Method of codifying data or generating a block of data based on matrix with a triple diagonal structure
A method including generating a matrix. The matrix includes first and second portions. The first portion includes data bits. The second portion includes parity bits and has a triple diagonal structure. The triple diagonal structure includes a first central diagonal, a second central diagonal, and a last row diagonal. Bits of the first central diagonal, the second central diagonal, and the last row diagonal are equal to 1 and a remainder of bits in the triple diagonal structure are equal to 0. The method further includes: determining parity bits based on the matrix; if the matrix is generated to codify data for transmission from a first device to a second device, transmitting the parity bits from the first device to the second device; and if the matrix is generated based on a vector of bits received from the second device, generating a block of data based on the parity bits.
1. A method comprising:
generating a first matrix, wherein
the first matrix includes a first portion and a second portion,
the first portion comprises data bits,
the second portion comprises parity bits,
the second portion has a triple diagonal structure,
the triple diagonal structure includes (i) a first central diagonal, (ii) a second central diagonal, and (iii) a last row diagonal, and
bits of the first central diagonal, the second central diagonal, and the last row diagonal are equal to 1 and a remainder of bits in the triple diagonal structure are equal to 0;
determining the parity bits based on the first matrix;
if the first matrix is generated to codify data for transmission from a first device to a second device, transmitting the parity bits from the first device to the second device; and
if the first matrix is generated based on a vector of bits received from the second device, generating a block of data based on the parity bits.
2. The method of claim 1 , wherein:
the first matrix comprises a plurality of rows and a plurality of columns; and
a number of the plurality of rows is equal to a sum of (i) a number of the plurality of columns and (ii) a predetermined number.
3. The method of claim 1 , wherein:
the first matrix comprises a second matrix and a third matrix;
the second matrix comprises the data bits; and
the third matrix comprises the parity bits.
4. The method of claim 3 , wherein:
the third matrix comprises a fourth matrix and a fifth matrix;
the fourth matrix is a pseudo-random column vector having a Hamming weight greater than 2;
the fifth matrix has the triple diagonal structure; and
a number of rows in the fourth matrix is equal to a number of rows in the fifth matrix.
5. The method of claim 1 , further comprising:
determining a number of the data bits;
selecting a factor, wherein the factor is greater than 1; and
based on the factor, generating a codeword based on the parity bits,
wherein
the first matrix comprises a plurality of rows and a plurality of columns,
a number of the plurality of rows is equal to a sum of (i) a number of the plurality of columns and (ii) a constant,
the constant is equal to the number of the data bits divided by the factor, and
a number of bits in the codeword divided by the factor is equal to a number of columns in the second portion of the first matrix.
6. The method of claim 1 , wherein the first matrix comprises:
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1.
7. The method of claim 1 , further comprising:
generating a second matrix based on the first matrix;
generating a third matrix based on the second matrix;
determining the parity bits based on the third matrix; and
transmitting a codeword, via the transmitter, from the first device to the second device, wherein the codeword comprises the parity bits.
8. The method of claim 7 , wherein the generating of the second matrix comprises:
replacing each element of the first matrix that is equal to 1 with a pseudo-random positive integer; and
replacing each element of the first matrix that is equal to 0 with −1.
9. The method of claim 7 , wherein the generating of the third matrix comprises:
replacing positive elements of the second matrix with an identity matrix, wherein the identity matrix is rotated cyclically a number of times indicated by a value of one of the positive elements; and
replacing elements of the second matrix that are equal to −1 with a null matrix.
10. The method of claim 9 , wherein (i) a number of rows in the identity matrix is equal to a number of columns in the identity matrix, or (ii) a number of rows in the null matrix is equal to a number of columns in the null matrix.
11. The method of claim 7 , wherein the second matrix comprises:
13
-
1
7
-
1
-
1
1
-
1
1
-
1
-
1
-
1
-
1
-
1
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
5
-
1
-
1
-
1
11
-
1
-
1
-
1
4
-
1
4
6
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
13
-
1
-
1
-
1
-
1
11
-
1
10
-
1
9
13
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
13
-
1
-
1
6
-
1
10
-
1
5
-
1
-
1
4
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
8
8
2
11
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
3
-
1
-
1
-
1
-
1
-
1
-
1
4
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
4
2
-
1
2
9
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
-
1
2
-
1
13
-
1
4
9
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
-
1
11
-
1
-
1
-
1
-
1
-
1
-
1
6
4
11
12
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
10
-
1
-
1
-
1
-
1
1
-
1
13
13
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
0
-
1
-
1
0
2
2
-
1
-
1
-
1
-
1
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
1
2
11
2
4
12
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0.
12. The method of claim 7 , wherein the second matrix comprises:
-
1
-
1
-
1
6
-
1
-
1
9
6
-
1
-
1
2
-
1
-
1
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
-
1
-
1
-
1
3
-
1
12
1
-
1
-
1
3
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
9
11
-
1
-
1
13
-
1
-
1
2
12
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
1
-
1
-
1
11
-
1
-
1
7
-
1
-
1
-
1
11
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
4
8
-
1
-
1
-
1
-
1
-
1
2
5
4
-
1
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
3
0
-
1
-
1
8
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
6
-
1
-
1
-
1
-
1
5
13
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
9
-
1
-
1
-
1
3
-
1
-
1
3
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
9
0
13
-
1
-
1
12
-
1
-
1
8
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
5
-
1
-
1
1
4
-
1
-
1
5
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
-
1
8
-
1
-
1
8
-
1
-
1
9
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
10
11
-
1
-
1
-
1
3
-
1
-
1
0
-
1
-
1
-
1
4
8
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0.
13. The method of claim 7 , wherein the second matrix comprises:
-
1
52
-
1
64
-
1
-
1
60
-
1
-
1
-
1
-
1
1
-
1
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
10
-
1
-
1
-
1
-
1
79
-
1
-
1
79
-
1
78
51
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
9
-
1
-
1
-
1
-
1
-
1
-
1
75
29
72
8
-
1
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
52
16
63
-
1
-
1
65
-
1
-
1
-
1
-
1
-
1
40
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
24
-
1
-
1
47
1
39
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
52
-
1
-
1
-
1
-
1
-
1
-
1
-
1
53
79
48
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
0
-
1
-
1
72
-
1
67
57
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
7
-
1
-
1
-
1
2
50
-
1
-
1
-
1
-
1
15
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
15
-
1
19
-
1
-
1
-
1
-
1
-
1
75
51
43
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
72
-
1
-
1
-
1
38
-
1
-
1
-
1
69
-
1
62
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
19
-
1
41
-
1
-
1
1
41
-
1
-
1
-
1
-
1
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
41
-
1
17
-
1
-
1
-
1
-
1
-
1
15
-
1
30
-
1
40
6
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0.
14. The method of claim 7 , wherein the second matrix comprises:
27
-
1
-
1
-
1
55
19
-
1
30
-
1
-
1
-
1
-
1
-
1
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
-
1
1
-
1
70
-
1
47
-
1
62
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
41
-
1
-
1
-
1
44
-
1
-
1
59
60
25
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
16
77
-
1
-
1
-
1
5
-
1
48
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
45
-
1
27
-
1
46
19
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
63
-
1
-
1
-
1
55
-
1
-
1
-
1
48
26
10
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
42
-
1
21
-
1
58
-
1
41
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
78
0
-
1
7
52
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
-
1
29
9
-
1
-
1
-
1
37
-
1
-
1
-
1
35
21
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
-
1
22
72
-
1
-
1
47
-
1
-
1
-
1
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
35
-
1
-
1
-
1
-
1
13
-
1
35
-
1
70
-
1
-
1
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
46
28
-
1
-
1
-
1
38
-
1
-
1
-
1
8
-
1
10
58
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0.
15. The method of claim 7 , wherein the second matrix comprises:
-
1
-
1
-
1
-
1
-
1
-
1
297
106
328
-
1
-
1
99
-
1
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
290
0
312
-
1
32
-
1
120
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
183
57
-
1
-
1
187
68
-
1
-
1
-
1
-
1
260
-
1
81
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
323
-
1
-
1
-
1
137
354
-
1
-
1
162
-
1
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
228
-
1
-
1
-
1
-
1
224
-
1
114
-
1
245
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
113
98
-
1
-
1
120
23
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
138
-
1
187
45
62
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
142
-
1
-
1
-
1
347
67
-
1
-
1
-
1
46
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
328
265
-
1
66
156
96
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
212
184
-
1
-
1
102
-
1
-
1
-
1
-
1
120
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
80
15
-
1
329
153
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
207
70
-
1
7
235
-
1
-
1
-
1
-
1
-
1
-
1
-
1
81
185
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0.
16. The method of claim 7 , wherein the second matrix comprises:
-
1
34
-
1
95
-
1
279
-
1
-
1
-
1
-
1
248
-
1
-
1
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
-
1
0
-
1
-
1
-
1
-
1
134
356
275
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
51
-
1
27
-
1
-
1
-
1
-
1
-
1
22
152
-
1
57
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
124
-
1
290
-
1
281
15
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
340
-
1
99
336
-
1
-
1
-
1
-
1
-
1
-
1
-
1
33
-
1
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
163
-
1
46
-
1
-
1
-
1
-
1
-
1
-
1
306
-
1
86
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
185
-
1
24
-
1
-
1
-
1
94
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
223
-
1
225
325
-
1
-
1
-
1
-
1
-
1
297
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
46
-
1
314
-
1
-
1
-
1
59
-
1
-
1
67
-
1
120
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
-
1
121
-
1
-
1
-
1
-
1
161
-
1
303
-
1
264
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
303
-
1
8
-
1
185
-
1
-
1
138
-
1
-
1
-
1
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
312
-
1
-
1
-
1
100
-
1
-
1
144
-
1
307
33
166
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
-
1
0.
17. The method of claim 7 , wherein the second matrix comprises:
49
-
1
-
1
21
31
-
1
57
-
1
-
1
19
-
1
29
2
-
1
19
-
1
-
1
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
7
22
-
1
-
1
37
-
1
32
10
-
1
26
-
1
-
1
59
-
1
48
-
1
0
0
-
1
-
1
-
1
-
1
-
1
53
-
1
-
1
20
50
-
1
-
1
3
16
-
1
49
-
1
-
1
28
14
-
1
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
58
23
-
1
-
1
15
54
-
1
-
1
5
-
1
18
49
-
1
-
1
13
-
1
-
1
-
1
0
0
-
1
-
1
-
1
55
-
1
-
1
58
-
1
9
-
1
26
57
-
1
41
-
1
31
-
1
21
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
10
49
-
1
59
-
1
7
-
1
-
1
30
-
1
18
-
1
48
-
1
7
59
-
1
-
1
-
1
-
1
0
0
-
1
48
-
1
-
1
50
18
-
1
-
1
11
52
-
1
59
-
1
-
1
37
-
1
10
0
-
1
-
1
-
1
-
1
-
1
0
0
-
1
24
16
-
1
-
1
0
53
-
1
-
1
41
-
1
38
51
-
1
58
-
1
59
8
-
1
-
1
-
1
-
1
-
1
0.
18. The method of claim 7 , wherein the second matrix comprises:
78
-
1
-
1
167
237
-
1
3
-
1
266
-
1
-
1
102
153
-
1
-
1
212
-
1
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
83
189
-
1
-
1
68
-
1
178
-
1
90
205
-
1
-
1
13
4
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
-
1
226
147
-
1
46
-
1
-
1
76
-
1
116
-
1
211
-
1
112
-
1
118
-
1
-
1
0
0
-
1
-
1
-
1
-
1
92
-
1
-
1
214
-
1
236
241
-
1
157
-
1
143
-
1
214
-
1
207
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
144
-
1
-
1
258
264
-
1
53
-
1
114
-
1
172
-
1
-
1
82
262
-
1
62
-
1
-
1
-
1
0
0
-
1
-
1
-
1
153
120
-
1
-
1
199
-
1
126
-
1
61
-
1
183
15
-
1
-
1
134
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
100
-
1
141
-
1
36
-
1
17
-
1
156
-
1
124
162
-
1
-
1
57
0
-
1
-
1
-
1
-
1
-
1
0
0
196
-
1
187
-
1
73
-
1
80
-
1
139
-
1
57
-
1
-
1
236
267
-
1
62
256
-
1
-
1
-
1
-
1
-
1
0.
19. The method of claim 7 , wherein the second matrix comprises:
-
1
13
32
47
41
24
-
1
25
22
40
1
31
8
15
20
15
42
30
13
3
-
1
0
-
1
-
1
25
46
15
43
45
29
39
47
23
38
39
12
-
1
21
-
1
38
33
0
0
-
1
39
0
0
-
1
35
45
45
38
14
16
6
11
-
1
18
7
41
35
17
32
45
41
-
1
18
17
0
-
1
0
0
9
32
6
22
26
31
9
8
22
32
40
4
18
40
36
-
1
-
1
23
31
41
39
20
-
1
0.
20. The method of claim 7 , wherein the second matrix comprises:
-
1
47
146
203
184
112
-
1
116
103
181
3
140
38
68
91
70
191
138
62
14
-
1
0
-
1
-
1
117
203
67
194
206
133
174
212
104
171
176
56
-
1
96
-
1
167
149
4
1
-
1
177
0
0
-
1
153
206
198
173
55
72
28
53
-
1
82
34
186
161
80
144
204
187
-
1
87
77
0
-
1
0
0
44
147
27
83
118
130
41
38
100
146
183
19
85
180
163
-
1
-
1
106
140
185
177
94
-
1
0.
21. The method of claim 1 , further comprising:
generating a codeword based on the parity bits; and
puncturing the codeword to remove bits of the codeword prior to the codeword being transmitted; and
subsequent to the puncturing, transmitting the codeword from the first device to the second device.
22. The method of claim 21 , wherein the puncturing includes the following puncturing pattern:
pp
1152
(
16
/
18
)
=
[
1
1
…
1
︸
720
0
0
…
0
︸
36
1
1
…
1
︸
360
0
0
…
0
︸
36
]
.
23. The method of claim 21 , wherein the puncturing includes the following puncturing pattern:
pp
5184
(
16
/
18
)
=
[
1
1
…
1
︸
3240
0
0
…
0
︸
162
1
1
…
1
︸
972
0
0
…
0
︸
162
1
1
…
1
︸
648
]
.
24. The method of claim 21 , wherein the puncturing includes the following puncturing pattern:
pp
1152
(
20
/
21
)
=
[
1
1
…
1
︸
720
0
0
…
0
︸
48
1
1
…
1
︸
240
0
0
…
0
︸
96
1
1
…
1
︸
48
]
.
25. The method of claim 21 , wherein the puncturing includes the following puncturing pattern:
pp
5184
(
20
/
21
)
=
[
0
0
…
0
︸
216
1
1
…
1
︸
4320
0
0
…
0
︸
432
1
1
…
1
︸
216
]
.