# US 2024/0204801 A1 · Low density parity check code encoding method and communication apparatus

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- Number: US 2024/0204801 A1
- Document ID: US20240204801A1
- Status: Published application
- Kind: A1
- Application number: 18/523,495
- Filed: 2023-11-29
- Published: 2024-06-20
- Earliest claimed: 2020-01-03
- Assignees: Huawei Technologies Co., Ltd.
- Applicants: Huawei Technologies Co., Ltd.
- Inventors: Guido Montorsi; Sergio Benedetto; Wei Lin; Yan Xin
- Web page: https://patentgrep.com/patent/US20240204801A1

## CPC

- H03M 13/116: {Quasi-cyclic LDPC [QC-LDPC] codes, i.e. the parity-check matrix being composed of permutation or circulant sub-matrices}
- H03M 13/118: {Parity check matrix structured for simplifying encoding, e.g. by having a triangular or an approximate triangular structure (H03M13/1165 takes precedence)}
- H03M 13/1188: {wherein in the part with the double-diagonal at least one column has an odd column weight equal or greater than three}
- H03M 13/616: {Matrix operations, especially for generator matrices or check matrices, e.g. column or row permutations}
- H03M 13/6306: {Error control coding in combination with Automatic Repeat reQuest [ARQ] and diversity transmission, e.g. coding schemes for the multiple transmission of the same information or the transmission of incremental redundancy (H03M13/3761, H03M13/3769 and H03M13/635 take precedence)}
- H03M 13/6393: {Rate compatible low-density parity check [LDPC] codes}
- H03M: CODING; DECODING; CODE CONVERSION IN GENERAL (using fluidic means F15C4/00; optical analogue/digital converters G02F7/00; coding, decoding or code conversion, specially adapted for particular applications, see the relevant subclasses, e.g. G01D, G01R, G06F, G06T, G09G, G10L, G11B, G11C, H04B, H04L, H04M, H04N; ciphering or deciphering for cryptography or other purposes involving the need for secrecy G09C)

## Abstract

This application provides an LDPC code encoding method and a communication apparatus, to meet a requirement of increasing redundant bits through retransmission in an IR-HARQ mechanism, so as to decrease a channel coding rate, and improve decoding performance of an LDPC code. In the method, a check matrix of the LDPC code is used as a basic matrix, and the basic matrix is extended to obtain a mother matrix compatible with a plurality of code rates. During LDPC encoding, a transmit device reads, from the mother matrix, a check matrix corresponding to a required code rate, and performs LDPC encoding on an information bit sequence based on the read check matrix. LDPC encoding is performed on the information bit sequence by using check matrices of different sizes, to obtain different quantities of redundant bits.

## Claims

### Claim 1

A computer program product comprising programming instructions stored in a computer readable storage medium for enabling a computer to perform operations comprising:
performing, based on a first check matrix, low-density parity-check (LDPC) code encoding on an information bit sequence to obtain a first codeword at a first code rate, wherein:
the first check matrix is obtained by reading i rows and j columns from a mother matrix,
the mother matrix comprises: a basic matrix, an extension matrix, a first fixed matrix, and a second fixed matrix,
the basic matrix is located at a top-left corner of the mother matrix,
the extension matrix is located at a bottom-left corner of the mother matrix,
the first fixed matrix is located at a top-right corner of the mother matrix,
the second fixed matrix is located at a bottom-right corner of the mother matrix,
a quantity of rows in the basic matrix is equal to a quantity of rows in the first fixed matrix,
a quantity of rows in the extension matrix is equal to a quantity of rows in the second fixed matrix,
a quantity of columns in the extension matrix is equal to a quantity of columns in the basic matrix,
a quantity of columns in the first fixed matrix is equal to a quantity of columns in the second fixed matrix,
i=p+k, j=q+k, p and q are respectively the quantity of rows and the quantity of columns in the basic matrix,
k≥0, and
i, j, p, q, and k are all integers; and
sending the first codeword.

### Claim 2 (depends on 1)

The computer program product according to claim 1, wherein the operations further comprises:
receiving retransmission indication information;
performing LDPC code encoding on the information bit sequence, based on a second check matrix, to obtain a second codeword at a second code rate, wherein the second check matrix is obtained by reading w rows and z columns from the mother matrix, where:
w=p+h, z=q+h, h>k, and
w, z, and h are all positive integers; and
sending the second codeword.

### Claim 3 (depends on 1)

The computer program product according to claim 1, wherein a code rate corresponding to the basic matrix is 1/2, and
wherein the mother matrix is shown as follows:
H
⁡
(
1
/
2
)
=
[
H
M
⁢
C
(
1
/
2
)
0
1
⁢
2
×
r
H
IR
(
1
/
2
)
I
r
×
r
]
,
where:
H (1/2) indicates the mother matrix, HMC(1/2) indicates the basic matrix, HIR(1/2) indicates the extension matrix, a size of HIR(1/2) is r rows and 24 columns, 1/2 indicates the code rate, 012×r indicates the first fixed matrix, Ir×r indicates the second fixed matrix, 012×r indicates an all-zero matrix with a size of 12 rows and r columns, Ir×r indicates an identity matrix with a size of r rows and r columns, r≥1, k≤r, and r is an integer; and
H
MC
(
1
/
2
)
[
57
-
-
-
50
-
11
-
50
-
79
-
1
0
-
-
-
-
-
-
-
-
-
-
3
-
28
-
0
-
-
-
55
7
-
-
-
0
0
-
-
-
-
-
-
-
-
-
30
-
-
-
24
37
-
-
56
14
-
-
-
-
0
0
-
-
-
-
-
-
-
-
62
53
-
-
53
-
-
3
35
-
-
-
-
-
-
0
0
-
-
-
-
-
-
-
40
-
-
20
66
-
-
22
28
-
-
-
-
-
-
-
0
0
-
-
-
-
-
-
0
-
-
-
8
-
42
-
50
-
-
8
-
-
-
-
-
0
0
-
-
-
-
-
69
79
79
-
-
-
56
-
52
-
-
-
0
-
-
-
-
-
0
0
-
-
-
-
65
-
-
-
38
57
-
-
72
-
27
-
-
-
-
-
-
-
-
0
0
-
-
-
64
-
-
-
14
52
-
-
30
-
-
32
-
-
-
-
-
-
-
-
0
0
-
-
-
45
-
70
0
-
-
-
77
9
-
-
-
-
-
-
-
-
-
-
-
0
0
-
2
56
-
57
35
-
-
-
-
-
12
-
-
-
-
-
-
-
-
-
-
-
0
0
24
-
61
-
60
-
-
27
51
-
-
16
1
-
-
-
-
-
-
-
-
-
-
0
]
wherein “-” indicates an all-zero matrix; and
wherein a Table A indicates a first matrix with a size of 100 rows and 24 columns, HIR(1/2) is obtained by reading r rows and 24 columns from the first matrix, the r rows are any r rows in the 100 rows in the first matrix, and Table A is shown as follows:
TABLE A
1.
nd
1
2
3
4
5
5
0.22
1.34
4.39
8.29
11.80
5
0.7
1.60
4.20
8.7
13.15
5
0.56
4.2
7.77
8.69
9.8
5
0.79
1.49
4.72
8.75
10.58
5
1.47
4.18
7.22
8.38
9.75
5
1.63
4.80
8.21
9.50
10.32
4
3.30
4.44
8.55
10.21
4
0.26
4.67
5.2
8.36
4
4.9
5.14
6.73
8.67
4
0.44
4.35
8.78
22.63
4
0.67
4.18
8.8
23.53
4
0.56
4.45
5.9
6.5
4
0.50
4.50
8.25
15.45
4
0.4
6.76
8.28
23.34
4
0.8
4.50
5.40
6.62
4
0.80
4.20
6.32
13.13
4
0.38
4.47
8.38
11.0
4
0.55
5.45
8.57
15.71
3
0.49
4.67
17.7
3
4.33
8.79
17.27
4
4.76
8.47
11.17
23.58
4
0.68
8.39
11.19
15.26
4
4.3
6.31
8.43
17.6
3
4.24
8.69
13.76
4
0.42
4.1
8.40
21.10
3
0.26
8.34
21.37
4
0.63
2.66
4.47
8.74
3
4.59
11.46
21.3
3
0.67
4.67
22.53
3
0.69
11.47
17.35
3
0.54
8.56
9.36
3
0.24
3.26
4.17
3
2.32
4.43
17.77
3
0.78
2.7
8.76
3
4.36
11.3
17.9
3
0.45
4.14
19.39
3
0.4
3.0
8.59
3
0.4
8.31
19.31
3
0.33
8.54
9.34
3
2.32
3.39
13.48
3
0.69
8.6
21.47
2
5.22
6.46
3
5.10
6.64
17.77
2
6.66
23.42
2
5.62
11.65
3
6.43
11.23
17.43
2
9.48
17.16
3
6.23
11.29
17.6
2
1.44
11.70
2
3.11
6.3
2
9.59
11.34
2
2.49
11.16
2
3.1
5.10
2
2.19
17.8
3
1.77
3.17
11.17
3
6.20
11.17
17.18
2
6.44
13.16
3
6.69
11.71
17.4
3
3.36
11.27
17.18
2
6.0
22.52
3
1.56
11.42
17.39
3
5.43
6.14
11.9
3
3.80
11.50
17.31
2
1.22
3.38
2
7.34
17.64
2
6.80
21.59
3
5.43
6.31
17.77
2
6.71
10.48
3
1.21
6.54
17.22
3
5.65
6.58
17.41
2
7.56
17.78
2
6.47
21.21
3
1.70
3.13
17.41
3
2.22
6.19
17.8
3
5.63
6.74
11.14
3
6.58
10.59
17.17
3
1.29
3.29
5.59
3
6.72
10.71
17.32
2
9.21
17.24
3
2.46
11.79
17.46
3
1.19
6.51
17.75
2
6.53
15.34
3
6.28
11.34
22.24
3
3.73
6.64
11.79
2
11.25
13.49
3
6.48
7.72
11.64
3
6.41
10.18
11.1
2
6.32
21.41
3
3.9
5.45
6.74
3
1.18
3.25
17.50
2
12.72
17.11
3
10.43
11.75
17.40
3
3.29
9.57
11.34
3
10.76
11.67
17.71
2
17.54
23.74
3
6.23
11.5
17.66
2
6.70
18.17
2
3.59
22.41
3
1.72
3.3
17.74
3
3.25
9.31
11.68
wherein an mth element from top to bottom in a column in which d is located indicates a row weight of row m in the first matrix, an nth element (a, b) from left to right in row m in the first matrix indicates that a cyclic shift coefficient of a cyclic shift matrix in row m and column (a+n) in the first matrix is b, all remaining locations in the first matrix are all-zero matrices, n∈{1, 2, 3, 4, 5}, and m, a, and b are all positive integers.

### Claim 4 (depends on 1)

The computer program product according to claim 1, wherein a code rate corresponding to the basic matrix is 1/2, and the mother matrix is shown as follows:
H
⁡
(
1
/
2
)
=
[
H
M
⁢
C
(
1
/
2
)
0
1
⁢
2
×
r
H
IR
(
1
/
2
)
I
r
×
r
]
,
wherein
H (1/2) indicates the mother matrix, HMC(1/2) indicates the basic matrix, HIR(1/2) indicates the extension matrix, a size of HIR(1/2) is r rows and 24 columns, 1/2 indicates the code rate, 012×r indicates the first fixed matrix, Ir×r indicates the second fixed matrix, 012×r indicates an all-zero matrix with a size of 12 rows and r columns, Ir×r indicates an identity matrix with a size of r rows and r columns, r≥1, k≤r, and r is an integer; and
H
MC
(
1
/
2
)
=

[
57
-
-
-
50
-
11
-
50
-
79
-
1
0
-
-
-
-
-
-
-
-
-
-
3
-
28
-
0
-
-
-
55
7
-
-
-
0
0
-
-
-
-
-
-
-
-
-
30
-
-
-
24
37
-
-
56
14
-
-
-
-
0
0
-
-
-
-
-
-
-
-
62
53
-
-
53
-
-
3
35
-
-
-
-
-
-
0
0
-
-
-
-
-
-
-
40
-
-
20
66
-
-
22
28
-
-
-
-
-
-
-
0
0
-
-
-
-
-
-
0
-
-
-
8
-
42
-
50
-
-
8
-
-
-
-
-
0
0
-
-
-
-
-
69
79
79
-
-
-
56
-
52
-
-
-
0
-
-
-
-
-
0
0
-
-
-
-
65
-
-
-
38
57
-
-
72
-
27
-
-
-
-
-
-
-
-
0
0
-
-
-
64
-
-
-
14
52
-
-
30
-
-
32
-
-
-
-
-
-
-
-
0
0
-
-
-
45
-
70
0
-
-
-
77
9
-
-
-
-
-
-
-
-
-
-
-
0
0
-
2
56
-
57
35
-
-
-
-
-
12
-
-
-
-
-
-
-
-
-
-
-
0
0
24
-
61
-
60
-
-
27
51
-
-
16
1
-
-
-
-
-
-
-
-
-
-
0
]
,
wherein “-” indicates an all-zero matrix; and
wherein a Table B indicates a second matrix with a size of 100 rows and 24 columns, HIR(1/2) is obtained by reading r rows and 24 columns from the second matrix, the r rows are any r rows in the 100 rows in the second matrix, and Table B is shown as follows:
TABLE B
2.
nd
1
2
3
4
5
5
0.29
4.22
6.80
8.34
10.39
3
1.60
7.20
11.15
3
2.7
5.7
12.77
2
9.56
13.69
2
14.2
15.8
2
3.49
16.75
2
17.79
20.72
2
19.58
21.22
5
4.47
4.80
18.75
22.18
23.38
2
0.21
8.50
2
5.32
6.63
2
1.30
7.55
2
9.21
11.44
2
2.67
12.36
2
13.26
14.2
2
15.14
16.67
2
3.9
17.73
2
18.35
20.78
2
21.63
22.44
4
0.67
8.53
19.8
23.18
2
4.9
8.56
2
1.5
5.45
2
7.50
9.25
2
6.50
15.45
2
2.76
11.4
2
12.34
14.28
2
13.62
16.8
2
3.50
17.40
2
20.32
23.13
2
18.20
21.80
4
8.38
8.47
19.0
22.38
2
0.71
4.57
2
1.55
7.45
2
5.49
11.67
2
6.7
9.79
2
15.27
16.33
2
2.76
3.47
2
14.17
17.58
2
12.39
19.26
2
13.68
21.19
2
22.3
23.31
4
8.69
8.76
18.43
20.6
2
0.24
4.1
2
1.40
7.42
2
5.10
9.37
2
3.26
11.34
2
15.66
16.63
2
6.47
20.74
2
2.59
14.46
2
17.53
21.3
2
13.67
18.67
2
12.69
22.47
3
4.36
19.54
23.35
2
0.17
8.56
2
1.24
9.26
2
7.32
11.77
2
5.7
15.43
2
3.78
10.76
2
2.3
20.9
2
16.36
19.14
2
6.45
14.39
2
12.0
23.59
2
13.4
17.4
2
21.31
22.31
3
8.33
8.34
18.54
2
0.32
1.39
2
3.6
7.48
2
5.47
9.69
2
11.46
18.22
2
2.10
15.77
2
6.66
10.64
2
12.42
23.65
2
16.62
17.23
2
14.43
20.43
2
13.16
19.48
3
8.23
21.29
22.6
2
0.44
4.70
2
1.3
7.11
2
9.34
11.59
2
3.49
5.16
2
15.10
18.1
2
2.19
21.8
2
14.77
16.17
2
6.17
17.20
2
10.18
20.17
2
12.44
23.16
2
13.69
22.4
3
8.27
8.36
19.71
2
1.18
4.0
2
7.52
9.39
2
3.42
5.56
2
11.43
21.9
2
10.14
15.31
2
19.50
20.80
2
6.22
18.38
2
12.64
14.34
2
2.80
16.59
2
22.43
23.31
3
8.71
13.77
17.48
2
0.22
4.21
wherein an mth element from top to bottom in a column in which d is located indicates a row weight of row m in the second matrix, an nth element (a, b) from left to right in row m in the second matrix indicates that a cyclic shift coefficient of a cyclic shift matrix in row m and column (a+n) in the second matrix is b, all remaining locations in the second matrix are all-zero matrices, n∈{1, 2, 3, 4, 5}, and m, a, and b are all positive integers.

### Claim 5 (depends on 1)

The computer program product according to claim 1, wherein a code rate corresponding to the basic matrix is 2/3, and the mother matrix is shown as follows:
H
⁡
(
2
/
3
)
=
[
H
M
⁢
C
(
2
/
3
)
0
8
×
r
H
IR
(
2
/
3
)
I
r
×
r
]
,
wherein
H(2/3) indicates the mother matrix, HMC(2/3) indicates the basic matrix, HIR(2/3) indicates the extension matrix, a size of HIR(2/3) is r rows and 8 columns, 2/3 indicates the code rate, 08×r, indicates the first fixed matrix, Ir×r indicates the second fixed matrix, 08×r indicates an all-zero matrix with a size of 8 rows and r columns, Ir×r indicates an identity matrix with a size of r rows and r columns, r≥1, k≤r, and r is an integer; and
H
M
⁢
C
(
2
/
3
)
=
[
61
75
4
63
56
-
-
-
-
-
-
8
-
2
17
25
1
0
-
-
-
-
-
-
56
74
77
20
-
-
-
64
24
4
67
-
7
-
-
-
-
0
0
-
-
-
-
-
28
21
68
10
7
14
65
-
-
-
23
-
-
-
75
-
-
-
0
0
-
-
-
-
48
38
43
78
76
-
-
-
-
5
36
-
15
72
-
-
-
-
-
0
0
-
-
-
40
2
53
25
-
52
62
-
20
-
-
44
-
-
-
-
-
-
-
-
0
0
-
-
69
23
64
10
22
-
21
-
-
-
-
-
68
23
29
-
-
-
-
-
-
0
0
-
12
0
68
20
55
61
-
40
-
-
-
52
-
-
-
44
-
-
-
-
-
-
0
0
58
8
34
64
78
-
-
11
78
24
-
-
-
-
-
58
-
-
-
-
-
-
-
0
]
,
wherein “-” indicates an all-zero matrix; and
wherein a Table C indicates a third matrix with a size of 100 rows and 24 columns, HIR(2/3) is obtained by reading r rows and 24 columns from the third matrix, the r rows are any r rows in the 100 rows in the third matrix, and Table C is shown as follows:
TABLE C
3.
n
d
1
2
3
4
5
6
7
6
1.39
2.34
3.22
4.80
7.29
12.15
6
0.77
1.7
2.7
3.20
7.69
12.60
7
0.75
1.2
2.49
3.8
7.72
12.79
13.56
7
0.38
2.18
3.22
4.75
8.80
12.47
13.58
7
0.21
2.32
3.63
4.50
8.21
12.55
14.30
6
0.67
1.67
2.26
3.36
7.2
18.44
6
1.9
2.35
3.78
5.73
8.14
12.44
5
0.18
1.63
2.67
3.53
17.8
5
1.45
2.5
3.56
7.50
11.9
6
0.28
1.76
2.50
3.25
7.45
21.4
6
0.32
1.40
2.34
3.50
12.62
19.8
5
0.38
1.80
3.0
6.20
12.13
5
1.71
2.47
3.57
12.55
23.38
5
0.45
1.79
2.7
10.49
12.67
5
0.27
1.47
2.17
3.76
22.33
5
0.58
1.68
2.26
12.39
16.19
4
0.31
1.3
3.43
20.6
5
0.40
2.69
3.76
12.24
15.1
5
1.34
2.26
3.42
12.37
20.10
4
0.66
2.63
3.74
9.47
5
0.67
1.53
3.59
5.46
20.3
4
2.47
3.67
12.69
17.35
4
0.54
1.56
3.17
11.36
5
1.43
2.24
3.77
6.26
10.32
4
0.76
2.7
3.78
5.3
4
0.9
1.45
6.14
23.36
4
1.4
2.0
3.39
14.59
4
0.4
2.54
3.31
16.31
4
1.34
3.33
9.32
16.39
3
2.6
3.48
22.47
4
1.46
2.69
3.22
21.77
4
1.64
2.66
3.42
19.10
4
1.43
3.65
9.23
14.62
4
0.16
1.6
3.48
15.43
4
1.44
2.23
3.70
11.29
3
2.34
10.3
11.11
3
0.59
1.49
18.16
3
1.10
2.8
14.1
4
1.17
2.19
5.17
21.77
4
1.44
2.20
5.17
15.18
3
1.4
2.69
14.16
4
0.27
7.18
13.36
14.71
3
0.0
9.39
12.52
3
0.43
5.56
14.42
3
0.31
6.9
21.14
2
0.80
9.50
3
0.64
9.22
10.38
3
0.34
14.59
16.80
3
0.43
11.31
14.77
3
0.71
6.22
9.48
3
0.21
11.54
16.41
3
5.78
9.58
14.65
2
14.47
15.56
3
12.21
14.13
16.41
3
10.19
12.70
16.8
3
9.74
11.63
14.22
3
9.17
12.14
20.59
2
11.58
12.29
3
6.29
14.59
16.32
2
5.72
6.71
3
11.79
14.24
15.21
2
9.46
10.46
3
9.75
15.51
16.19
3
9.34
12.28
14.53
3
6.24
7.64
14.34
2
5.73
16.79
2
11.49
13.25
3
9.64
12.72
14.48
3
15.18
16.41
18.1
3
11.45
12.41
14.32
3
6.9
12.25
14.74
3
8.50
12.18
14.72
3
5.75
9.43
14.11
3
12.34
14.40
21.57
3
12.76
13.71
14.29
3
6.67
11.54
14.74
2
12.23
13.5
3
5.66
10.17
14.70
3
7.59
12.72
14.41
3
12.3
14.74
15.31
3
9.25
14.68
23.54
3
5.65
10.18
14.15
3
5.11
6.21
14.29
3
7.30
9.33
12.29
3
6.80
12.50
16.79
2
4.41
14.51
2
14.41
20.45
3
9.18
11.51
15.77
3
5.67
11.3
12.6
3
10.58
14.56
15.34
3
6.64
12.30
16.14
3
4.69
11.11
12.58
2
11.59
21.74
3
5.38
7.52
14.48
3
5.16
7.58
12.41
3
6.2
14.80
15.63
3
6.25
12.8
20.35
3
10.26
11.64
15.4
3
7.39
14.68
15.61
3
10.26
12.66
15.50
wherein an mth element from top to bottom in a column in which d is located indicates a row weight of row m in the third matrix, an nth element (a, b) from left to right in row m in the third matrix indicates that a cyclic shift coefficient of a cyclic shift matrix in row m and column (a+n) in the third matrix is b, all remaining locations in the third matrix are all-zero matrices, n∈{1, 2, 3, 4, 5, 6, 7}, and m, a, and b are all positive integers.

### Claim 6 (depends on 1)

The computer program product according to claim 1, wherein a code rate corresponding to the basic matrix is 2/3, and the mother matrix is shown as follows:
H
⁡
(
2
/
3
)
=
[
H
M
⁢
C
(
2
/
3
)
0
8
×
r
H
IR
(
2
/
3
)
I
r
×
r
]
,
where:
H(2/3) indicates the mother matrix, HMC(2/3) indicates the basic matrix, HIR(2/3) indicates the extension matrix, a size of HIR(2/3) is r rows and 24 columns, 2/3 indicates the code rate, 08×r indicates the first fixed matrix, Ir×r indicates the second fixed matrix, 08×r indicates an all-zero matrix with a size of 8 rows and r columns, Ir×r indicates an identity matrix with a size of r rows and r columns, r≥1, k≤r, and r is an integer; and
H
M
⁢
C
(
2
/
3
)
=
[
61
75
4
63
56
-
-
-
-
-
-
8
-
2
17
25
1
0
-
-
-
-
-
-
56
74
77
20
-
-
-
64
24
4
67
-
7
-
-
-
-
0
0
-
-
-
-
-
28
21
68
10
7
14
65
-
-
-
23
-
-
-
75
-
-
-
0
0
-
-
-
-
48
38
43
78
76
-
-
-
-
5
36
-
15
72
-
-
-
-
-
0
0
-
-
-
40
2
53
25
-
52
62
-
20
-
-
44
-
-
-
-
-
-
-
-
0
0
-
-
69
23
64
10
22
-
21
-
-
-
-
-
68
23
29
-
-
-
-
-
-
0
0
-
12
0
68
20
55
61
-
40
-
-
-
52
-
-
-
44
-
-
-
-
-
-
0
0
58
8
34
64
78
-
-
11
78
24
-
-
-
-
-
58
-
-
-
-
-
-
-
0
]
,
wherein “-” indicates an all-zero matrix; and
wherein a Table D indicates a fourth matrix with a size of 100 rows and 24 columns, HIR(2/3) is obtained by reading r rows and 24 columns from the fourth matrix, the r rows are any r rows in the 100 rows in the fourth matrix, the 24 columns in HIR(2/3) are the 24 columns in the fourth matrix, and Table D is shown as follows:
TABLE D
4.
nd
1
2
3
4
5
5
0.34
1.39
2.22
3.80
4.29
5
7.15
11.20
14.7
15.60
16.7
4
5.77
8.2
9.56
13.69
3
6.8
10.49
12.75
3
17.79
18.58
19.72
5
3.47
20.22
21.18
22.38
23.75
4
0.32
1.21
2.80
4.50
3
13.63
14.30
15.55
3
7.21
11.67
16.44
3
5.26
8.2
9.36
3
6.9
10.14
12.67
2
22.73
23.78
2
20.44
21.35
5
0.53
1.67
17.8
18.63
19.18
2
0.56
3.9
3
4.50
13.45
14.5
3
11.50
15.45
16.25
3
7.28
8.76
9.4
3
5.8
10.34
12.62
2
6.40
19.50
2
17.13
18.32
5
0.47
20.20
21.0
22.80
23.38
3
1.57
3.71
4.38
2
2.55
13.45
3
11.7
14.49
15.67
2
7.79
16.27
3
5.47
8.76
9.33
3
6.17
10.39
12.58
3
17.19
18.68
19.26
2
20.3
23.31
4
1.69
1.76
21.6
22.43
3
0.1
2.24
3.40
2
13.10
14.42
3
11.34
15.26
16.37
2
9.63
12.66
3
5.47
7.74
8.59
2
10.46
22.3
2
6.53
21.67
2
17.47
18.67
4
0.36
19.54
20.35
23.69
2
1.56
3.17
2
2.26
4.24
3
13.32
14.77
15.43
2
11.78
16.7
2
5.3
8.76
3
7.36
9.9
10.14
2
6.45
22.39
2
12.59
23.0
2
20.4
21.4
4
0.34
17.31
18.31
19.54
3
1.39
2.32
3.33
2
4.6
13.48
2
5.69
15.47
2
7.46
14.22
2
8.10
11.77
2
9.66
19.64
2
16.65
17.42
2
6.62
10.23
2
12.43
18.43
2
20.16
23.48
4
1.23
1.44
21.29
22.6
2
0.3
2.70
2
4.11
13.34
2
15.16
21.59
2
7.49
14.1
2
5.10
22.8
3
6.19
8.17
12.77
2
9.20
16.17
2
11.18
20.17
2
10.16
19.44
4
3.27
17.71
18.69
23.4
2
0.18
1.36
2
2.0
4.52
3
7.56
11.39
13.42
3
14.9
15.43
21.14
2
8.50
22.31
2
9.80
17.38
3
5.64
6.22
12.34
2
16.59
19.80
2
10.31
18.43
4
1.22
1.71
20.77
23.48
2
0.54
2.21
2
4.41
5.65
3
11.58
13.78
14.56
2
15.47
21.21
2
12.13
23.41
3
6.8
9.19
10.70
3
7.74
8.22
16.63
2
20.17
22.14
4
1.59
17.58
18.29
19.59
2
0.32
3.29
2
2.72
4.71
3
5.79
6.24
13.21
2
11.46
15.46
3
9.19
12.75
22.51
2
14.34
16.53
2
18.34
23.28
3
7.24
8.64
10.79
3
19.73
20.25
21.49
3
1.64
1.72
17.48
wherein an mth element from top to bottom in a column in which d is located indicates a row weight of row m in the fourth matrix, an nth element (a, b) from left to right in row m in the fourth matrix indicates that a cyclic shift coefficient of a cyclic shift matrix in row m and column (a+n) in the fourth matrix is b, all remaining locations in the fourth matrix are all-zero matrices, n∈{1, 2, 3, 4, 5}, and m, a, and b are all positive integers.

### Claim 7 (depends on 1)

The computer program product according to claim 1, wherein a code rate corresponding to the basic matrix is 3/4, and the mother matrix is shown as follows:
H
⁡
(
3
/
4
)
=
[
H
M
⁢
C
(
3
/
4
)
0
6
×
r
H
IR
(
3
/
4
)
I
r
×
r
]
,
where:
H(3/4) indicates the mother matrix, HMC (3/4) indicates the basic matrix, HIR(3/4) indicates the extension matrix, a size of HIR(3/4) is r rows and 24 columns, 3/4 indicates the code rate, 06×r indicates the first fixed matrix, Ir×r indicates the second fixed matrix, 06×r indicates an all-zero matrix with a size of 6 rows and r columns, Ir×r indicates an identity matrix with a size of r rows and r columns, r≥1, k≤r, and r is an integer; and
H
M
⁢
C
(
3
/
4
)
=
[
48
29
28
39
9
61
-
-
-
63
45
80
-
-
-
37
32
22
1
0
-
-
-
-
4
49
42
48
11
30
-
-
-
49
17
41
37
15
-
54
-
-
-
0
0
-
-
-
35
76
78
51
37
35
21
-
17
64
-
-
-
59
7
-
-
32
-
-
0
0
-
-
9
65
44
9
54
56
73
34
42
-
-
-
35
-
-
-
46
39
0
-
-
0
0
-
3
62
7
80
68
26
-
80
55
-
36
-
26
-
9
-
72
-
-
-
-
-
0
0
26
75
33
21
69
59
3
38
-
-
-
35
-
62
36
26
-
-
1
-
-
-
-
0
]
,
wherein “-” indicates an all-zero matrix; and
wherein a Table E indicates a fifth matrix with a size of 100 rows and 24 columns, HIR(3/4) is obtained by reading r rows and 24 columns from the fifth matrix, the r rows are any r rows in the 100 rows in the fifth matrix, and Table E is shown as follows:
TABLE E
5.
n
d
1
2
3
4
5
6
7
8
9
9
0.22
1.20
2.7
3.29
4.15
5.60
9.39
17.34
19.80
7
0.8
2.2
3.69
5.75
9.7
17.56
19.77
7
1.58
2.72
3.38
4.18
5.49
11.79
19.22
8
1.30
2.75
3.21
4.80
5.32
9.47
10.50
17.63
8
0.21
2.67
3.2
4.44
5.36
10.26
14.67
19.55
7
1.73
2.63
3.35
5.44
7.14
17.78
19.9
7
0.9
1.67
2.8
3.18
5.56
8.5
9.53
6
3.50
4.45
5.25
6.76
17.50
19.45
6
0.28
1.62
2.34
3.8
5.4
12.40
5
0.32
2.50
5.20
17.80
23.13
6
0.38
2.71
3.57
5.47
13.0
17.38
5
0.67
2.49
3.55
5.7
21.45
5
2.33
3.76
5.47
17.79
18.27
6
0.26
2.39
3.58
4.17
5.68
22.19
6
0.69
2.3
3.31
13.6
17.43
19.76
5
0.42
2.40
5.1
15.24
17.10
6
0.74
3.26
5.34
16.66
17.63
19.37
6
0.67
2.46
3.47
5.59
14.53
17.3
5
0.54
5.35
15.47
17.67
21.69
5
0.17
2.26
5.24
8.56
17.36
5
0.32
2.78
3.77
5.7
20.43
5
0.3
2.36
3.14
17.9
22.76
5
2.59
3.0
5.39
8.45
18.4
4
0.4
3.31
5.31
7.54
4
2.34
3.39
6.33
17.32
5
0.48
3.6
5.47
16.69
17.22
5
2.77
5.46
11.10
17.66
21.64
5
0.62
3.42
5.23
12.43
17.65
5
0.29
2.43
3.16
15.6
18.48
4
0.23
2.70
17.44
23.3
4
2.16
5.34
10.11
17.59
5
0.19
2.10
5.8
6.49
7.1
4
0.17
3.77
11.17
17.20
4
2.17
5.18
6.16
7.44
4
3.4
5.71
17.69
20.27
4
0.0
2.52
3.36
14.18
4
2.39
3.43
10.42
18.56
3
0.9
3.14
12.31
4
3.50
5.38
11.80
16.22
4
0.80
3.64
5.59
13.34
3
6.31
14.43
17.77
3
6.22
16.48
17.71
4
0.21
3.41
5.65
9.54
3
0.58
12.56
18.78
3
5.47
11.21
12.13
3
2.41
5.8
10.70
3
3.19
8.22
11.63
3
3.14
17.17
22.74
3
0.58
13.29
16.59
3
2.32
15.29
17.59
4
2.71
6.72
8.21
12.24
3
0.46
2.46
10.79
3
6.19
17.75
20.51
3
0.53
7.28
16.34
3
0.24
2.34
4.64
3
11.79
12.49
17.73
3
0.48
10.72
16.25
3
11.1
18.64
21.18
3
11.41
16.41
17.32
2
17.45
22.74
3
4.9
10.50
17.25
3
10.11
15.72
16.18
3
8.40
16.75
17.43
3
10.29
12.34
17.57
3
11.76
12.71
17.67
3
4.74
6.54
18.23
2
17.66
20.5
3
7.17
10.70
17.41
3
7.59
15.72
18.74
2
10.3
16.31
3
4.25
6.54
11.68
3
11.65
13.18
16.15
3
10.11
12.21
16.29
3
4.33
10.29
16.30
3
8.80
13.50
16.79
2
11.51
12.41
2
6.41
13.45
3
4.18
10.77
12.51
3
12.67
16.6
18.3
3
4.58
7.56
10.34
3
11.30
13.64
20.14
3
4.58
6.11
12.69
3
10.48
11.74
12.59
2
4.38
8.52
3
1.16
11.41
12.58
2
7.80
11.63
3
12.25
16.2
18.8
3
4.35
6.4
13.64
3
8.26
11.61
12.68
3
6.39
8.50
12.66
3
4.31
6.11
12.26
3
6.80
12.73
14.18
2
6.28
14.44
3
6.68
9.54
10.0
2
10.55
15.53
3
6.42
11.72
15.3
2
6.73
18.65
3
8.11
11.54
16.69
2
9.70
16.15
3
10.61
11.44
13.48
wherein an mth element from top to bottom in a column in which d is located indicates a row weight of row m in the fifth matrix, an nth element (a, b) from left to right in row m in the fifth matrix indicates that a cyclic shift coefficient of a cyclic shift matrix in row m and column (a+n) in the fifth matrix is b, all remaining locations in the fifth matrix are all-zero matrices, n∈{1, 2, 3, 4, 5, 6, 7, 8, 9}, and m, a, and b are all positive integers.

### Claim 8 (depends on 1)

The computer program product according to claim 1, wherein a code rate corresponding to the basic matrix is 3/4, and the mother matrix is shown as follows:
H
⁡
(
3
/
4
)
=
[
H
M
⁢
C
(
3
/
4
)
0
6
×
r
H
IR
(
3
/
4
)
I
r
×
r
]
,
where:
H (3/4) indicates the mother matrix, HMC(3/4) indicates the basic matrix, HIR(3/4) indicates the extension matrix, a size of HIR(3/4) is r rows and 24 columns, 3/4 indicates the code rate, 06×r indicates the first fixed matrix, Ir×r indicates the second fixed matrix, 06×r indicates an all-zero matrix with a size of 6 rows and r columns, Ir×r indicates an identity matrix with a size of r rows and r columns, r≥1, k≤r, and r is an integer; and
H
M
⁢
C
(
3
/
4
)
=
[
48
29
28
39
9
61
-
-
-
63
45
80
-
-
-
37
32
22
1
0
-
-
-
-
4
49
42
48
11
30
-
-
-
49
17
41
37
15
-
54
-
-
-
0
0
-
-
-
35
76
78
51
37
35
21
-
17
64
-
-
-
59
7
-
-
32
-
-
0
0
-
-
9
65
44
9
54
56
73
34
42
-
-
-
35
-
-
-
46
39
0
-
-
0
0
-
3
62
7
80
68
26
-
80
55
-
36
-
26
-
9
-
72
-
-
-
-
-
0
0
26
75
33
21
69
59
3
38
-
-
-
35
-
62
36
26
-
-
1
-
-
-
-
0
]
,
wherein “-” indicates an all-zero matrix; and
wherein a Table F indicates a sixth matrix with a size of 100 rows and 24 columns, HMC(3/4) is obtained by reading r rows and 24 columns from the sixth matrix, the r rows are any r rows in the 100 rows in the sixth matrix, and Table F is shown as follows:
TABLE F
6.
nd
1
2
3
4
5
5
0.34
1.39
2.22
3.80
4.29
5
5.7
9.15
10.60
13.20
15.7
5
11.8
12.77
16.2
17.69
18.56
4
6.49
7.79
8.75
14.72
4
19.58
20.38
21.22
23.18
5
0.21
1.47
4.50
4.80
22.75
5
1.63
5.32
9.21
13.55
15.30
4
10.26
11.67
17.36
22.44
4
12.2
14.14
16.67
18.9
3
6.35
7.73
8.78
5
0.53
19.8
20.44
21.18
23.63
4
1.56
2.5
3.67
4.9
4
5.50
9.45
13.45
15.25
3
10.76
11.4
22.50
4
12.34
16.28
17.62
18.8
4
6.13
7.50
8.32
14.40
5
1.47
19.80
20.38
21.0
23.20
4
0.71
2.55
3.57
4.38
3
5.67
9.45
15.49
3
10.7
13.79
22.27
3
11.33
16.47
18.76
3
12.58
14.17
17.39
3
6.68
7.26
8.19
2
21.31
23.3
4
4.69
4.76
19.6
20.43
3
0.24
2.40
3.1
3
5.42
9.37
13.10
3
10.34
15.26
20.66
3
11.74
19.63
22.47
3
12.46
16.59
18.3
3
14.67
17.53
23.67
5
4.36
6.47
7.35
8.69
21.54
3
0.56
2.17
3.26
2
1.24
5.77
3
9.32
13.43
15.7
3
10.76
19.3
20.78
3
11.14
12.9
22.36
3
16.45
17.39
18.0
3
6.4
7.4
8.59
4
4.34
14.31
21.31
23.54
3
0.32
2.39
3.33
3
1.6
5.47
15.48
3
9.69
10.22
13.46
2
14.10
20.77
2
6.64
19.66
3
16.62
17.65
18.42
3
11.43
12.23
22.43
3
7.6
8.48
21.16
3
4.23
4.44
23.29
2
0.3
2.70
3
1.11
5.59
13.34
3
9.1
10.49
15.16
3
12.10
17.8
22.19
3
14.17
16.77
23.17
3
11.17
19.20
20.18
2
7.16
18.44
4
4.27
6.4
8.69
21.71
2
0.18
3.36
3
1.0
2.39
5.52
3
9.43
13.56
15.42
3
10.14
18.31
20.9
2
14.80
23.50
2
8.22
22.38
3
11.64
12.80
16.34
2
19.59
21.43
4
4.71
6.77
7.31
17.48
3
0.22
2.21
5.54
2
1.41
9.65
3
3.78
10.58
15.56
2
13.21
17.47
2
6.13
16.41
3
8.8
11.70
12.19
2
7.63
23.22
3
14.14
18.17
22.74
4
0.59
19.59
20.29
21.58
2
2.32
4.29
3
1.71
3.72
5.24
3
9.79
10.46
15.21
2
11.46
13.51
3
6.53
12.19
17.75
2
8.34
14.28
2
18.24
19.34
3
7.64
20.79
23.73
4
0.72
16.49
21.25
22.48
3
2.18
4.64
5.1
2
1.41
3.41
3
9.74
13.45
15.32
2
10.25
17.9
3
11.72
12.18
23.50
2
16.11
20.75
3
6.43
14.40
22.34
3
8.29
18.71
19.57
3
4.54
7.67
21.76
2
0.74
5.23
2
1.5
2.66
3
3.41
9.17
15.70
3
7.59
11.74
17.72
3
10.25
13.31
18.3
3
12.54
14.65
20.68
2
6.15
21.18
wherein an mth element from top to bottom in a column in which d is located indicates a row weight of row m in the sixth matrix, an nth element (a, b) from left to right in row m in the sixth matrix indicates that a cyclic shift coefficient of a cyclic shift matrix in row m and column (a+n) in the sixth matrix is b, all remaining locations in the sixth matrix are all-zero matrices, n∈{1, 2, 3, 4, 5}, and m, a, and b are all positive integers.

### Claim 9 (depends on 1)

The computer program product according to claim 1, wherein a code rate corresponding to the basic matrix is 5/6, and the mother matrix is shown as follows:
H
⁡
(
5
/
6
)
=
[
H
M
⁢
C
(
5
/
6
)
0
4
×
r
H
IR
(
5
/
6
)
I
r
×
r
]
,
where:
H(5/6) indicates the mother matrix, HMC(5/6) indicates the basic matrix, HIR(5/6) indicates the extension matrix, a size of HIR(5/6) is r rows and 24 columns, 5/6 indicates the code rate, 04×r indicates the first fixed matrix, Ir×r indicates the second fixed matrix, 04×r indicates an all-zero matrix with a size of 4 rows and r columns, Ir×r indicates an identity matrix with a size of r rows and r columns, r≥1, k≤r, and r is an integer; and
H
MC
(
5
/
6
)
=
[
13
48
80
66
4
74
7
30
76
52
37
60
-
49
-
73
31
74
73
23
1
0
-
-
69
63
74
56
64
77
57
65
6
16
51
-
64
-
64
68
9
48
62
54
-
0
0
-
51
15
0
80
24
25
42
54
44
71
71
9
67
35
67
-
58
-
29
-
0
-
0
0
16
29
36
41
44
56
59
37
50
24
-
65
4
65
4
52
-
4
-
73
1
-
-
0
]
,
wherein “-” indicates an all-zero matrix; and
wherein a Table G indicates a seventh matrix with a size of 100 rows and 24 columns, HIR(5/6) is obtained by reading r rows and 24 columns from the seventh matrix, the r rows are any r rows in the 100 rows in the seventh matrix, and Table G is shown as follows:
TABLE G
7.
n
d
1
2
3
4
5
6
7
8
9
10
11
11
0.60
1.15
3.34
4.80
5.20
6.29
7.39
9.22
11.77
12.7
18.7
10
0.72
2.79
3.69
4.49
5.75
6.8
9.2
11.56
12.22
14.58
8
1.18
2.47
4.21
5.80
6.38
7.50
9.75
11.32
9
0.21
1.26
2.30
3.36
4.44
5.67
6.63
7.2
11.55
9
0.18
2.63
3.78
4.44
6.67
8.14
9.35
11.73
14.9
9
1.56
2.5
3.9
5.45
6.67
7.50
9.25
17.8
19.53
8
0.45
1.28
3.50
4.62
6.34
7.8
9.4
20.76
7
2.80
3.50
4.13
5.40
6.32
9.0
10.20
8
1.47
2.38
3.55
4.45
6.67
7.71
9.57
23.38
7
1.47
2.79
3.7
4.76
6.27
9.33
21.49
7
1.58
2.19
3.26
4.31
5.39
9.68
15.17
6
2.6
3.76
5.24
6.69
7.3
16.43
6
1.40
3.34
6.37
7.42
9.1
13.10
6
1.59
2.47
3.66
6.63
9.74
17.26
6
2.47
3.3
4.53
5.67
7.67
22.46
6
3.69
4.56
5.35
6.36
9.54
18.17
6
3.7
6.26
7.77
9.24
16.43
22.32
5
1.36
2.9
3.76
6.3
8.78
5
1.14
2.45
6.0
7.59
19.39
5
1.4
3.4
6.54
8.31
13.31
5
1.48
2.39
3.33
6.32
10.34
5
1.46
4.47
6.6
13.69
20.22
5
1.66
3.64
6.10
9.77
23.42
5
1.23
2.62
6.65
15.43
16.43
5
1.6
2.48
3.16
6.29
12.23
5
2.3
3.11
6.44
8.34
16.70
4
1.59
2.49
3.16
14.1
5
2.77
3.19
6.8
13.10
21.17
5
1.44
2.20
3.18
14.17
19.17
4
3.71
6.16
9.4
10.69
4
2.27
3.18
12.36
14.0
5
1.52
3.43
6.42
8.39
20.56
4
1.31
6.14
8.50
22.9
4
3.22
6.38
9.64
18.80
4
1.43
2.80
3.59
17.34
5
2.48
3.31
6.22
15.77
16.71
4
3.21
6.54
10.41
13.65
4
3.58
6.78
14.47
18.56
5
1.70
3.21
6.13
11.8
13.41
4
1.22
6.19
18.63
21.74
4
1.59
2.58
6.17
12.14
5
1.59
3.72
6.32
15.29
20.29
4
1.71
2.79
14.21
20.24
4
2.46
3.46
16.19
17.51
4
1.53
2.75
13.34
22.28
4
0.79
1.24
2.34
8.64
3
1.73
2.25
10.49
4
1.48
2.18
17.64
19.72
3
0.41
2.41
10.1
3
1.32
12.74
15.45
3
2.9
12.50
19.25
4
1.72
2.18
12.75
21.11
3
0.40
1.34
2.43
4
1.57
2.71
8.76
11.29
3
0.74
10.67
15.54
3
7.5
8.23
14.66
3
10.70
12.41
13.17
3
10.59
12.72
14.74
3
0.3
8.25
14.31
3
8.54
14.65
22.68
3
0.15
12.18
13.29
3
0.11
8.21
19.33
3
0.30
13.29
19.80
3
0.50
8.41
16.79
3
12.51
14.41
22.45
2
8.18
17.77
3
0.3
4.51
8.6
3
8.34
10.58
14.67
3
10.14
17.30
18.56
2
14.69
18.64
3
9.58
12.59
15.11
3
0.74
12.48
14.38
3
0.41
10.52
15.16
3
12.58
16.63
20.80
3
0.8
12.2
18.25
2
0.64
20.35
3
0.68
11.4
12.26
3
0.39
12.66
22.61
3
11.26
12.50
18.31
2
14.11
16.18
3
9.73
10.80
19.44
2
11.54
13.28
3
0.68
14.0
19.55
3
0.53
7.3
15.42
3
0.65
10.72
16.73
3
0.54
12.11
23.69
3
0.44
12.15
17.70
3
12.57
16.48
18.61
3
7.48
14.30
18.72
2
7.80
10.47
3
0.4
12.23
19.72
3
9.59
13.4
17.69
2
9.66
18.22
3
12.52
16.53
19.60
2
8.35
21.13
3
7.65
9.44
16.68
3
12.16
13.9
17.9
3
7.10
12.3
14.7
2
17.50
22.5
3
9.62
16.20
17.80
wherein an mth element from top to bottom in a column in which d is located indicates a row weight of row m in the seventh matrix, an nth element (a, b) from left to right in row m in the seventh matrix indicates that a cyclic shift coefficient of a cyclic shift matrix in row m and column (a+n) in the seventh matrix is b, all remaining locations in the seventh matrix are all-zero matrices, n∈{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}, and m, a, and b are all positive integers.

### Claim 10 (depends on 1)

The computer program product according to claim 1, wherein a code rate corresponding to the basic matrix is 5/6, and the mother matrix is shown as follows:
H
⁡
(
5
/
6
)
=
[
H
M
⁢
C
(
5
/
6
)
0
4
×
r
H
IR
(
5
/
6
)
I
r
×
r
]
,
where:
H(5/6) indicates the mother matrix, HMC (5/6) indicates the basic matrix, HIR(5/6) indicates the extension matrix, a size of HIR(5/6) is r rows and 24 columns, 5/6 indicates the code rate, 04×r indicates the first fixed matrix, Ir×r indicates the second fixed matrix, 04×r indicates an all-zero matrix with a size of 4 rows and r columns, Ir×r indicates an identity matrix with a size of r rows and r columns, r≥1, k≤r, and r is an integer, and
H
MC
(
5
/
6
)
=
[
13
48
80
66
4
74
7
30
76
52
37
60
-
49
-
73
31
74
73
23
1
0
-
-
69
63
74
56
64
77
57
65
6
16
51
-
64
-
64
68
9
48
62
54
-
0
0
-
51
15
0
80
24
25
42
54
44
71
71
9
67
35
67
-
58
-
29
-
0
-
0
0
16
29
36
41
44
56
59
37
50
24
-
65
4
65
4
52
-
4
-
73
1
-
-
0
]
,
wherein “-” indicates an all-zero matrix; and
wherein a Table H indicates an eighth matrix with a size of 100 rows and 24 columns, HIR(5/6) is obtained by reading r rows and 24 columns from the eighth matrix, the r rows are any r rows in the 100 rows in the eighth matrix, and Table H is shown as follows:
TABLE H
8.
nd
1
2
3
4
5
5
0.80
1.29
2.34
8.39
9.22
5
3.7
4.20
5.60
6.15
7.7
5
11.8
13.2
14.77
18.69
20.56
5
12.72
15.58
16.79
17.75
19.49
5
5.47
10.75
21.18
22.22
23.38
5
2.32
3.80
6.21
7.63
9.50
5
0.44
1.30
4.55
8.21
20.67
5
11.26
13.67
14.14
16.2
18.36
5
10.35
12.78
15.73
17.9
19.44
5
4.53
6.67
21.18
22.8
23.63
5
0.56
1.5
2.50
4.45
9.9
5
5.76
7.45
8.4
13.25
20.50
4
11.34
14.8
16.62
18.28
4
12.32
15.13
17.40
19.50
5
9.47
10.38
21.80
22.20
23.0
5
1.71
2.38
4.45
6.57
7.55
4
0.67
5.7
8.79
20.49
4
3.27
13.47
14.76
18.33
4
11.58
12.17
16.26
17.39
4
10.68
15.31
19.3
23.19
5
1.76
4.24
4.69
21.6
22.43
4
0.40
6.10
7.42
9.1
4
3.37
5.66
8.26
20.34
3
13.63
21.47
22.74
3
10.3
18.59
23.46
3
11.67
14.53
16.67
5
4.36
12.54
15.35
17.47
19.69
3
0.17
1.26
6.56
4
5.32
7.24
8.77
20.43
3
2.76
3.78
9.7
3
13.36
21.3
22.9
3
11.45
14.39
18.14
3
10.4
16.59
23.0
3
12.31
15.31
19.4
4
4.32
4.33
4.34
17.54
3
1.39
7.48
20.6
3
5.69
8.47
9.22
3
2.77
3.10
17.46
3
12.66
15.42
19.64
3
10.65
21.23
22.62
3
11.48
13.43
18.43
5
4.23
4.44
14.16
16.6
23.29
3
5.11
7.3
8.70
3
1.16
9.59
20.34
3
0.10
16.49
17.1
3
3.8
12.77
19.19
3
13.17
15.20
21.17
3
10.17
14.18
23.44
3
2.4
11.16
22.69
4
4.18
4.27
4.36
18.71
3
5.52
7.39
20.0
3
1.42
9.56
19.43
3
15.14
17.31
18.9
3
3.50
12.38
16.80
3
0.34
11.22
22.64
2
2.59
14.80
3
13.77
21.31
23.43
4
4.22
4.71
5.21
10.48
3
1.41
4.65
7.54
3
9.58
18.56
20.78
3
0.47
17.21
19.13
3
10.8
11.41
22.70
3
12.22
15.19
21.63
3
2.17
13.14
16.74
5
3.59
4.29
4.59
14.58
23.29
3
1.71
16.72
17.32
3
5.79
10.21
20.24
2
7.46
19.46
3
9.51
14.19
18.75
2
0.53
8.34
3
11.34
12.28
15.24
3
2.64
13.79
23.73
4
3.49
4.72
21.25
22.48
3
1.64
10.1
17.18
3
5.41
13.32
23.41
2
9.74
18.45
3
0.50
7.25
14.9
3
3.18
16.11
20.72
2
12.43
21.75
3
2.40
11.57
19.34
2
6.71
8.29
3
4.54
15.67
22.76
3
3.74
5.23
9.5
3
1.17
11.66
20.70
2
7.41
17.59
3
0.3
2.72
18.74
3
10.68
13.31
14.25
3
8.65
15.54
16.18
3
12.29
19.15
23.21
3
6.11
21.33
22.29
3
4.79
5.30
9.80
3
3.41
14.50
15.51
3
1.41
8.18
18.45
3
0.51
2.3
13.77
3
7.67
19.58
20.6
3
11.14
16.56
23.34
2
10.64
22.30
2
6.11
12.69
4
4.48
9.74
17.59
21.58
3
0.52
14.38
15.16
wherein an mth element from top to bottom in a column in which d is located indicates a row weight of row m in the eighth matrix, an nth element (a, b) from left to right in row m in the eighth matrix indicates that a cyclic shift coefficient of a cyclic shift matrix in row m and column (a+n) in the eighth matrix is b, all remaining locations in the eighth matrix are all-zero matrices, n∈{1, 2, 3, 4, 5}, and m, a, and b are all positive integers.

### Claim 11

A computer-readable recording medium on which a program is recorded, wherein the program, when executed, enables the computer to perform operations comprising:
performing, based on a first check matrix, low-density parity-check (LDPC) code encoding on an information bit sequence to obtain a first codeword at a first code rate, wherein:
the first check matrix is obtained by reading i rows and j columns from a mother matrix,
the mother matrix comprises a basic matrix, an extension matrix, a first fixed matrix, and a second fixed matrix,
the basic matrix is located at a top-left corner of the mother matrix,
the extension matrix is located at a bottom-left corner of the mother matrix,
the first fixed matrix is located at a top-right corner of the mother matrix,
the second fixed matrix is located at a bottom-right corner of the mother matrix,
a quantity of rows in the basic matrix is equal to a quantity of rows in the first fixed matrix,
a quantity of rows in the extension matrix is equal to a quantity of rows in the second fixed matrix,
a quantity of columns in the extension matrix is equal to a quantity of columns in the basic matrix,
a quantity of columns in the first fixed matrix is equal to a quantity of columns in the second fixed matrix,
i=p+k, j=q+k, p and q are respectively the quantity of rows and the quantity of columns in the basic matrix,
k≥0, and
i, j, p, q, and k are all integers; and
sending the first codeword.

### Claim 12 (depends on 11)

The computer-readable recording medium according to claim 11, wherein the operations further comprising:
receiving retransmission indication information;
performing LDPC code encoding on the information bit sequence based on a second check matrix, to obtain a second codeword at a second code rate, wherein the second check matrix is obtained by reading w rows and z columns from the mother matrix, w=p+h, z=q+h, h>k, and w, z, and h are all positive integers; and
sending the second codeword.

### Claim 13 (depends on 11)

The computer-readable recording medium according to claim 11, wherein a code rate corresponding to the basic matrix is 1/2, and the mother matrix is shown as follows:
H
⁡
(
1
/
2
)
=
[
H
M
⁢
C
(
1
/
2
)
0
1
⁢
2
×
r
H
IR
(
1
/
2
)
I
r
×
r
]
,
where:
H(1/2) indicates the mother matrix, HMC(1/2) indicates the basic matrix, HIR(1/2) indicates the extension matrix, a size of HIR(1/2) is r rows and 24 columns, 1/2 indicates the code rate, 012×r indicates the first fixed matrix, Ir×r indicates the second fixed matrix, 012×r indicates an all-zero matrix with a size of 12 rows and r columns, Ir×r indicates an identity matrix with a size of r rows and r columns, r≥1, k≤r, and r is an integer; and
H
M
⁢
C
(
1
/
2
)
=
[
57
-
-
-
50
-
11
-
50
-
79
-
1
0
-
-
-
-
-
-
-
-
-
-
3
-
28
-
0
-
-
-
55
7
-
-
-
0
0
-
-
-
-
-
-
-
-
-
30
-
-
-
24
37
-
-
56
14
-
-
-
-
0
0
-
-
-
-
-
-
-
-
62
53
-
-
53
-
-
3
35
-
-
-
-
-
-
0
0
-
-
-
-
-
-
-
40
-
-
20
66
-
-
22
28
-
-
-
-
-
-
-
0
0
-
-
-
-
-
-
0
-
-
-
8
-
42
-
50
-
-
8
-
-
-
-
-
0
0
-
-
-
-
-
69
79
79
-
-
-
56
-
52
-
-
-
0
-
-
-
-
-
0
0
-
-
-
-
65
-
-
-
38
57
-
-
72
-
27
-
-
-
-
-
-
-
-
0
0
-
-
-
64
-
-
-
14
52
-
-
30
-
-
32
-
-
-
-
-
-
-
-
0
0
-
-
-
45
-
70
0
-
-
-
77
9
-
-
-
-
-
-
-
-
-
-
-
0
0
-
2
56
-
57
35
-
-
-
-
-
12
-
-
-
-
-
-
-
-
-
-
-
0
0
24
-
61
-
60
-
-
27
51
-
-
16
1
-
-
-
-
-
-
-
-
-
-
0
]
,
wherein “-” indicates an all-zero matrix; and
wherein a Table A indicates a first matrix with a size of 100 rows and 24 columns, HIR(1/2) is obtained by reading r rows and 24 columns from the first matrix, the r rows are any r rows in the 100 rows in the first matrix, and Table A is shown as follows:
TABLE A
9.
n
d
1
2
3
4
5
5
0.22
1.34
4.39
8.29
11.80
5
0.7
1.60
4.20
8.7
13.15
5
0.56
4.2
7.77
8.69
9.8
5
0.79
1.49
4.72
8.75
10.58
5
1.47
4.18
7.22
8.38
9.75
5
1.63
4.80
8.21
9.50
10.32
4
3.30
4.44
8.55
10.21
4
0.26
4.67
5.2
8.36
4
4.9
5.14
6.73
8.67
4
0.44
4.35
8.78
22.63
4
0.67
4.18
8.8
23.53
4
0.56
4.45
5.9
6.5
4
0.50
4.50
8.25
15.45
4
0.4
6.76
8.28
23.34
4
0.8
4.50
5.40
6.62
4
0.80
4.20
6.32
13.13
4
0.38
4.47
8.38
11.0
4
0.55
5.45
8.57
15.71
3
0.49
4.67
17.7
3
4.33
8.79
17.27
4
4.76
8.47
11.17
23.58
4
0.68
8.39
11.19
15.26
4
4.3
6.31
8.43
17.6
3
4.24
8.69
13.76
4
0.42
4.1
8.40
21.10
3
0.26
8.34
21.37
4
0.63
2.66
4.47
8.74
3
4.59
11.46
21.3
3
0.67
4.67
22.53
3
0.69
11.47
17.35
3
0.54
8.56
9.36
3
0.24
3.26
4.17
3
2.32
4.43
17.77
3
0.78
2.7
8.76
3
4.36
11.3
17.9
3
0.45
4.14
19.39
3
0.4
3.0
8.59
3
0.4
8.31
19.31
3
0.33
8.54
9.34
3
2.32
3.39
13.48
3
0.69
8.6
21.47
2
5.22
6.46
3
5.10
6.64
17.77
2
6.66
23.42
2
5.62
11.65
3
6.43
11.23
17.43
2
9.48
17.16
3
6.23
11.29
17.6
2
1.44
11.70
2
3.11
6.3
2
9.59
11.34
2
2.49
11.16
2
3.1
5.10
2
2.19
17.8
3
1.77
3.17
11.17
3
6.20
11.17
17.18
2
6.44
13.16
3
6.69
11.71
17.4
3
3.36
11.27
17.18
2
6.0
22.52
3
1.56
11.42
17.39
3
5.43
6.14
11.9
3
3.80
11.50
17.31
2
1.22
3.38
2
7.34
17.64
2
6.80
21.59
3
5.43
6.31
17.77
2
6.71
10.48
3
1.21
6.54
17.22
3
5.65
6.58
17.41
2
7.56
17.78
2
6.47
21.21
3
1.70
3.13
17.41
3
2.22
6.19
17.8
3
5.63
6.74
11.14
3
6.58
10.59
17.17
3
1.29
3.29
5.59
3
6.72
10.71
17.32
2
9.21
17.24
3
2.46
11.79
17.46
3
1.19
6.51
17.75
2
6.53
15.34
3
6.28
11.34
22.24
3
3.73
6.64
11.79
2
11.25
13.49
3
6.48
7.72
11.64
3
6.41
10.18
11.1
2
6.32
21.41
3
3.9
5.45
6.74
3
1.18
3.25
17.50
2
12.72
17.11
3
10.43
11.75
17.40
3
3.29
9.57
11.34
3
10.76
11.67
17.71
2
17.54
23.74
3
6.23
11.5
17.66
2
6.70
18.17
2
3.59
22.41
3
1.72
3.3
17.74
3
3.25
9.31
11.68
wherein an mth element from top to bottom in a column in which d is located indicates a row weight of row m in the first matrix, an nth element (a, b) from left to right in row m in the first matrix indicates that a cyclic shift coefficient of a cyclic shift matrix in row m and column (a+n) in the first matrix is b, all remaining locations in the first matrix are all-zero matrices, n∈{1, 2, 3, 4, 5}, and m, a, and b are all positive integers.

### Claim 14 (depends on 11)

The computer-readable recording medium according to claim 11, wherein a code rate corresponding to the basic matrix is 1/2, and the mother matrix is shown as follows:
H
⁡
(
1
/
2
)
=
[
H
M
⁢
C
(
1
/
2
)
0
1
⁢
2
×
r
H
IR
(
1
/
2
)
I
r
×
r
]
,
where:
H(1/2) indicates the mother matrix, HMC(1/2) indicates the basic matrix, HIR(1/2) indicates the extension matrix, a size of HIR(1/2) is r rows and 24 columns, 1/2 indicates the code rate, 012×r indicates the first fixed matrix, Ir×r indicates the second fixed matrix, 012×r indicates an all-zero matrix with a size of 12 rows and r columns, Ir×r indicates an identity matrix with a size of r rows and r columns, r≥1, k≤r, and r is an integer; and
H
M
⁢
C
(
1
/
2
)
=
[
57
-
-
-
50
-
11
-
50
-
79
-
1
0
-
-
-
-
-
-
-
-
-
-
3
-
28
-
0
-
-
-
55
7
-
-
-
0
0
-
-
-
-
-
-
-
-
-
30
-
-
-
24
37
-
-
56
14
-
-
-
-
0
0
-
-
-
-
-
-
-
-
62
53
-
-
53
-
-
3
35
-
-
-
-
-
-
0
0
-
-
-
-
-
-
-
40
-
-
20
66
-
-
22
28
-
-
-
-
-
-
-
0
0
-
-
-
-
-
-
0
-
-
-
8
-
42
-
50
-
-
8
-
-
-
-
-
0
0
-
-
-
-
-
69
79
79
-
-
-
56
-
52
-
-
-
0
-
-
-
-
-
0
0
-
-
-
-
65
-
-
-
38
57
-
-
72
-
27
-
-
-
-
-
-
-
-
0
0
-
-
-
64
-
-
-
14
52
-
-
30
-
-
32
-
-
-
-
-
-
-
-
0
0
-
-
-
45
-
70
0
-
-
-
77
9
-
-
-
-
-
-
-
-
-
-
-
0
0
-
2
56
-
57
35
-
-
-
-
-
12
-
-
-
-
-
-
-
-
-
-
-
0
0
24
-
61
-
60
-
-
27
51
-
-
16
1
-
-
-
-
-
-
-
-
-
-
0
]
,
wherein “-” indicates an all-zero matrix; and
wherein a Table B indicates a second matrix with a size of 100 rows and 24 columns, HIR(1/2) is obtained by reading r rows and 24 columns from the second matrix, the r rows are any r rows in the 100 rows in the second matrix, and Table B is shown as follows:
TABLE B
10.
n
d
1
2
3
4
5
5
0.29
4.22
6.80
8.34
10.39
3
1.60
7.20
11.15
3
2.7
5.7
12.77
2
9.56
13.69
2
14.2
15.8
2
3.49
16.75
2
17.79
20.72
2
19.58
21.22
5
4.47
4.80
18.75
22.18
23.38
2
0.21
8.50
2
5.32
6.63
2
1.30
7.55
2
9.21
11.44
2
2.67
12.36
2
13.26
14.2
2
15.14
16.67
2
3.9
17.73
2
18.35
20.78
2
21.63
22.44
4
0.67
8.53
19.8
23.18
2
4.9
8.56
2
1.5
5.45
2
7.50
9.25
2
6.50
15.45
2
2.76
11.4
2
12.34
14.28
2
13.62
16.8
2
3.50
17.40
2
20.32
23.13
2
18.20
21.80
4
8.38
8.47
19.0
22.38
2
0.71
4.57
2
1.55
7.45
2
5.49
11.67
2
6.7
9.79
2
15.27
16.33
2
2.76
3.47
2
14.17
17.58
2
12.39
19.26
2
13.68
21.19
2
22.3
23.31
4
8.69
8.76
18.43
20.6
2
0.24
4.1
2
1.40
7.42
2
5.10
9.37
2
3.26
11.34
2
15.66
16.63
2
6.47
20.74
2
2.59
14.46
2
17.53
21.3
2
13.67
18.67
2
12.69
22.47
3
4.36
19.54
23.35
2
0.17
8.56
2
1.24
9.26
2
7.32
11.77
2
5.7
15.43
2
3.78
10.76
2
2.3
20.9
2
16.36
19.14
2
6.45
14.39
2
12.0
23.59
2
13.4
17.4
2
21.31
22.31
3
8.33
8.34
18.54
2
0.32
1.39
2
3.6
7.48
2
5.47
9.69
2
11.46
18.22
2
2.10
15.77
2
6.66
10.64
2
12.42
23.65
2
16.62
17.23
2
14.43
20.43
2
13.16
19.48
3
8.23
21.29
22.6
2
0.44
4.70
2
1.3
7.11
2
9.34
11.59
2
3.49
5.16
2
15.10
18.1
2
2.19
21.8
2
14.77
16.17
2
6.17
17.20
2
10.18
20.17
2
12.44
23.16
2
13.69
22.4
3
8.27
8.36
19.71
2
1.18
4.0
2
7.52
9.39
2
3.42
5.56
2
11.43
21.9
2
10.14
15.31
2
19.50
20.80
2
6.22
18.38
2
12.64
14.34
2
2.80
16.59
2
22.43
23.31
3
8.71
13.77
17.48
2
0.22
4.21
wherein an mth element from top to bottom in a column in which d is located indicates a row weight of row m in the second matrix, an nth element (a, b) from left to right in row m in the second matrix indicates that a cyclic shift coefficient of a cyclic shift matrix in row m and column (a+n) in the second matrix is b, all remaining locations in the second matrix are all-zero matrices, n∈{1, 2, 3, 4, 5}, and m, a, and b are all positive integers.

### Claim 15 (depends on 11)

The computer-readable recording medium according to claim 11, wherein a code rate corresponding to the basic matrix is 2/3, and the mother matrix is shown as follows:
H
⁡
(
2
/
3
)
=
[
H
M
⁢
C
(
2
/
3
)
0
8
×
r
H
IR
(
2
/
3
)
I
r
×
r
]
,
where:
H(2/3) indicates the mother matrix, HMC (2/3) indicates the basic matrix, HIR(2/3) indicates the extension matrix, a size of HIR(2/3) is r rows and 8 columns, 2/3 indicates the code rate, 08×r indicates the first fixed matrix, Ir×r indicates the second fixed matrix, 08×r indicates an all-zero matrix with a size of 8 rows and r columns, Ir×r indicates an identity matrix with a size of r rows and r columns, r≥1, k≤r, and r is an integer; and
H
M
⁢
C
(
2
/
3
)
=
[
61
75
4
63
56
-
-
-
-
-
-
8
-
2
17
25
1
0
-
-
-
-
-
-
56
74
77
20
-
-
-
64
24
4
67
-
7
-
-
-
-
0
0
-
-
-
-
-
28
21
68
10
7
14
65
-
-
-
23
-
-
-
75
-
-
-
0
0
-
-
-
-
48
38
43
78
76
-
-
-
-
5
36
-
15
72
-
-
-
-
-
0
0
-
-
-
40
2
53
25
-
52
62
-
20
-
-
44
-
-
-
-
-
-
-
-
0
0
-
-
69
23
64
10
22
-
21
-
-
-
-
-
68
23
29
-
-
-
-
-
-
0
0
-
12
0
68
20
55
61
-
40
-
-
-
52
-
-
-
44
-
-
-
-
-
-
0
0
58
8
34
64
78
-
-
11
78
24
-
-
-
-
-
58
-
-
-
-
-
-
-
0
]
,
wherein “-” indicates an all-zero matrix; and
wherein a Table C indicates a third matrix with a size of 100 rows and 24 columns, HIR(2/3) is obtained by reading r rows and 24 columns from the third matrix, the r rows are any r rows in the 100 rows in the third matrix, and Table C is shown as follows:
TABLE C
11.
n
d
1
2
3
4
5
6
7
6
1.39
2.34
3.22
4.80
7.29
12.15
6
0.77
1.7
2.7
3.20
7.69
12.60
7
0.75
1.2
2.49
3.8
7.72
12.79
13.56
7
0.38
2.18
3.22
4.75
8.80
12.47
13.58
7
0.21
2.32
3.63
4.50
8.21
12.55
14.30
6
0.67
1.67
2.26
3.36
7.2
18.44
6
1.9
2.35
3.78
5.73
8.14
12.44
5
0.18
1.63
2.67
3.53
17.8
5
1.45
2.5
3.56
7.50
11.9
6
0.28
1.76
2.50
3.25
7.45
21.4
6
0.32
1.40
2.34
3.50
12.62
19.8
5
0.38
1.80
3.0
6.20
12.13
5
1.71
2.47
3.57
12.55
23.38
5
0.45
1.79
2.7
10.49
12.67
5
0.27
1.47
2.17
3.76
22.33
5
0.58
1.68
2.26
12.39
16.19
4
0.31
1.3
3.43
20.6
5
0.40
2.69
3.76
12.24
15.1
5
1.34
2.26
3.42
12.37
20.10
4
0.66
2.63
3.74
9.47
5
0.67
1.53
3.59
5.46
20.3
4
2.47
3.67
12.69
17.35
4
0.54
1.56
3.17
11.36
5
1.43
2.24
3.77
6.26
10.32
4
0.76
2.7
3.78
5.3
4
0.9
1.45
6.14
23.36
4
1.4
2.0
3.39
14.59
4
0.4
2.54
3.31
16.31
4
1.34
3.33
9.32
16.39
3
2.6
3.48
22.47
4
1.46
2.69
3.22
21.77
4
1.64
2.66
3.42
19.10
4
1.43
3.65
9.23
14.62
4
0.16
1.6
3.48
15.43
4
1.44
2.23
3.70
11.29
3
2.34
10.3
11.11
3
0.59
1.49
18.16
3
1.10
2.8
14.1
4
1.17
2.19
5.17
21.77
4
1.44
2.20
5.17
15.18
3
1.4
2.69
14.16
4
0.27
7.18
13.36
14.71
3
0.0
9.39
12.52
3
0.43
5.56
14.42
3
0.31
6.9
21.14
2
0.80
9.50
3
0.64
9.22
10.38
3
0.34
14.59
16.80
3
0.43
11.31
14.77
3
0.71
6.22
9.48
3
0.21
11.54
16.41
3
5.78
9.58
14.65
2
14.47
15.56
3
12.21
14.13
16.41
3
10.19
12.70
16.8
3
9.74
11.63
14.22
3
9.17
12.14
20.59
2
11.58
12.29
3
6.29
14.59
16.32
2
5.72
6.71
3
11.79
14.24
15.21
2
9.46
10.46
3
9.75
15.51
16.19
3
9.34
12.28
14.53
3
6.24
7.64
14.34
2
5.73
16.79
2
11.49
13.25
3
9.64
12.72
14.48
3
15.18
16.41
18.1
3
11.45
12.41
14.32
3
6.9
12.25
14.74
3
8.50
12.18
14.72
3
5.75
9.43
14.11
3
12.34
14.40
21.57
3
12.76
13.71
14.29
3
6.67
11.54
14.74
2
12.23
13.5
3
5.66
10.17
14.70
3
7.59
12.72
14.41
3
12.3
14.74
15.31
3
9.25
14.68
23.54
3
5.65
10.18
14.15
3
5.11
6.21
14.29
3
7.30
9.33
12.29
3
6.80
12.50
16.79
2
4.41
14.51
2
14.41
20.45
3
9.18
11.51
15.77
3
5.67
11.3
12.6
3
10.58
14.56
15.34
3
6.64
12.30
16.14
3
4.69
11.11
12.58
2
11.59
21.74
3
5.38
7.52
14.48
3
5.16
7.58
12.41
3
6.2
14.80
15.63
3
6.25
12.8
20.35
3
10.26
11.64
15.4
3
7.39
14.68
15.61
3
10.26
12.66
15.50
wherein an mth element from top to bottom in a column in which d is located indicates a row weight of row m in the third matrix, an nth element (a, b) from left to right in row m in the third matrix indicates that a cyclic shift coefficient of a cyclic shift matrix in row m and column (a+n) in the third matrix is b, all remaining locations in the third matrix are all-zero matrices, n∈{1, 2, 3, 4, 5, 6, 7}, and m, a, and b are all positive integers.

### Claim 16 (depends on 11)

The computer-readable recording medium according to claim 11, wherein a code rate corresponding to the basic matrix is 2/3, and the mother matrix is shown as follows:
H
⁡
(
2
/
3
)
=
[
H
M
⁢
C
(
2
/
3
)
0
8
×
r
H
IR
(
2
/
3
)
I
r
×
r
]
,
where:
H(2/3) indicates the mother matrix, HMC (2/3) indicates the basic matrix, HIR(2/3) indicates the extension matrix, a size of HIR(2/3) is r rows and 24 columns, 2/3 indicates the code rate, 08×r indicates the first fixed matrix, Ir×r indicates the second fixed matrix, 08×r, indicates an all-zero matrix with a size of 8 rows and r columns, Ir×r indicates an identity matrix with a size of r rows and r columns, r≥1, k≤r, and r is an integer; and
H
M
⁢
C
(
2
/
3
)
=
[
61
75
4
63
56
-
-
-
-
-
-
8
-
2
17
25
1
0
-
-
-
-
-
-
56
74
77
20
-
-
-
64
24
4
67
-
7
-
-
-
-
0
0
-
-
-
-
-
28
21
68
10
7
14
65
-
-
-
23
-
-
-
75
-
-
-
0
0
-
-
-
-
48
38
43
78
76
-
-
-
-
5
36
-
15
72
-
-
-
-
-
0
0
-
-
-
40
2
53
25
-
52
62
-
20
-
-
44
-
-
-
-
-
-
-
-
0
0
-
-
69
23
64
10
22
-
21
-
-
-
-
-
68
23
29
-
-
-
-
-
-
0
0
-
12
0
68
20
55
61
-
40
-
-
-
52
-
-
-
44
-
-
-
-
-
-
0
0
58
8
34
64
78
-
-
11
78
24
-
-
-
-
-
58
-
-
-
-
-
-
-
0
]
,
wherein “-” indicates an all-zero matrix; and
wherein a Table D indicates a fourth matrix with a size of 100 rows and 24 columns, HIR(2/3) is obtained by reading r rows and 24 columns from the fourth matrix, the r rows are any r rows in the 100 rows in the fourth matrix, the 24 columns in HIR(2/3) are the 24 columns in the fourth matrix, and Table D is shown as follows:
TABLE D
12.
n
d
1
2
3
4
5
5
0.34
1.39
2.22
3.80
4.29
5
7.15
11.20
14.7
15.60
16.7
4
5.77
8.2
9.56
13.69
3
6.8
10.49
12.75
3
17.79
18.58
19.72
5
3.47
20.22
21.18
22.38
23.75
4
0.32
1.21
2.80
4.50
3
13.63
14.30
15.55
3
7.21
11.67
16.44
3
5.26
8.2
9.36
3
6.9
10.14
12.67
2
22.73
23.78
2
20.44
21.35
5
0.53
1.67
17.8
18.63
19.18
2
0.56
3.9
3
4.50
13.45
14.5
3
11.50
15.45
16.25
3
7.28
8.76
9.4
3
5.8
10.34
12.62
2
6.40
19.50
2
17.13
18.32
5
0.47
20.20
21.0
22.80
23.38
3
1.57
3.71
4.38
2
2.55
13.45
3
11.7
14.49
15.67
2
7.79
16.27
3
5.47
8.76
9.33
3
6.17
10.39
12.58
3
17.19
18.68
19.26
2
20.3
23.31
4
1.69
1.76
21.6
22.43
3
0.1
2.24
3.40
2
13.10
14.42
3
11.34
15.26
16.37
2
9.63
12.66
3
5.47
7.74
8.59
2
10.46
22.3
2
6.53
21.67
2
17.47
18.67
4
0.36
19.54
20.35
23.69
2
1.56
3.17
2
2.26
4.24
3
13.32
14.77
15.43
2
11.78
16.7
2
5.3
8.76
3
7.36
9.9
10.14
2
6.45
22.39
2
12.59
23.0
2
20.4
21.4
4
0.34
17.31
18.31
19.54
3
1.39
2.32
3.33
2
4.6
13.48
2
5.69
15.47
2
7.46
14.22
2
8.10
11.77
2
9.66
19.64
2
16.65
17.42
2
6.62
10.23
2
12.43
18.43
2
20.16
23.48
4
1.23
1.44
21.29
22.6
2
0.3
2.70
2
4.11
13.34
2
15.16
21.59
2
7.49
14.1
2
5.10
22.8
3
6.19
8.17
12.77
2
9.20
16.17
2
11.18
20.17
2
10.16
19.44
4
3.27
17.71
18.69
23.4
2
0.18
1.36
2
2.0
4.52
3
7.56
11.39
13.42
3
14.9
15.43
21.14
2
8.50
22.31
2
9.80
17.38
3
5.64
6.22
12.34
2
16.59
19.80
2
10.31
18.43
4
1.22
1.71
20.77
23.48
2
0.54
2.21
2
4.41
5.65
3
11.58
13.78
14.56
2
15.47
21.21
2
12.13
23.41
3
6.8
9.19
10.70
3
7.74
8.22
16.63
2
20.17
22.14
4
1.59
17.58
18.29
19.59
2
0.32
3.29
2
2.72
4.71
3
5.79
6.24
13.21
2
11.46
15.46
3
9.19
12.75
22.51
2
14.34
16.53
2
18.34
23.28
3
7.24
8.64
10.79
3
19.73
20.25
21.49
3
1.64
1.72
17.48
wherein an mth element from top to bottom in a column in which d is located indicates a row weight of row m in the fourth matrix, an nth element (a, b) from left to right in row m in the fourth matrix indicates that a cyclic shift coefficient of a cyclic shift matrix in row m and column (a+n) in the fourth matrix is b, all remaining locations in the fourth matrix are all-zero matrices, n∈{1, 2, 3, 4, 5}, and m, a, and b are all positive integers.

### Claim 17 (depends on 11)

The computer-readable recording medium according to claim 11, wherein a code rate corresponding to the basic matrix is 3/4, and the mother matrix is shown as follows:
H
⁡
(
3
/
4
)
=
[
H
M
⁢
C
(
3
/
4
)
0
6
×
r
H
IR
(
3
/
4
)
I
r
×
r
]
,
where:
H(3/4) indicates the mother matrix, HMC(3/4) indicates the basic matrix, HIR(3/4) indicates the extension matrix, a size of HIR(3/4) is r rows and 24 columns, 3/4 indicates the code rate, 06×r indicates the first fixed matrix, Ir×r indicates the second fixed matrix, 06×r indicates an all-zero matrix with a size of 6 rows and r columns, Ir×r indicates an identity matrix with a size of r rows and r columns, r≥1, k≤r, and r is an integer; and
H
MC
(
3
/
4
)
=
[
48
29
28
39
9
61
-
-
-
63
45
80
-
-
-
37
32
22
1
0
-
-
-
-
4
49
42
48
11
30
-
-
-
49
17
41
37
15
-
54
-
-
-
0
0
-
-
-
35
76
78
51
37
35
21
-
17
64
-
-
-
59
7
-
-
32
-
-
0
0
-
-
9
65
44
9
54
56
73
34
42
-
-
-
35
-
-
-
46
39
0
-
-
0
0
-
3
62
7
80
68
26
-
80
55
-
36
-
26
-
9
-
72
-
-
-
-
-
0
0
26
75
33
21
69
59
3
38
-
-
-
35
-
68
36
26
-
-
1
-
-
-
-
0
]
,
wherein “-” indicates an all-zero matrix; and
wherein a Table E indicates a fifth matrix with a size of 100 rows and 24 columns, HIR(3/4) is obtained by reading r rows and 24 columns from the fifth matrix, the r rows are any r rows in the 100 rows in the fifth matrix, and Table E is shown as follows:
TABLE E
13.
n
d
1
2
3
4
5
6
7
8
9
9
0.22
1.20
2.7
3.29
4.15
5.60
9.39
17.34
19.80
7
0.8
2.2
3.69
5.75
9.7
17.56
19.77
7
1.58
2.72
3.38
4.18
5.49
11.79
19.22
8
1.30
2.75
3.21
4.80
5.32
9.47
10.50
17.63
8
0.21
2.67
3.2
4.44
5.36
10.26
14.67
19.55
7
1.73
2.63
3.35
5.44
7.14
17.78
19.9
7
0.9
1.67
2.8
3.18
5.56
8.5
9.53
6
3.50
4.45
5.25
6.76
17.50
19.45
6
0.28
1.62
2.34
3.8
5.4
12.40
5
0.32
2.50
5.20
17.80
23.13
6
0.38
2.71
3.57
5.47
13.0
17.38
5
0.67
2.49
3.55
5.7
21.45
5
2.33
3.76
5.47
17.79
18.27
6
0.26
2.39
3.58
4.17
5.68
22.19
6
0.69
2.3
3.31
13.6
17.43
19.76
5
0.42
2.40
5.1
15.24
17.10
6
0.74
3.26
5.34
16.66
17.63
19.37
6
0.67
2.46
3.47
5.59
14.53
17.3
5
0.54
5.35
15.47
17.67
21.69
5
0.17
2.26
5.24
8.56
17.36
5
0.32
2.78
3.77
5.7
20.43
5
0.3
2.36
3.14
17.9
22.76
5
2.59
3.0
5.39
8.45
18.4
4
0.4
3.31
5.31
7.54
4
2.34
3.39
6.33
17.32
5
0.48
3.6
5.47
16.69
17.22
5
2.77
5.46
11.10
17.66
21.64
5
0.62
3.42
5.23
12.43
17.65
5
0.29
2.43
3.16
15.6
18.48
4
0.23
2.70
17.44
23.3
4
2.16
5.34
10.11
17.59
5
0.19
2.10
5.8
6.49
7.1
4
0.17
3.77
11.17
17.20
4
2.17
5.18
6.16
7.44
4
3.4
5.71
17.69
20.27
4
0.0
2.52
3.36
14.18
4
2.39
3.43
10.42
18.56
3
0.9
3.14
12.31
4
3.50
5.38
11.80
16.22
4
0.80
3.64
5.59
13.34
3
6.31
14.43
17.77
3
6.22
16.48
17.71
4
0.21
3.41
5.65
9.54
3
0.58
12.56
18.78
3
5.47
11.21
12.13
3
2.41
5.8
10.70
3
3.19
8.22
11.63
3
3.14
17.17
22.74
3
0.58
13.29
16.59
3
2.32
15.29
17.59
4
2.71
6.72
8.21
12.24
3
0.46
2.46
10.79
3
6.19
17.75
20.51
3
0.53
7.28
16.34
3
0.24
2.34
4.64
3
11.79
12.49
17.73
3
0.48
10.72
16.25
3
11.1
18.64
21.18
3
11.41
16.41
17.32
2
17.45
22.74
3
4.9
10.50
17.25
3
10.11
15.72
16.18
3
8.40
16.75
17.43
3
10.29
12.34
17.57
3
11.76
12.71
17.67
3
4.74
6.54
18.23
2
17.66
20.5
3
7.17
10.70
17.41
3
7.59
15.72
18.74
2
10.3
16.31
3
4.25
6.54
11.68
3
11.65
13.18
16.15
3
10.11
12.21
16.29
3
4.33
10.29
16.30
3
8.80
13.50
16.79
2
11.51
12.41
2
6.41
13.45
3
4.18
10.77
12.51
3
12.67
16.6
18.3
3
4.58
7.56
10.34
3
11.30
13.64
20.14
3
4.58
6.11
12.69
3
10.48
11.74
12.59
2
4.38
8.52
3
1.16
11.41
12.58
2
7.80
11.63
3
12.25
16.2
18.8
3
4.35
6.4
13.64
3
8.26
11.61
12.68
3
6.39
8.50
12.66
3
4.31
6.11
12.26
3
6.80
12.73
14.18
2
6.28
14.44
3
6.68
9.54
10.0
2
10.55
15.53
3
6.42
11.72
15.3
2
6.73
18.65
3
8.11
11.54
16.69
2
9.70
16.15
3
10.61
11.44
13.48
wherein an mth element from top to bottom in a column in which d is located indicates a row weight of row m in the fifth matrix, an nth element (a, b) from left to right in row m in the fifth matrix indicates that a cyclic shift coefficient of a cyclic shift matrix in row m and column (a+n) in the fifth matrix is b, all remaining locations in the fifth matrix are all-zero matrices, n∈{1, 2, 3, 4, 5, 6, 7, 8, 9}, and m, a, and b are all positive integers.

### Claim 18 (depends on 11)

The computer-readable recording medium according to claim 11, wherein a code rate corresponding to the basic matrix is 3/4, and the mother matrix is shown as follows:
H
⁡
(
3
/
4
)
=
[
H
M
⁢
C
(
3
/
4
)
0
6
×
r
H
IR
(
3
/
4
)
I
r
×
r
]
,
where:
H(3/4) indicates the mother matrix, HMC(3/4) indicates the basic matrix, HIR(3/4) indicates the extension matrix, a size of HIR(3/4) is r rows and 24 columns, 3/4 indicates the code rate, 06×r indicates the first fixed matrix, Ir×r indicates the second fixed matrix, 06×r indicates an all-zero matrix with a size of 6 rows and r columns, Ir×r indicates an identity matrix with a size of r rows and r columns, r≥1, k≤r, and r is an integer; and
H
MC
(
3
/
4
)
=
[
48
29
28
39
9
61
-
-
-
63
45
80
-
-
-
37
32
22
1
0
-
-
-
-
4
49
42
48
11
30
-
-
-
49
17
41
37
15
-
54
-
-
-
0
0
-
-
-
35
76
78
51
37
35
21
-
17
64
-
-
-
59
7
-
-
32
-
-
0
0
-
-
9
65
44
9
54
56
73
34
42
-
-
-
35
-
-
-
46
39
0
-
-
0
0
-
3
62
7
80
68
26
-
80
55
-
36
-
26
-
9
-
72
-
-
-
-
-
0
0
26
75
33
21
69
59
3
38
-
-
-
35
-
68
36
26
-
-
1
-
-
-
-
0
]
,
wherein “-” indicates an all-zero matrix; and
wherein a Table F indicates a sixth matrix with a size of 100 rows and 24 columns, HMC(3/4) is obtained by reading r rows and 24 columns from the sixth matrix, the r rows are any r rows in the 100 rows in the sixth matrix, and Table F is shown as follows:
TABLE F
14.
n
d
1
2
3
4
5
5
0.34
1.39
2.22
3.80
4.29
5
5.7
9.15
10.60
13.20
15.7
5
11.8
12.77
16.2
17.69
18.56
4
6.49
7.79
8.75
14.72
4
19.58
20.38
21.22
23.18
5
0.21
1.47
4.50
4.80
22.75
5
1.63
5.32
9.21
13.55
15.30
4
10.26
11.67
17.36
22.44
4
12.2
14.14
16.67
18.9
3
6.35
7.73
8.78
5
0.53
19.8
20.44
21.18
23.63
4
1.56
2.5
3.67
4.9
4
5.50
9.45
13.45
15.25
3
10.76
11.4
22.50
4
12.34
16.28
17.62
18.8
4
6.13
7.50
8.32
14.40
5
1.47
19.80
20.38
21.0
23.20
4
0.71
2.55
3.57
4.38
3
5.67
9.45
15.49
3
10.7
13.79
22.27
3
11.33
16.47
18.76
3
12.58
14.17
17.39
3
6.68
7.26
8.19
2
21.31
23.3
4
4.69
4.76
19.6
20.43
3
0.24
2.40
3.1
3
5.42
9.37
13.10
3
10.34
15.26
20.66
3
11.74
19.63
22.47
3
12.46
16.59
18.3
3
14.67
17.53
23.67
5
4.36
6.47
7.35
8.69
21.54
3
0.56
2.17
3.26
2
1.24
5.77
3
9.32
13.43
15.7
3
10.76
19.3
20.78
3
11.14
12.9
22.36
3
16.45
17.39
18.0
3
6.4
7.4
8.59
4
4.34
14.31
21.31
23.54
3
0.32
2.39
3.33
3
1.6
5.47
15.48
3
9.69
10.22
13.46
2
14.10
20.77
2
6.64
19.66
3
16.62
17.65
18.42
3
11.43
12.23
22.43
3
7.6
8.48
21.16
3
4.23
4.44
23.29
2
0.3
2.70
3
1.11
5.59
13.34
3
9.1
10.49
15.16
3
12.10
17.8
22.19
3
14.17
16.77
23.17
3
11.17
19.20
20.18
2
7.16
18.44
4
4.27
6.4
8.69
21.71
2
0.18
3.36
3
1.0
2.39
5.52
3
9.43
13.56
15.42
3
10.14
18.31
20.9
2
14.80
23.50
2
8.22
22.38
3
11.64
12.80
16.34
2
19.59
21.43
4
4.71
6.77
7.31
17.48
3
0.22
2.21
5.54
2
1.41
9.65
3
3.78
10.58
15.56
2
13.21
17.47
2
6.13
16.41
3
8.8
11.70
12.19
2
7.63
23.22
3
14.14
18.17
22.74
4
0.59
19.59
20.29
21.58
2
2.32
4.29
3
1.71
3.72
5.24
3
9.79
10.46
15.21
2
11.46
13.51
3
6.53
12.19
17.75
2
8.34
14.28
2
18.24
19.34
3
7.64
20.79
23.73
4
0.72
16.49
21.25
22.48
3
2.18
4.64
5.1
2
1.41
3.41
3
9.74
13.45
15.32
2
10.25
17.9
3
11.72
12.18
23.50
2
16.11
20.75
3
6.43
14.40
22.34
3
8.29
18.71
19.57
3
4.54
7.67
21.76
2
0.74
5.23
2
1.5
2.66
3
3.41
9.17
15.70
3
7.59
11.74
17.72
3
10.25
13.31
18.3
3
12.54
14.65
20.68
2
6.15
21.18
wherein an mth element from top to bottom in a column in which d is located indicates a row weight of row m in the sixth matrix, an nth element (a, b) from left to right in row m in the sixth matrix indicates that a cyclic shift coefficient of a cyclic shift matrix in row m and column (a+n) in the sixth matrix is b, all remaining locations in the sixth matrix are all-zero matrices, n∈{1, 2, 3, 4, 5}, and m, a, and b are all positive integers.

### Claim 19 (depends on 11)

The computer-readable recording medium according to claim 11, wherein a code rate corresponding to the basic matrix is 5/6, and the mother matrix is shown as follows:
H
⁡
(
5
/
6
)
=
[
H
M
⁢
C
(
5
/
6
)
0
4
×
r
H
IR
(
5
/
6
)
I
r
×
r
]
,
where:
H(5/6) indicates the mother matrix, HMC(5/6) indicates the basic matrix, HIR(5/6) indicates the extension matrix, a size of HIR(5/6) is r rows and 24 columns, 5/6 indicates the code rate, 04×r indicates the first fixed matrix, Ir×r indicates the second fixed matrix, 04×r indicates an all-zero matrix with a size of 4 rows and r columns, Ir×r indicates an identity matrix with a size of r rows and r columns, r≥1, k≤r, and r is an integer; and
H
MC
(
5
/
6
)
=
[
13
48
80
66
4
74
7
30
76
52
37
60
-
49
-
73
31
74
73
21
1
0
-
-
69
63
74
56
64
77
57
65
6
16
51
-
64
-
64
68
9
48
62
54
-
0
0
-
51
15
0
80
24
25
42
54
44
71
71
9
67
35
67
-
58
-
29
-
0
-
0
0
16
29
36
41
44
56
59
37
50
24
-
65
4
65
4
52
-
4
-
73
1
-
-
0
]
,
wherein “-” indicates an all-zero matrix; and
wherein a Table G indicates a seventh matrix with a size of 100 rows and 24 columns, HIR(5/6) is obtained by reading r rows and 24 columns from the seventh matrix, the r rows are any r rows in the 100 rows in the seventh matrix, and Table G is shown as follows:
TABLE G
15.
n
d
1
2
3
4
5
6
7
8
9
10
11
11
0.60
1.15
3.34
4.80
5.20
6.29
7.39
9.22
11.77
12.7
18.7
10
0.72
2.79
3.69
4.49
5.75
6.8
9.2
11.56
12.22
14.58
8
1.18
2.47
4.21
5.80
6.38
7.50
9.75
11.32
9
0.21
1.26
2.30
3.36
4.44
5.67
6.63
7.2
11.55
9
0.18
2.63
3.78
4.44
6.67
8.14
9.35
11.73
14.9
9
1.56
2.5
3.9
5.45
6.67
7.50
9.25
17.8
19.53
8
0.45
1.28
3.50
4.62
6.34
7.8
9.4
20.76
7
2.80
3.50
4.13
5.40
6.32
9.0
10.20
8
1.47
2.38
3.55
4.45
6.67
7.71
9.57
23.38
7
1.47
2.79
3.7
4.76
6.27
9.33
21.49
7
1.58
2.19
3.26
4.31
5.39
9.68
15.17
6
2.6
3.76
5.24
6.69
7.3
16.43
6
1.40
3.34
6.37
7.42
9.1
13.10
6
1.59
2.47
3.66
6.63
9.74
17.26
6
2.47
3.3
4.53
5.67
7.67
22.46
6
3.69
4.56
5.35
6.36
9.54
18.17
6
3.7
6.26
7.77
9.24
16.43
22.32
5
1.36
2.9
3.76
6.3
8.78
5
1.14
2.45
6.0
7.59
19.39
5
1.4
3.4
6.54
8.31
13.31
5
1.48
2.39
3.33
6.32
10.34
5
1.46
4.47
6.6
13.69
20.22
5
1.66
3.64
6.10
9.77
23.42
5
1.23
2.62
6.65
15.43
16.43
5
1.6
2.48
3.16
6.29
12.23
5
2.3
3.11
6.44
8.34
16.70
4
1.59
2.49
3.16
14.1
5
2.77
3.19
6.8
13.10
21.17
5
1.44
2.20
3.18
14.17
19.17
4
3.71
6.16
9.4
10.69
4
2.27
3.18
12.36
14.0
5
1.52
3.43
6.42
8.39
20.56
4
1.31
6.14
8.50
22.9
4
3.22
6.38
9.64
18.80
4
1.43
2.80
3.59
17.34
5
2.48
3.31
6.22
15.77
16.71
4
3.21
6.54
10.41
13.65
4
3.58
6.78
14.47
18.56
5
1.70
3.21
6.13
11.8
13.41
4
1.22
6.19
18.63
21.74
4
1.59
2.58
6.17
12.14
5
1.59
3.72
6.32
15.29
20.29
4
1.71
2.79
14.21
20.24
4
2.46
3.46
16.19
17.51
4
1.53
2.75
13.34
22.28
4
0.79
1.24
2.34
8.64
3
1.73
2.25
10.49
4
1.48
2.18
17.64
19.72
3
0.41
2.41
10.1
3
1.32
12.74
15.45
3
2.9
12.50
19.25
4
1.72
2.18
12.75
21.11
3
0.40
1.34
2.43
4
1.57
2.71
8.76
11.29
3
0.74
10.67
15.54
3
7.5
8.23
14.66
3
10.70
12.41
13.17
3
10.59
12.72
14.74
3
0.3
8.25
14.31
3
8.54
14.65
22.68
3
0.15
12.18
13.29
3
0.11
8.21
19.33
3
0.30
13.29
19.80
3
0.50
8.41
16.79
3
12.51
14.41
22.45
2
8.18
17.77
3
0.3
4.51
8.6
3
8.34
10.58
14.67
3
10.14
17.30
18.56
2
14.69
18.64
3
9.58
12.59
15.11
3
0.74
12.48
14.38
3
0.41
10.52
15.16
3
12.58
16.63
20.80
3
0.8
12.2
18.25
2
0.64
20.35
3
0.68
11.4
12.26
3
0.39
12.66
22.61
3
11.26
12.50
18.31
2
14.11
16.18
3
9.73
10.80
19.44
2
11.54
13.28
3
0.68
14.0
19.55
3
0.53
7.3
15.42
3
0.65
10.72
16.73
3
0.54
12.11
23.69
3
0.44
12.15
17.70
3
12.57
16.48
18.61
3
7.48
14.30
18.72
2
7.80
10.47
3
0.4
12.23
19.72
3
9.59
13.4
17.69
2
9.66
18.22
3
12.52
16.53
19.60
2
8.35
21.13
3
7.65
9.44
16.68
3
12.16
13.9
17.9
3
7.10
12.3
14.7
2
17.50
22.5
3
9.62
16.20
17.80
wherein an mth element from top to bottom in a column in which d is located indicates a row weight of row m in the seventh matrix, an nth element (a, b) from left to right in row m in the seventh matrix indicates that a cyclic shift coefficient of a cyclic shift matrix in row m and column (a+n) in the seventh matrix is b, all remaining locations in the seventh matrix are all-zero matrices, n∈{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}, and m, a, and b are all positive integers.

### Claim 20 (depends on 11)

The computer-readable recording medium according to claim 11, wherein a code rate corresponding to the basic matrix is 5/6, and the mother matrix is shown as follows:
H
⁡
(
5
/
6
)
=
[
H
M
⁢
C
(
5
/
6
)
0
4
×
r
H
IR
(
5
/
6
)
I
r
×
r
]
,
where:
H(5/6) indicates the mother matrix, HMC(5/6) indicates the basic matrix, HIR(5/6) indicates the extension matrix, a size of HIR(5/6) is r rows and 24 columns, 5/6 indicates the code rate, 04%, indicates the first fixed matrix, Ir×r indicates the second fixed matrix, 04×r indicates an all-zero matrix with a size of 4 rows and r columns, Ir×r indicates an identity matrix with a size of r rows and r columns, r≥1, k≤r, and r is an integer; and
H
MC
(
5
/
6
)
=
[
13
48
80
66
4
74
7
30
76
52
37
60
-
49
-
73
31
74
73
21
1
0
-
-
69
63
74
56
64
77
57
65
6
16
51
-
64
-
64
68
9
48
62
54
-
0
0
-
51
15
0
80
24
25
42
54
44
71
71
9
67
35
67
-
58
-
29
-
0
-
0
0
16
29
36
41
44
56
59
37
50
24
-
65
4
65
4
52
-
4
-
73
1
-
-
0
]
,
wherein “-” indicates an all-zero matrix; and
wherein a Table H indicates an eighth matrix with a size of 100 rows and 24 columns, HIR(5/6) is obtained by reading r rows and 24 columns from the eighth matrix, the r rows are any r rows in the 100 rows in the eighth matrix, and Table H is shown as follows:
TABLE H
16.
n
d
1
2
3
4
5
5
0.80
1.29
2.34
8.39
9.22
5
3.7
4.20
5.60
6.15
7.7
5
11.8
13.2
14.77
18.69
20.56
5
12.72
15.58
16.79
17.75
19.49
5
5.47
10.75
21.18
22.22
23.38
5
2.32
3.80
6.21
7.63
9.50
5
0.44
1.30
4.55
8.21
20.67
5
11.26
13.67
14.14
16.2
18.36
5
10.35
12.78
15.73
17.9
19.44
5
4.53
6.67
21.18
22.8
23.63
5
0.56
1.5
2.50
4.45
9.9
5
5.76
7.45
8.4
13.25
20.50
4
11.34
14.8
16.62
18.28
4
12.32
15.13
17.40
19.50
5
9.47
10.38
21.80
22.20
23.0
5
1.71
2.38
4.45
6.57
7.55
4
0.67
5.7
8.79
20.49
4
3.27
13.47
14.76
18.33
4
11.58
12.17
16.26
17.39
4
10.68
15.31
19.3
23.19
5
1.76
4.24
4.69
21.6
22.43
4
0.40
6.10
7.42
9.1
4
3.37
5.66
8.26
20.34
3
13.63
21.47
22.74
3
10.3
18.59
23.46
3
11.67
14.53
16.67
5
4.36
12.54
15.35
17.47
19.69
3
0.17
1.26
6.56
4
5.32
7.24
8.77
20.43
3
2.76
3.78
9.7
3
13.36
21.3
22.9
3
11.45
14.39
18.14
3
10.4
16.59
23.0
3
12.31
15.31
19.4
4
4.32
4.33
4.34
17.54
3
1.39
7.48
20.6
3
5.69
8.47
9.22
3
2.77
3.10
17.46
3
12.66
15.42
19.64
3
10.65
21.23
22.62
3
11.48
13.43
18.43
5
4.23
4.44
14.16
16.6
23.29
3
5.11
7.3
8.70
3
1.16
9.59
20.34
3
0.10
16.49
17.1
3
3.8
12.77
19.19
3
13.17
15.20
21.17
3
10.17
14.18
23.44
3
2.4
11.16
22.69
4
4.18
4.27
4.36
18.71
3
5.52
7.39
20.0
3
1.42
9.56
19.43
3
15.14
17.31
18.9
3
3.50
12.38
16.80
3
0.34
11.22
22.64
2
2.59
14.80
3
13.77
21.31
23.43
4
4.22
4.71
5.21
10.48
3
1.41
4.65
7.54
3
9.58
18.56
20.78
3
0.47
17.21
19.13
3
10.8
11.41
22.70
3
12.22
15.19
21.63
3
2.17
13.14
16.74
5
3.59
4.29
4.59
14.58
23.29
3
1.71
16.72
17.32
3
5.79
10.21
20.24
2
7.46
19.46
3
9.51
14.19
18.75
2
0.53
8.34
3
11.34
12.28
15.24
3
2.64
13.79
23.73
4
3.49
4.72
21.25
22.48
3
1.64
10.1
17.18
3
5.41
13.32
23.41
2
9.74
18.45
3
0.50
7.25
14.9
3
3.18
16.11
20.72
2
12.43
21.75
3
2.40
11.57
19.34
2
6.71
8.29
3
4.54
15.67
22.76
3
3.74
5.23
9.5
3
1.17
11.66
20.70
2
7.41
17.59
3
0.3
2.72
18.74
3
10.68
13.31
14.25
3
8.65
15.54
16.18
3
12.29
19.15
23.21
3
6.11
21.33
22.29
3
4.79
5.30
9.80
3
3.41
14.50
15.51
3
1.41
8.18
18.45
3
0.51
2.3
13.77
3
7.67
19.58
20.6
3
11.14
16.56
23.34
2
10.64
22.30
2
6.11
12.69
4
4.48
9.74
17.59
21.58
3
0.52
14.38
15.16
wherein an mth element from top to bottom in a column in which d is located indicates a row weight of row m in the eighth matrix, an nth element (a, b) from left to right in row m in the eighth matrix indicates that a cyclic shift coefficient of a cyclic shift matrix in row m and column (a+n) in the eighth matrix is b, all remaining locations in the eighth matrix are all-zero matrices, n∈{1, 2, 3, 4, 5}, and m, a, and b are all positive integers.