ith row represents the column position with the median value of 1 in the 42 ith row in the H matrix, and the column position with the median value of 1 in the 42 ith to 42i +41 rows in the H matrix is obtained by circularly shifting the column position with the median value of 1 in the 42 ith row according to the circularly shifted matrix.

13. An apparatus for encoding a low density parity check, LDPC, code, the apparatus comprising:

a generating module for obtaining k information bits, wherein k =8064;

the coding module is used for carrying out LDPC coding on the k information bits according to the parity check H matrix to obtain a coded code word C, wherein the code length of the code word C is n, the code rate R is k/n, and n is a positive integer greater than k; the H matrix is a parity check matrix of (n + s-k) x (n + s), the H matrix is divided into a sub-square matrix with the size of Z x Z, the value of Z is 64 or 42, the sub-square matrix is a cyclic shift or null matrix of a unit matrix, and s is a positive integer multiple of Z, wherein the number of columns corresponding to bits to be shortened and the H matrix is s;

the device further comprises:

a filling module, configured to fill s bits to be shortened before the k information bits to obtain (s + k) bits to be encoded, where a value of the s bits to be shortened is 0;

the encoding module is configured to perform LDPC encoding on the (s + k) bits to be encoded to obtain an encoded codeword C ₁ Said code word C ₁ Has a code length of (s + n), said code word C ₁ Comprising the s bits to be shortened, k information bits and (n-k) parity bits;

a deletion module: for deleting the code word C ₁ Obtaining the codeword C from the s bits to be shortened, where the s bits to be shortened correspond to a first s columns of the H matrix.

14. The apparatus of claim 13, wherein the apparatus is applied in a wireless local area network communication system with 60 gigahertz GHz.

15. The encoding apparatus as claimed in claim 13, wherein the code length n =9216, the code rate is R =7/8, the Z =64, and the H matrix is represented as:

Line 3: 2779 374 897 1267 1766 2159 2655 3048 3395 3657 4053 4910 4964 5501 6184 6629 6719 7292 7445 8213 8277 8320

Line 4: 61 102 448 832 1389 1728 2112 2809 3008 3456 3840 4288 4893 5120 5568 5952 6550 6848 7104 7336 7680 8064 8384

16. The encoding apparatus as claimed in claim 13, wherein the code length n =9984, the code rate is R =13/16, the Z =64, and the H matrix is represented as:

line 0: 17 156 413 1371 2211 2561 3397 3910 4614 6070 6244 6662 7213 7430 8128

Line 2: 19 155 800 1344 2112 2688 3936 4160 4992 5504 6860 7168 7334 7973 8256

Line 3: 48 135 999 1628 2045 2709 3763 4032 5153 5591 6272 6912 7959 8309 8320

Line 4: 489 376 939 1303 1936 2829 3232 4458 4612 5953 6685 6824 7484 8354 8384

Line 5: 96 180 862 1675 2317 3045 3599 3968 5146 5561 6331 7090 8069 8384 8448

Line 6: 43 148 705 1146 1849 2901 3887 4300 4931 5987 6343 7160 7789 8488 8512

Line 7: 2 130 576 2010 2335 2705 3782 4163 5097 5832 6208 6848 8192 8512 8576

Line 8: 90 263 510 1630 1821 2670 3390 4148 4734 5385 6384 7354 8089 8637 8640

Line 9: 61 114 581 1337 2389 2533 3223 3946 4716 5565 6061 7606 7788 8698 8704

Line 12: 6 186 384 1088 2556 2560 3514 4584 4888 5368 6107 7148 7627 7680 8896

Line 16: 57 170 889 1759 2297 2937 3715 4409 5113 5753 6642 7161 8050 9145 9152

Line 20: 72 149 788 1730 2443 2671 3449 4500 4793 5433 6463 6841 7673 9401 9408

Line 21: 1 168 768 1472 2176 2816 3584 4288 5210 5632 6400 7292 7872 9408 9472

Line 29: 19 171 959 1280 2048 2624 3582 4096 5295 5902 6485 7040 7911 9920 9984

Line 30: 5594 684 1480 1758 2756 3814 4265 4754 5834 6531 8740 8848 9994 10048

17. The encoding apparatus as claimed in claim 13, wherein the code length n =10752, the code rate R =3/4, the Z =64, and the H matrix when s =256 is represented as:

line 0: 53 199 1356 1994 3149 3624 4661 6453 7300 7458 7839 8128

Line 1: 8 234 1096 1992 3080 3976 6024 7432 7870 8072 8136 8192

Line 2: 113 234 1495 1914 3270 3613 5526 6582 7061 8067 8233 8256

Line 3: 89 168 533 896 1792 3025 4354 4861 5824 6848 7945 8256 8320

Line 4: 5238 1087 1600 2624 3520 5075 6239 6968 7558 8359 8384

Line 5: 29 224 830 1550 2590 4015 4693 5504 6500 7884 8390 8448

Line 6: 18 255 1147 1630 2738 4041 5187 5441 7002 7767 8504 8512

Line 7: 69 194 1154 2114 3138 4098 4994 6082 7282 7405 8514 8576

Line 8: 243 789 1709 2557 3491 4541 5812 6692 7580 8447 8640

Line 9: 55 155 1212 1537 2543 4231 5031 5577 6739 8577 8641 8704

Line 10: 78 485 1398 2254 3439 4238 5134 6222 7118 7374 8595 8768

Line 11: 126 320 1280 2304 3264 4288 5184 6272 7168 8704 8768 8832

Line 12: 127 197 551 2358 2632 3733 5191 5563 7039 7660 8868 8896

Line 13: 0 235 686 3069 3819 3952 4756 4982 5590 6625 8918 8960

Line 14: 72 187 1427 2159 2730 3863 4586 5882 6506 7937 9002 9024

Line 15: 49 217 704 1949 3135 3648 3776 4785 5917 6801 9024 9088

Line 16: 21 191 863 1970 2659 3579 4544 5479 7129 7525 9115 9152

Line 17: 40 177 562 2203 2710 4109 5070 5912 6892 7527 9063 9216

Line 18: 41 246 640 1895 3493 3886 5124 5747 6528 7488 9216 9280

Line 19: 26 250 695 2205 2858 3543 4522 6342 6956 9195 9299 9344

Line 20: 80 138 1116 1821 2816 4132 4608 5632 6656 7680 9344 9408

Line 21: 78 220 1429 2450 2557 3727 3801 5053 5665 6461 7869 9472

Line 22: 112 174 989 1729 2960 4672 4946 6227 6720 8736 9472 9536

Line 23: 121 128 576 1624 2560 3690 5434 6004 7108 8192 9573 9600

Line 24: 106 154 455 1013 1597 2810 3959 5293 5823 6478 7935 9627 9664

Line 25: 114 197 1244 1704 3256 4318 4454 6162 6407 7786 9431 9728

Line 26: 64 384 1344 2368 3328 4413 5248 6360 7232 9664 9728 9792

Line 27: 131 280 1179 2490 2970 4178 4880 5839 7276 7643 8319 9856

Line 28: 67 228 1343 2048 3166 4032 6004 6284 6976 8000 9856 9920

Line 29: 147 400 1064 2158 2930 4427 4635 5455 7349 8062 9980 9984

Line 30: 24 128 960 1728 1856 3374 4800 5888 6912 9818 9984 10048

Line 31: 21 201 1233 2080 2944 3840 4864 6305 7040 7168 8033 10112

Line 32: 6 225 950 1835 2609 4279 5299 5644 6672 9804 10146 10176

Line 33: 159 361 633 2296 3255 3696 6085 7696 8088 10095 10232 10240

Line 34: 43 137 1309 2397 2752 4329 4676 6207 6865 7616 10048 10304

Line 35: 49 215 710 2100 2870 4204 4914 5618 6811 7727 10367 10368

Line 36: 117 131 901 2002 3446 4079 5138 6125 6603 7563 9562 10432

Line 37: 125 256 1216 2176 3200 4160 5056 6144 10240 10368 10432 10496

Line 38: 69 345 834 2396 3335 4013 5410 5738 6577 9439 10551 10560

Line 39: 112 162 730 1711 2912 3631 4841 5743 7194 7791 10607 10624

Line 40: 57 188 832 2346 3088 3712 4736 5760 6784 10514 10624 10688

Line 41: 34 243 599 1485 3310 3518 4486 5389 6777 9335 10694 10752

Line 42: 92 317 1534 1745 2290 2775 4590 6022 6654 8932 10766 10816

Line 43: 189 420 1058 1954 3042 3938 5367 5986 7970 10269 10850 10880

Line 44: 140 448 1408 2432 3392 4352 5312 6336 7296 9184 10880 10944

Line 45: 1146 788 2900 4434 4948 5355 6040 7892 10628 10810 10944;

18. The encoding apparatus as claimed in claim 13, wherein the code length n =12928, the code rate R =5/8, the Z =64, and the H matrix when s =576 is represented as:

line 0: 430 1216 3550 3802 5326 6769 8128

Line 1: 492 1119 2525 4253 6761 8187 8192

Line 2: 98 366 1938 3708 5707 7296 8192 8256

Line 3: 42 625 2493 2900 4718 6574 8271 8320

Line 4: 363 2091 3883 6105 7659 8363 8384

Line 5: 111 512 2240 3776 3968 5888 8384 8448

Line 6: 471 1728 3520 5376 7168 8000 8512

Line 7: 18 440 2144 4169 5184 7040 8569 8576

Line 8: 58 482 1324 2794 4922 6387 8629 8640

Line 9: 129 2334 3969 4394 7654 8645 8704

Line 10: 103 247 1424 3909 5268 6188 8748 8768

Line 11: 66 217 1676 3261 5511 6582 8768 8832

Line 12: 428 2332 2946 4510 7232 8849 8896

Line 13: 465 2296 5859 7552 8064 8896 8960

Line 14: 570 1049 2612 5834 7876 9022 9024

Line 15: 427 1159 3167 5594 7081 9063 9088

Line 16: 34 311 1344 5125 7054 8084 9088 9152

Line 17: 262 1280 3846 4928 6784 9171 9216

Line 18: 415 1882 2880 4736 7606 9257 9280

Line 19: 224 1809 2562 5315 6814 9293 9344

Line 20: 472 768 4141 5918 6808 9363 9408

Line 21: 701 905 3352 5385 7157 9451 9472

Line 22: 159 2188 3593 4863 6463 9479 9536

Line 23: 29 342 1979 3328 5430 7939 9536 9600

Line 24: 46 426 872 4397 6046 7360 9659 9664

Line 25: 48 405 1655 4228 4330 7761 8048 9728

Line 26: 138 223 960 2913 5241 6895 9728 9792

Line 27: 267 892 4134 4521 6322 9828 9856

Line 28: 256 1984 3712 5696 7488 9856 9920

Line 29: 442 2369 2877 4879 7784 9954 9984

Line 30: 4317 2289 3392 5686 7489 9984 10048

Line 31: 28 549 1472 3990 6159 7490 10056 10112

Line 32: 275 2084 3327 4309 6680 10116 10176

Line 33: 122 278 1266 2688 5217 6400 10176 10240

Line 34: 25 138 1228 3057 5042 7277 10247 10304

Line 35: 86 136 1733 2760 4969 6560 10312 10368

Line 36: 64 656 2304 4032 5952 7872 10368 10432

Line 37: 327 2417 3713 4396 6940 10441 10496

Line 38: 28 380 1088 3055 5137 6615 10496 10560

Line 39: 340 1503 3459 4733 6621 10604 10624

Line 40: 518 1819 2676 5453 8479 10632 10688

Line 41: 319 896 2624 5962 6272 10688 10752

Line 42: 34 183 1560 4266 4779 7230 10793 10816

Line 43: 521 1748 3200 4992 6848 10816 10880

Line 44: 40 242 1989 2944 5951 6592 10908 10944

Line 45: 125 269 1325 2688 4288 7719 10992 11008

Line 46: 0 310 829 3129 5081 6517 11017 11072

Line 47: 570 2004 3648 5632 7424 11072 11136

Line 48: 44 310 994 3475 4544 7683 11191 11200

Line 49: 193 2064 2954 4735 7026 11256 11264

Line 50: 24 217 793 2727 6128 7363 9668 11328

Line 51: 148 576 2368 4096 6016 7936 11328 11392

Line 52: 187 720 1153 3009 4837 6657 11396 11456

Line 53: 0 448 2176 4033 5824 7744 11456 11520

Line 54: 9 394 1459 4477 5111 6270 11558 11584

Line 55: 320 1600 3456 5120 6976 11584 11648

Line 56: 97 454 2114 4665 6022 7204 11654 11712

Line 57: 191 938 1566 2816 4608 6464 11712 11776

Line 58: 46 489 1708 3097 4419 6211 11827 11840

Line 59: 143 592 2549 4602 5312 7104 11840 11904

Line 60: 94 330 1029 2560 4741 7624 11907 11968

Line 61: 436 2187 2856 4491 6276 12008 12032

Line 62: 2394 1792 3584 5440 7331 12032 12096

Line 63: 108 366 1664 3607 5248 7348 12124 12160

Line 64: 552 1024 3701 5595 6978 12199 12224

Line 65: 20 368 1161 3526 4625 6701 12244 12288

Line 66: 2 232 1359 3841 4958 6922 12288 12352

Line 67: 33 518 1490 5443 5819 6235 11321 12416

Line 68: 503 1536 5056 7592 8072 12416 12480

Line 69: 36 233 832 3439 5551 6479 12513 12544

Line 70: 114 490 1631 3328 5302 12359 12580 12608

Line 71: 498 747 3245 5658 6418 7844 12672

Line 72: 139 530 2523 3136 4864 7112 12672 12736

Line 73: 1515 3167 4047 6007 6861 12799 12800

Line 74: 3 284 2465 3120 4848 6768 12836 12864

Line 75: 384 2112 3904 5760 7680 12864 12928

Line 76: 57 559 986 3924 4560 6148 12990 12992

Line 77: 10 221 1112 3408 6356 7473 12993 13056

Line 78: 343 1920 3750 5568 7360 13056 13120

Line 79: 234 727 2678 4417 7468 13142 13184

Line 80: 47 365 1902 3269 5008 6341 13189 13248

Line 81: 478 1346 2779 5752 7822 8459 13312

Line 82: 228 1892 4212 5540 7268 13348 13376

Line 83: 176 640 2432 4160 6080 12608 13376 13440

Line 84: 22 533 1471 3327 5767 6975 13311 13440;

19. The encoding apparatus as claimed in claim 13, wherein the code length n =16128, the code rate is R =1/2, the Z =64, and when s =960, the H matrix is represented as:

line 0: 384 2304 5312 7680 7936 8128

Line 1: 96 798 7691 7940 8156 8192

Line 2: 83 739 3123 5976 7552 8256

Line 3: 91 728 2696 7105 8298 8320

Line 4: 101 851 3881 6331 7612 8384

Line 5: 328 738 3762 6261 8381 8448

Line 6: 5 416 1809 3325 8404 8475 8512

Line 7: 436 1188 4860 7405 7523 8576

Line 8: 144 832 6891 8244 8597 8640

Line 9: 94 991 3257 6667 7855 8704

Line 10: 331 871 4668 7847 8743 8768

Line 11: 2638 1917 3520 7340 8640 8832

Line 12: 43 343 1805 5174 8775 8882 8896

Line 13: 114 911 4419 6607 8898 8960

Line 14: 77 890 2624 6352 8960 9024

Line 15: 49 206 653 3342 6953 9037 9088

Line 16: 104 906 3705 6408 9096 9152

Line 17: 546 714 3472 8080 9168 9216

Line 18: 62 161 1051 5039 5828 6303 9280

Line 19: 32 338 1984 5056 9216 9280 9344

Line 20: 103 698 2196 3243 7449 8114 9408

Line 21: 39 459 687 2646 5585 9430 9472

Line 22: 33 368 1303 4329 6553 9505 9536

Line 23: 83 786 4697 6788 9392 9600

Line 24: 64 864 3852 5589 9573 9664

Line 25: 91 247 709 2497 5863 9655 9728

Line 26: 41 77 2387 2901 9685 9749 9792

Line 27: 212 942 2807 5715 8971 9856

Line 28: 57 550 1683 4165 8561 9856 9920

Line 29: 58 259 682 4136 6144 9977 9984

Line 30: 58 144 2272 5358 9255 10002 10048

Line 31: 191 754 4009 6995 10098 10112

Line 32: 116 822 3702 9802 10166 10176

Line 33: 595 1157 4332 7237 10181 10240

Line 34: 102 313 1344 5307 7424 10240 10304

Line 35: 305 681 4395 6063 10306 10368

Line 36: 565 2747 4612 8048 10368 10432

Line 37: 160 846 3529 8024 10478 10496

Line 38: 8 602 1239 2969 6278 10502 10560

Line 39: 481 743 3912 5669 9122 10624

Line 40: 28 475 896 3904 7657 10624 10688

Line 41: 95 525 2437 4691 5808 10727 10752

Line 42: 58 207 1620 3008 6935 10752 10816

Line 43: 95 755 5271 7778 10841 10880

Line 44: 31 214 953 2776 5984 10912 10944

Line 45: 95 670 3502 6622 10974 11008

Line 46: 583 2176 5184 10560 11008 11072

Line 47: 29 280 1302 3542 5658 9657 11136

Line 48: 526 1728 4800 7744 11136 11200

Line 49: 62 912 1460 4352 7894 11215 11264

Line 50: 117 628 2623 5631 11294 11328

Line 51: 120 1469 3806 6503 11387 11392

Line 52: 67 959 2867 6169 11392 11456

Line 53: 81 626 2846 7657 11509 11520

Line 54: 501 757 4250 6341 11520 11584

Line 55: 21 385 2174 4595 7511 11584 11648

Line 56: 36 403 927 4777 6511 11649 11712

Line 57: 23 461 1739 4421 11124 11712 11776

Line 58: 18 173 1146 2977 11077 11810 11840

Line 59: 76 875 3392 6995 11840 11904

Line 60: 98 731 2816 6208 11904 11968

Line 61: 57 323 2376 3095 6369 10817 12032

Line 62: 229 721 4354 6687 12063 12096

Line 63: 58 165 1581 3776 7188 12096 12160

Line 64: 368 815 3832 5766 12027 12224

Line 65: 40 128 1046 3840 6976 12224 12288

Line 66: 94 811 5504 12201 12294 12352

Line 67: 313 1206 4917 5464 6109 12416

Line 68: 56 273 2464 3366 5478 6566 12480

Line 69: 10 518 1792 5342 9792 12480 12544

Line 70: 617 1140 3200 12416 12590 12608

Line 71: 16 432 1216 4288 4992 7296 12672

Line 72: 89 690 4089 7909 12680 12736

Line 73: 61 448 2368 5376 12608 12736 12800

Line 74: 29 545 2328 3017 5733 12825 12864

Line 75: 59 407 912 2499 7121 11490 12928

Line 76: 569 890 3145 5824 12928 12992

Line 77: 106 778 4122 6685 13014 13056

Line 78: 21 575 1642 4714 7658 12906 13120

Line 79: 360 2112 5120 13056 13120 13184

Line 80: 88 781 2587 5518 8363 13248

Line 81: 202 2002 5186 6735 13248 13312

Line 82: 5372 2129 5239 13214 13330 13376

Line 83: 95 938 3338 6079 13439 13440

Line 84: 113 886 3448 5950 13441 13504

Line 85: 327 775 3712 6789 9495 13568

Line 86: 124 719 3032 6541 13576 13632

Line 87: 17 256 2048 5911 13504 13632 13696

Line 88: 779 1011 2635 5680 13031 13760

Line 89: 11 192 1856 4928 12352 13760 13824

Line 90: 9 119 775 3304 6762 13831 13888

Line 91: 25 508 2090 3493 13711 13888 13952

Line 92: 31 144 1368 5087 7250 11968 14016

Line 93: 43 495 1586 4526 5986 14010 14080

Line 94: 461 1896 3968 7040 14080 14144

Line 95: 73487 805 4909 12655 14186 14208

Line 96: 48 143 1626 4520 6401 14214 14272

Line 97: 26 497 1024 4160 7168 14016 14336

Line 98: 63 627 2005 4227 12391 14272 14400

Line 99: 64 776 5432 14370 14449 14464

Line 100: 78 667 3618 13195 13498 14528

Line 101: 295 1536 4608 8512 14528 14592

Line 102: 549 1514 4966 14509 14592 14656

Line 103: 214 878 3620 6054 14696 14720

Line 104: 405 1513 3584 7221 14720 14784

Line 105: 64 806 2881 6080 14814 14848

Line 106: 117 935 5406 5519 14881 14912

Row 107: 32 129 620 2752 7044 14912 14976

Line 108: 436 576 3448 6464 14976 15040

Line 109: 33 398 1922 2736 5921 15081 15104

Line 110: 257 1408 4480 7360 7789 15168

Line 111: 5 280 661 4089 6114 15207 15232

Line 112: 294 928 5152 13721 15252 15296

Line 113: 229 2503 2905 6263 15129 15360

Line 114: 20 304 1664 4736 14464 15360 15424

Line 115: 52 701 1472 4544 7488 15454 15488

Line 116: 15 222 883 3176 6856 15493 15552

Line 117: 24 553 2268 3287 7346 15319 15616

Line 118: 1457 1742 6869 15573 15637 15680

Line 119: 33 540 1666 3656 7255 14866 15744

Line 120: 43 223 891 4773 7431 15760 15808

Line 121: 333 637 3143 5817 11340 15872

Line 122: 24 196 1280 4416 15808 15872 15936

Line 123: 102 671 3973 6427 14980 16000

Line 124: 64 2071 3939 6912 16000 16064

Line 125: 68 852 2944 8148 15104 16128

Line 126: 178 760 5058 16102 16170 16192

Line 127: 108 813 4956 9673 15963 16256

Line 128: 7 261 2618 4601 6204 16313 16320

Line 129: 122 687 5755 7566 15740 16384

Line 130: 1350 2234 4864 7872 16384 16448

Line 131: 641 2365 4172 6767 16454 16512

Line 132: 496 1088 4224 15985 16512 16576

Line 133: 24 621 1930 4096 16236 16627 16640

Line 134: 21 406 1015 4087 7159 16663 16704

Line 135: 614 1958 15718 16230 16742 16768

Line 136: 57 320 2240 5248 8000 16768 16832

Line 137: 21 174 899 4832 7040 16320 16896

Line 138: 38 404 1360 3118 6634 16946 16960

Line 139: 0 512 2432 8192 8768 16960 17024

Line 140: 33 384 1261 3732 6804 16837 17024;

wherein, the number in the ith row represents the column position with the median value of 1 in the 64 th i row in the H matrix, and the column positions with the median value of 1 in the 64 th row to 64i +63 row in the H matrix are obtained by cyclic shift according to the cyclic shift matrix.

20. The encoding apparatus as claimed in claim 13, wherein the code length n =9240, the code rate is R =7/8, the Z =42, and the H matrix is represented as:

21. The encoding apparatus as claimed in claim 13, wherein the code length n =9954, the code rate R =13/16, the Z =42, and the H matrix when s =210 is represented as:

line 0: 48 749 1801 2039 2142 2856 3612 4242 4956 5628 6426 7056 7812 8022 8106

Line 1: 14 141 410 1080 2350 2536 3310 4312 4923 5279 6078 6898 7923 8137 8148

Line 2: 40 184 459 1581 1953 2727 3399 4029 4827 5945 6462 6843 7515 8187 8190

Line 3: 47 150 714 1428 2100 2968 3849 4564 4914 5792 6384 7225 7770 8190 8232

Line 4: 186 344 1069 2282 2578 3154 3935 5013 5370 5972 6686 7358 8237 8274

Line 5: 7 114 399 1113 2510 2583 3852 4341 5047 5803 6111 7252 7664 8295 8316

Line 6: 19 177 776 1450 1864 2656 3311 4478 5263 5759 6390 6776 7935 8330 8358

Line 7: 161 462 1218 1806 2730 3645 4166 4994 5857 6174 6989 7537 8358 8400

Line 8: 5186 459 1617 2115 3121 3568 3903 4783 5515 6633 6672 7514 8420 8442

Line 9: 167 334 1653 2011 2712 3500 4317 4610 5695 6267 7138 7737 8482 8484

Line 10: 151 861 1717 2058 2932 3570 4398 4872 5586 6342 7346 7953 8484 8526

Line 11: 59 108 491 1451 2152 3133 3779 4171 4705 5558 6012 6679 7532 8549 8568

Line 12: 52 267 590 1264 1683 2481 3656 4440 4581 5920 6242 6955 7951 8571 8610

Line 13: 51 122 750 1155 1818 2754 3255 4241 4683 5313 6222 6830 7425 8631 8652

Line 14: 0 126 798 1470 2226 2940 3713 4326 4998 5712 6513 7140 7854 8652 8694

Line 15: 1177 992 1259 2417 2887 3329 4137 5245 5412 6271 7069 7874 8735 8736

Line 17: 154 803 1222 1895 2774 3180 4105 5235 5851 5994 6732 7889 8813 8820

Line 18: 42 210 882 1554 2268 3024 3696 4410 5082 5796 6510 7224 7938 8820 8862

Line 19: 186 518 1734 2248 3437 4094 4606 5357 6172 7216 7571 8102 8892 8904

Line 20: 66 133 559 1273 1903 2986 3457 4087 4843 5528 6344 6859 7573 8917 8946

Line 21: 91 355 588 1479 2403 3034 3749 4247 4988 5460 6216 6888 7602 8946 8988

Line 22: 14 181 299 1159 1983 3035 3240 3978 4729 5671 5922 7120 7823 9005 9030

Line 23: 45 156 479 986 2053 3785 3842 5164 5630 64737169 7468 8025 8080 9072

Line 26: 195 992 1008 1856 2721 3726 4490 4698 5470 6094 7142 7512 9156 9198

Line 27: 43 131 366 1355 1945 2436 3245 4070 4536 5613 6076 6947 7786 9219 9240

Line 28: 4122 646 1661 2320 2586 3497 4041 5155 5496 5981 7284 7415 9037 9282

Line 29: 52 184 857 1273 2387 2814 3333 4201 4853 5388 6496 6774 7624 9316 9324

Line 30: 57 192 560 1551 1794 3104 3651 3978 4682 5457 6200 7223 7735 9354 9366

Line 31: 138 630 1302 1932 2857 3486 4116 5092 5502 6415 6930 7644 9366 9408

Line 32: 165 909 1176 2075 2646 3318 4419 4746 5418 6211 6814 7999 9421 9450

Line 33: 27 207 950 1426 1754 3099 3461 3910 4925 5434 6137 6720 7703 9485 9492

Line 34: 148 300 1073 1721 2559 3373 4012 5181 5315 6427 6735 7997 9263 9534

Line 35: 38 96 700 1375 2184 3276 4359 4890 5334 6132 7284 7392 8064 9534 9576

Line 36: 6130 550 1101 1722 2520 3393 3906 4620 5549 6697 6780 7606 9612 9618

Line 37: 4 199 603 1023 2241 2808 3224 4006 4824 5926 6043 6658 7824 9645 9660

Line 38: 36 133 761 1891 2096 2394 3414 3864 4789 5728 6083 7022 7566 9496 9702

Line 39: 35 261 428 1549 2102 2510 3594 3973 4544 5314 6368 7034 7387 9739 9744

Line 40: 65 168 840 1512 2454 2982 3654 4368 5040 5754 6583 7182 7896 9744 9786

Line 41: 8384 826 1396 2203 2752 3532 4375 4704 5376 6527 6997 7434 9660 9828

Line 43: 38 185 773 1557 2201 2915 3800 4301 5037 5687 6485 7115 9825 9887 9912

Line 44: 71 149 393 1197 1678 2606 2976 3693 4501 4771 5812 6318 6674 7376 9954

Line 45: 81 208 887 1145 2286 2848 3203 4523 4634 5261 6587 7061 7687 9965 9996

Line 49: 109 199 521 1313 1865 2789 3419 4049 5616 6617 7318 7535 10013 10122;

22. The encoding apparatus as claimed in claim 13, wherein the code length n =10752, the code rate R =3/4, the Z =42, and the H matrix when s =294 is represented as:

line 0: 72 241 462 1386 3402 4452 5749 6504 7571 7812 8096 8106

Line 1: 33 89 439 1253 2965 3161 4248 5697 6830 7833 8140 8148

Line 2: 201 786 1893 2541 3251 4341 5663 6589 7787 8165 8190

Line 3: 146 672 1512 2520 3712 4578 5628 6678 7518 8190 8232

Line 4: 93 280 2121 2213 3550 4579 5512 6328 7274 7801 8274

Line 5: 106 672 1998 2903 3620 4410 5418 6342 7573 8274 8316

Line 6: 150 544 1372 2290 3138 4559 6029 6831 7223 8347 8358

Line 7: 99 630 2038 2883 3858 4521 5886 6607 8241 8386 8400

Line 8: 38 227 978 1896 2177 3278 4668 5203 6859 7112 8022 8442

Line 9: 204 429 1353 2319 3369 4654 5469 6393 7531 8451 8484

Line 10: 272 840 1764 2856 3780 4830 5796 6893 7854 8484 8526

Line 11: 169 600 1218 2246 3192 4421 5166 6333 7411 8566 8568

Line 12: 73 177 1130 1215 2181 3441 4789 5425 6697 7888 8598 8610

Line 13: 22 87 961 1602 2402 3577 4820 5765 6644 7406 8610 8652

Line 14: 59 150 411 1428 2438 3711 4281 6087 6452 7140 8670 8694

Line 15: 121 282 1562 2196 2639 3224 4779 5326 6452 8717 8736

Line 16: 189 645 1422 2512 3143 4303 5924 6532 7340 8025 8778

Line 17: 99 592 2128 3369 3532 4991 5506 6556 7671 8782 8820

Line 18: 206 882 1848 2940 3864 4914 5880 6888 7896 8820 8862

Line 19: 47 185 496 1987 2701 3163 4934 5171 6275 7479 8864 8904

Line 20: 203 449 1941 2346 3609 4284 5511 6659 7292 8904 8946

Line 21: 261 363 2175 2398 3258 4475 5355 6406 7527 8975 8988

Line 22: 20 43 261 1528 2531 3990 4159 5351 6095 7103 8756 9030

Line 23: 84 295 1629 2671 3263 4664 6201 6756 7381 9041 9072

Line 24: 4 290 1018 1596 2646 3807 4620 5876 6762 7644 9072 9114

Line 25: 55 153 331 1301 2633 2914 3230 5066 5590 6368 9152 9156

Line 26: 173 546 1452 2978 3444 4546 5805 6468 7350 9156 9198

Line 27: 223 545 1709 2593 3983 4168 5464 6895 7682 9210 9240

Line 28: 2129 732 1319 2809 3986 5000 5753 6220 7903 9244 9282

Line 29: 277 350 1489 2577 3290 4382 6150 7015 7280 9296 9324

Line 30: 244 682 1302 2383 3661 4898 5686 6300 7310 9324 9366

Line 31: 93 852 1260 2268 3325 4242 5292 6856 7712 9366 9408

Line 32: 39 213 897 1193 2702 3108 4926 5921 7137 8414 9434 9450

Line 33: 37 244 756 1779 2688 3612 4662 5712 6804 7686 9477 9492

Line 34: 164 317 1339 2388 4054 4349 5357 6288 7955 9524 9534

Line 35: 41 135 470 2093 2795 3939 4908 5967 6414 7380 9551 9576

Line 36: 262 924 1890 2982 3906 4956 6028 6930 7938 9576 9618

Line 37: 150 802 1501 2663 4062 4410 5290 6242 7719 9627 9660

Line 38: 239 798 1680 2772 3696 4746 5754 7060 8400 9660 9702

Line 39: 54 134 256 1735 2230 4155 4762 5960 6726 7497 9708 9744

Line 40: 286 1077 2073 2488 3580 4546 5596 6646 7486 9754 9786

Line 41: 3 134 935 1814 2906 3830 4880 5846 6854 7991 9794 9828

Line 42: 21 188 966 1932 3024 3948 4998 5922 6972 8004 9828 9870

Line 43: 42 847 1810 2562 4130 4960 5670 6720 7560 9891 9912

Line 44: 79 249 578 1160 2126 3456 4192 5132 6589 7617 9937 9954

Line 45: 70 163 714 1554 4112 4842 5758 6969 7602 8064 9954 9996

Line 46: 151 1159 1640 3094 3334 4341 5568 6515 7263 10027 10038

Line 47: 75 285 1832 2870 3903 5110 5389 6132 7887 10038 10080

Line 48: 70 267 1781 3037 3670 4607 5407 6946 7957 10114 10122

Line 49: 98 571 1358 2184 3545 4200 5298 6363 7453 10122 10164

Line 50: 114 973 1881 2346 4098 4399 5556 6153 7231 10205 10206

Line 51: 141 620 1186 3398 5073 5424 6503 7735 8069 10232 10248

Line 52: 39 245 405 2234 3494 3873 4386 5223 6189 8049 10263 10290

Line 53: 64 154 630 1470 2436 3842 5036 5544 6594 7434 10290 10332

Line 54: 197 765 1664 3017 3415 4625 5254 6990 7926 10370 10374

Line 55: 110 1164 1638 2730 3654 4704 5810 7054 7728 10374 10416

Line 56: 99 1099 1422 2748 4024 4294 5286 6798 7766 10457 10458

Line 57: 204 731 1428 2846 3751 5211 5992 6510 7626 10458 10500

Line 58: 168 504 1541 2352 3910 4842 5866 6426 7308 10528 10542

Line 59: 1669 809 1861 3047 3150 4498 5636 6604 7182 10560 10584

Line 60: 95 266 1274 2306 3456 4122 5226 6111 9007 10592 10626

Line 61: 202 372 1717 2831 3306 4213 5130 6981 7240 9007 10668

Line 62: 82 229 1008 1974 3087 3990 5040 5964 7058 7980 10668 10710

Line 63: 224 378 1591 2740 3318 4745 5376 6258 10649 10715 10752

Line 64: 236 1023 1218 2452 3522 4204 5468 6130 7179 10758 10794

Line 65: 143 280 2057 2999 3753 4455 5138 6796 7436 10808 10836

Line 66: 84 882 1722 2814 3738 4788 6256 7162 10626 10836 10878

Line 67: 230 254 1745 2499 3792 4734 5609 6179 7188 8741 10920

Line 68: 7 201 1083 2049 3099 4065 5100 6039 7047 8181 10953 10962

Line 69: 0 210 1092 2058 2604 3627 4074 5082 6048 7056 10962 11004

Line 70: 213 1077 1946 2400 3492 4500 6074 6698 7398 10899 11004;

23. The encoding apparatus as claimed in claim 13, wherein the code length n =12936, the code rate is R =5/8, the Z =42, and the H matrix when s =504 is represented as:

line 0: 11 239 1276 1605 4020 5316 7189 7320 8106

Line 1: 72 1042 2455 3948 5796 7644 8106 8148

Line 2: 121 399 3219 3290 5455 6902 8174 8190

Line 3: 284 450 1800 4067 5565 6725 8221 8232

Line 4: 34 212 1153 1801 3435 6530 6963 7354 8274

Line 5: 51 849 2571 4523 6015 7905 8283 8316

Line 6: 35 261 939 3041 4176 5940 7911 8356 8358

Line 7: 205 795 3331 4200 6170 7350 8358 8400

Line 8: 36 258 644 2338 5003 5923 6730 7125 8442

Line 9: 53 498 1696 2630 4694 6605 8482 8484

Line 10: 19 377 1870 4168 5482 7246 8484 8526

Line 11: 3289 359 2099 3708 5598 7404 8538 8568

Line 12: 76 294 1680 4353 5469 7555 7938 8610

Line 13: 52 503 3132 3713 5178 6877 8614 8652

Line 14: 26 473 1669 3524 5654 6943 7195 8694

Line 15: 130 1387 2254 3510 6893 8658 8718 8736

Line 16: 334 826 2268 4794 5754 7602 8568 8778

Line 17: 241 1036 2566 5163 5673 8751 8792 8820

Line 18: 3577 434 2583 3320 5130 7741 8849 8862

Line 19: 8192 836 3370 4490 6200 7766 8900 8904

Line 20: 32 230 966 2772 4750 6258 8736 8904 8946

Line 21: 53 717 2685 3866 6485 7891 8983 8988

Line 22: 0 229 1134 2898 5082 6342 7879 8988 9030

Line 23: 59 490 2939 4258 5847 7656 9064 9072

Line 24: 21 100 434 1574 3960 5106 7712 9093 9114

Line 25: 3493 1193 2117 3797 6057 7493 9131 9156

Line 26: 1310 1295 2604 4494 6048 8064 9156 9198

Line 27: 14 213 714 2855 4368 6365 7930 9216 9240

Line 28: 40 336 2142 3822 5904 7518 7595 9282

Line 29: 170 487 2170 4229 5293 7279 9296 9324

Line 30: 1394 1184 2394 4074 6284 6720 8232 9366

Line 31: 201 443 2118 3563 5124 9351 9374 9408

Line 32: 10 340 1006 2399 4451 5930 8182 9271 9450

Line 33: 185 681 1848 4205 5347 7111 9463 9492

Line 34: 69 350 1994 4297 5288 7810 9500 9534

Line 35: 141 1075 2700 5167 6554 7452 9571 9576

Line 36: 104 423 2445 4334 6337 7191 7420 9618

Line 37: 171 467 2788 4991 5563 9595 9637 9660

Line 38: 44 460 1919 4029 6575 9596 9685 9702

Line 39: 295 517 2310 4678 5864 7770 9702 9744

Line 40: 15 314 1350 1617 3509 5260 7982 9765 9786

Line 41: 52 874 2494 3316 5541 7259 9786 9828

Line 42: 70 460 1932 5034 5622 7308 9156 9870

Line 43: 21 347 1643 3449 6824 7659 9878 9912

Line 44: 40 195 446 3071 3612 6027 8030 9912 9954

Line 45: 145 434 1639 4833 5977 8045 9982 9996

Line 46: 9 251 1302 3066 4746 6510 9861 9996 10038

Line 47: 62 480 2790 4390 5236 8427 10043 10080

Line 48: 73 387 1974 3769 6193 7495 10080 10122

Line 49: 136 638 3082 4323 5573 7154 10149 10164

Line 50: 50 400 1826 4599 6092 7433 9945 10206

Line 51: 37 312 1024 2830 4636 6335 10180 10222 10248

Line 52: 2393 837 2436 4284 6542 7980 9324 10290

Line 53: 5 201 1511 2226 3864 5670 10284 10309 10332

Line 54: 160 630 2837 4242 5964 7938 10332 10374

Line 55: 125 1349 1940 3649 5058 6822 10415 10416

Line 56: 285 615 2071 5062 5801 9264 10451 10458

Line 57: 216 898 3168 3685 5513 7010 10496 10500

Line 58: 74 458 2058 4989 6035 7434 10534 10542

Line 59: 147 339 2158 3570 5418 7619 10551 10584

Line 60: 265 504 3413 4539 5838 9432 10500 10626

Line 61: 66 400 2138 3407 6433 8259 10654 10668

Line 62: 80 492 2199 3603 6358 7250 10702 10710

Line 63: 57 1328 2427 4405 5218 10621 10745 10752

Line 64: 81 356 3016 3597 6229 7951 8606 10794

Line 65: 0 348 546 2352 4032 6488 7812 10794 10836

Line 66: 165 321 1825 4104 5180 7049 10838 10878

Line 67: 357 1231 2364 4954 6651 8014 9853 10920

Line 68: 55 348 1956 5109 5768 7498 10961 10962

Line 69: 168 1260 3024 5634 6468 10878 10962 11004

Line 70: 59 450 4576 5512 8071 10868 11026 11046

Line 71: 216 954 3342 3906 5712 7560 11046 11088

Line 72: 72 480 1722 3552 5250 7056 10088 11130

Line 73: 281 405 2291 3905 6669 11102 11130 11172

Line 74: 33 296 1228 2740 4621 6114 7140 9768 11214

Line 75: 49 1131 1562 4644 6892 10785 11254 11256

Line 76: 26 215 1103 2646 4536 6090 11173 11256 11298

Line 77: 169 392 2921 3752 6384 7828 11324 11340

Line 78: 104 414 2023 3270 5696 7032 10614 11382

Line 79: 0 462 2321 3990 6958 7686 11382 11424

Line 80: 38 147 1077 1891 3392 6448 7703 11340 11466

Line 81: 49 407 1977 4450 5415 7178 11505 11508

Line 82: 66 410 2745 4487 5418 6868 11424 11550

Line 83: 123 1455 1754 4752 6998 11509 11581 11592

Line 84: 57 404 2210 4179 5830 7584 8510 11634

Line 85: 148 434 2253 5057 5642 7823 11648 11676

Line 86: 0 126 1050 2975 4838 6300 11597 11676 11718

Line 87: 218 1552 1564 3671 5345 10431 11755 11760

Line 88: 64 703 2882 3712 7118 7267 8670 11802

Line 89: 52 381 2269 4874 5909 9492 11802 11844

Line 90: 8 252 588 2612 2675 4116 5880 7353 11886

Line 91: 43 441 1699 3360 5340 7014 11922 11928

Line 92: 221 477 3267 4107 5214 11794 11941 11970

Line 93: 18 316 1344 3111 4788 6552 9660 11970 12012

Line 94: 118 672 2478 4326 6224 8022 10668 12054

Line 95: 4 277 519 3055 3811 5379 11852 12095 12096

Line 96: 26 264 1404 3108 4830 6594 11592 12096 12138

Line 97: 169 868 3763 5725 8081 12045 12155 12180

Line 98: 56 380 2885 3640 5741 7070 7541 12222

Line 99: 177 403 1734 4245 6763 12201 12252 12264

Line 100: 85 399 2055 3918 6608 11379 11799 12306

Line 101: 274 1092 2856 4662 6860 10248 12306 12348

Line 102: 48 895 2199 4585 6770 7334 12376 12390

Line 103: 37 257 1430 3152 4916 6680 12188 12392 12432

Line 104: 190 331 3202 4063 5974 11952 12286 12474

Line 105: 7252 1470 3192 4956 7854 12432 12474 12516

Line 106: 166 756 2520 4410 6418 10752 11508 12558

Row 107: 85 577 2553 4928 6683 7619 12562 12600

Line 108: 21 341 882 3187 4578 6174 8316 12600 12642

Line 109: 370 731 1905 3679 6070 7291 12683 12684

Line 110: 299 575 2026 4120 6821 7075 8860 12726

Line 111: 20 328 773 3258 4505 6684 7779 12740 12768

Line 112: 54 429 2516 3977 5795 11885 12725 12810

Line 113: 22 254 1176 2940 4874 6384 12768 12810 12852

Line 114: 15 160 1338 1629 3459 5414 11447 12852 12894

Line 115: 21 234 1466 3014 4132 6151 12852 12931 12936

Line 116: 344 1493 2688 4807 6132 11172 12936 12978

Line 117: 74 1171 1806 3528 9072 12516 12999 13020

Line 118: 159 996 1764 3848 5491 8423 11112 13062

Line 119: 165 473 2530 3841 5324 13032 13074 13104

Line 120: 54 490 2727 3811 5626 10361 13023 13146

Line 121: 33 84 924 2730 4719 6216 9408 13146 13188

Line 122: 68 468 1881 4704 6984 7744 13198 13230

Line 123: 9 200 602 2392 3937 7448 12532 13242 13272

Line 124: 6 264 1224 2988 4710 6432 11045 13278 13314

Line 125: 33 218 1394 3481 4880 6644 13145 13322 13356

Line 126: 313 1512 3301 4998 6762 13140 13356 13398

Line 127: 6 298 1520 2942 4473 6279 12296 12716 13398;

24. The encoding apparatus as claimed in claim 13, wherein the code length n =16128, the code rate is R =1/2, the Z =42, and the H matrix when s =924 is represented as:

line 0: 289 924 4942 5554 7862 8106

Line 1: 348 803 4359 6838 8132 8148

Line 2: 86 767 2716 7099 7872 8190

Line 3: 37 473 1999 4817 7799 8190 8232

Line 4: 8 555 2727 3888 6453 8273 8274

Line 5: 194 882 4507 7182 8274 8316

Line 6: 31 520 1088 5226 7966 8329 8358

Line 7: 7 312 1561 3451 7943 8373 8400

Line 8: 19 357 1050 4580 7266 8400 8442

Line 9: 288 859 5461 6111 8477 8484

Line 10: 21 494 1974 5040 8022 8484 8526

Line 11: 25 454 675 2568 6392 8566 8568

Line 12: 5 205 1551 4410 8025 8568 8610

Line 13: 120 616 2680 6841 8620 8652

Line 14: 122 794 3357 6300 8148 8694

Line 15: 136 835 2842 7922 8699 8736

Line 16: 246 1846 3098 6645 8656 8778

Line 17: 563 1019 4017 6362 8818 8820

Line 18: 42 530 1554 4751 7825 8820 8862

Line 19: 262 736 2811 5592 8888 8904

Line 20: 447 1277 2688 6977 8768 8946

Line 21: 80 752 3344 5760 8973 8988

Line 22: 24 394 1764 4788 7933 8988 9030

Line 23: 109 2294 5028 6372 9049 9072

Line 24: 18 150 943 2892 7832 8940 9114

Line 25: 54 431 853 5006 7158 9114 9156

Line 26: 50 246 1615 5310 6427 9177 9198

Line 27: 36 563 1596 4214 7077 9213 9240

Line 28: 32 344 1424 3311 5650 9247 9282

Line 29: 79 183 1344 4494 7476 9282 9324

Line 30: 69 684 2856 6973 9072 9366

Line 31: 40 339 707 3569 9328 9403 9408

Line 32: 35 430 627 4083 6034 7879 9450

Line 33: 513 585 3116 5877 9489 9492

Line 34: 3289 814 2522 7558 9505 9534

Line 35: 101 859 3799 6991 9553 9576

Line 36: 126 1134 4974 8000 9576 9618

Line 37: 72 304 1329 3741 6891 9654 9660

Line 38: 36 210 2118 4830 9408 9660 9702

Line 39: 76 441 1379 4160 6135 9740 9744

Line 40: 57 870 3234 7028 9744 9786

Line 41: 54 855 4202 6243 9819 9828

Line 42: 65 191 1944 4185 5968 9244 9870

Line 43: 73 612 3570 6174 9870 9912

Line 44: 545 2251 3669 6390 9917 9954

Line 45: 0 629 2159 3005 7400 9977 9996

Line 46: 38 413 1932 4998 7980 9996 10038

Line 47: 426 1339 2924 5874 10078 10080

Line 48: 33 467 1103 2606 6935 9865 10122

Line 49: 13 352 1592 4700 7682 10160 10164

Line 50: 97 679 3181 6336 10111 10206

Line 51: 70 586 1848 4914 10164 10206 10248

Line 52: 85 779 3381 5895 8763 10290

Line 53: 504 1553 3753 6370 10318 10332

Line 54: 110 646 5493 6048 9492 10374

Line 55: 269 1149 4448 7790 10359 10416

Line 56: 24 487 1092 4242 7308 10416 10458

Line 57: 81 326 2126 4139 10384 10494 10500

Line 58: 125 785 2922 7164 9930 10542

Line 59: 0 380 1596 5132 7686 10542 10584

Line 60: 233 833 3095 8080 10586 10626

Line 61: 3 567 1442 4530 7098 10626 10668

Line 62: 580 1436 4617 7260 10690 10710

Line 63: 108 828 2771 6471 10751 10752

Line 64: 227 2326 3519 5922 10752 10794

Line 65: 78 571 3383 6797 10825 10836

Line 66: 37 334 720 4623 5931 8928 10878

Line 67: 84 844 2976 6881 10919 10920

Line 68: 124 599 3035 5659 10864 10962

Line 69: 14 462 2394 5376 10920 10962 11004

Line 70: 51 817 4344 5700 9078 11046

Line 71: 102 693 2562 6201 11046 11088

Line 72: 101 647 3458 6922 11104 11130

Line 73: 19 214 1033 2607 7742 11133 11172

Line 74: 482 610 3042 5898 11190 11214

Line 75: 102 1389 3910 7380 11218 11256

Line 76: 36 384 2058 5082 7896 11256 11298

Line 77: 523 2288 3727 6552 11307 11340

Line 78: 415 670 5084 7449 11370 11382

Line 79: 107 973 2940 6685 11382 11424

Line 80: 77 920 3972 11040 11424 11466

Line 81: 37 475 1007 6059 11014 11489 11508

Line 82: 607 1680 4809 7770 11508 11550

Line 83: 164 1482 4243 6475 11586 11592

Line 84: 24 554 1722 4746 7812 11592 11634

Line 85: 2559 1428 5380 7560 11636 11676

Line 86: 550 2188 3723 10261 11693 11718

Line 87: 65 410 2448 3330 10260 11730 11760

Line 88: 57 816 5378 6384 11760 11802

Line 89: 53 795 3297 7220 11804 11844

Line 90: 230 750 2786 5642 8666 11886

Line 91: 71 736 3549 7132 11924 11928

Line 92: 193 852 5217 6594 11928 11970

Line 93: 74 220 2229 4910 7570 12001 12012

Line 94: 291 785 2965 5578 11880 12054

Line 95: 304 2014 3784 6905 12079 12096

Line 96: 53 607 3379 6487 12031 12138

Line 97: 61 292 720 3442 12136 12178 12180

Line 98: 39 226 716 2637 6281 12203 12222

Line 99: 348 1765 4077 6029 12236 12264

Line 100: 75 763 4053 5718 11199 12306

Line 101: 88 2391 5334 7498 12264 12348

Line 102: 92 918 3627 6777 12384 12390

Line 103: 69 524 2268 5250 12306 12390 12432

Line 104: 514 696 3492 5712 10785 12474

Line 105: 94 612 3166 8100 12512 12516

Line 106: 120 342 1470 4578 7602 12516 12558

Row 107: 72 807 2991 5531 12579 12600

Line 108: 209 713 2531 5689 11097 12642

Line 109: 352 1176 4326 7686 12642 12684

Line 110: 464 1173 4542 6510 12724 12726

Line 111: 336 677 4026 10514 12735 12768

Line 112: 123 835 3444 7453 12768 12810

Line 113: 74 489 2550 5256 6286 12828 12852

Line 114: 259 1269 2680 5714 12619 12894

Line 115: 388 2396 4885 7350 12894 12936

Line 116: 7 731 1726 3121 7658 12936 12978

Line 117: 110 901 4032 7056 12978 13020

Line 118: 478 1129 4863 7055 12893 13062

Line 119: 7552 1512 4620 7995 13062 13104

Line 120: 3431 1914 3948 7202 13035 13146

Line 121: 272 1663 4706 13116 13154 13188

Line 122: 338 740 3265 5796 8177 13230

Line 123: 63 398 918 4980 6662 13255 13272

Line 124: 95 920 3822 7607 13272 13314

Line 125: 15 161 1816 3663 5820 13326 13356

Line 126: 303 1853 4953 5605 13361 13398

Line 127: 109 650 3276 6216 13398 13440

Line 128: 59 691 2767 5611 9828 13482

Line 129: 172 2788 5057 6679 13499 13524

Line 130: 551 2436 5418 13188 13524 13566

Line 131: 310 858 2648 6120 13573 13608

Line 132: 444 701 3883 7375 13637 13650

Line 133: 72 883 4104 7170 13680 13692

Line 134: 22 378 2184 5166 10500 13692 13734

Line 135: 517 638 3631 5868 13745 13776

Line 136: 84 1008 4200 7398 13776 13818

Line 137: 106 644 2571 5502 13443 13860

Line 138: 15 334 892 4299 6587 13881 13902

Line 139: 73 206 1774 4656 7702 13940 13944

Line 140: 212 798 5328 6846 13819 13986

Line 141: 154 761 3652 12437 14003 14028

Line 142: 21 152 1900 3486 7298 14028 14070

Line 143: 37 666 2030 5533 6526 14090 14112

Line 144: 8 433 2387 4284 12449 14112 14154

Line 145: 127 750 5207 7618 14161 14196

Line 146: 13 252 1890 4956 8044 14196 14238

Row 147: 130 841 3439 7513 14254 14280

Line 148: 391 1260 5145 7392 14280 14322

Line 149: 3 266 1386 4536 7518 13944 14364

Line 150: 118 1058 3221 6064 14324 14406

Line 151: 21 67 843 2842 14404 14410 14448

Line 152: 141 2071 2909 6274 9747 14490

Line 153: 296 2351 4692 5761 14497 14532

Line 154: 92 920 6235 9435 13458 14574

Line 155: 108 740 4417 6772 14574 14616

Line 156: 36 409 1936 2744 5965 14651 14658

Line 157: 16 336 2142 5199 8064 14658 14700

Line 158: 282 645 4043 6655 14735 14742

Line 159: 72 414 1218 5767 6731 14742 14784

Line 160: 437 1376 3571 7259 14804 14826

Line 161: 49 508 2310 5292 6720 14826 14868

Line 162: 19 149 823 3103 6752 14889 14910

Line 163: 96 2481 5351 6930 14910 14952

Line 164: 374 774 5046 7667 14984 14994

Line 165: 110 1642 4138 6129 15035 15036

Line 166: 93 744 3776 6520 14539 15078

Line 167: 28 420 2226 5208 7938 15078 15120

Line 168: 200 877 4676 6187 15152 15162

Line 169: 29 470 1227 3796 6964 15200 15204

Line 170: 67 760 3700 14475 15208 15246

Line 171: 9316 1700 4116 7224 15246 15288

Line 172: 432 2088 3528 6678 15036 15330

Line 173: 23 243 771 4466 15325 15330 15372

Line 174: 97 683 3212 7043 10869 15414

Line 175: 5 196 2408 4461 6887 12638 15456

Line 176: 8 248 650 3936 6171 15481 15498

Line 177: 536 2100 5124 15414 15498 15540

Line 178: 17 382 2197 3192 7317 14532 15582

Line 179: 521 1236 3242 5834 15598 15624

Line 180: 56 257 966 4291 7588 15624 15666

Line 181: 627 2446 5100 6635 15701 15708

Line 182: 13 623 1203 5259 15544 15713 15750

Line 183: 61 589 1806 4872 15372 15750 15792

Line 184: 62 754 3694 6844 15815 15834

Line 185: 86 897 5434 15564 15834 15876

Line 186: 2 468 893 3437 6142 15905 15918

Line 187: 30 314 1748 2884 7275 15947 15960

Line 188: 134 608 3018 6627 11853 16002

Line 189: 67 652 1669 4735 7759 16033 16044

Row 190: 16 639 2352 5334 12194 16044 16086

Line 191: 261 2490 3846 5670 15960 16128

Line 192: 365 768 4400 5889 16129 16170

Line 193: 294 2016 5421 16124 16170 16212

Line 194: 120 900 3065 7325 13371 16254

Line 195: 56 816 3108 6006 16254 16296

Line 196: 80 631 4376 6464 16303 16338

Line 197: 208 2039 3990 16249 16338 16380

Line 198: 88 694 4255 6577 16384 16422

Line 199: 10 187 2161 4767 7769 16422 16464

Line 200: 117 779 3849 5561 10083 16506

Line 201: 23 454 1302 4452 13194 16506 16548

Line 202: 143 879 3160 6005 16487 16590

Line 203: 34 309 1878 3928 16578 16625 16632

Line 204: 85 863 2852 7086 16330 16674

Line 205: 210 1504 4368 7434 16674 16716

Line 206: 14 472 1209 3864 16247 16730 16758

Line 207: 121 908 4836 5928 16777 16800

Line 208: 112 924 4158 15402 16800 16842

Line 209: 73 634 3574 16636 16845 16884

Line 210: 97 819 4567 15990 16663 16926

Line 211: 92 691 4706 6309 16952 16968

Line 212: 0 504 2478 5460 14448 16968 17010

Line 213: 36 202 1712 3961 7532 16896 17010;

25. A chip comprising a processor configured to retrieve from a memory and execute instructions stored in the memory, such that a communication device on which the chip is installed performs the method of any of claims 1-12.

26. A computer-readable storage medium for storing a computer program comprising instructions for performing the method of any one of claims 1-12.