Low density parity check (LDPC) code
View Patent ↗Low density parity check code (LDPC) base parity check matrices and the method for use thereof in communication systems. The method of expanding the base check parity matrix is described. Examples of expanded LDPC codes with different code lengths and expansion factors are also shown.
1. A method for low-density parity-check (LDPC) encoding data, comprising:
receiving input data from a data source;
applying the following expanded parity check matrix to the input data to generate encoded data with a code length of 1944:
61
75
4
63
56
−1
−1
−1
−1
−1
−1
8
56
74
77
20
−1
−1
−1
64
24
4
67
−1
28
21
68
10
7
14
65
−1
−1
−1
23
−1
48
38
43
78
76
−1
−1
−1
−1
5
36
−1
40
2
53
25
−1
52
62
−1
20
−1
−1
44
69
23
64
10
22
−1
21
−1
−1
−1
−1
−1
12
0
68
20
55
61
−1
40
−1
−1
−1
52
58
8
34
64
78
−1
−1
11
78
24
−1
−1
−1
2
17
25
1
0
−1
−1
−1
−1
−1
−1
7
−1
−1
−1
−1
0
0
−1
−1
−1
−1
−1
−1
−1
75
−1
−1
−1
0
0
−1
−1
−1
−1
15
72
−1
−1
−1
−1
−1
0
0
−1
−1
−1
−1
−1
−1
−1
0
−1
−1
−1
0
0
−1
−1
68
23
29
−1
−1
−1
−1
−1
−1
0
0
−1
−1
−1
−1
44
−1
−1
−1
−1
−1
−1
0
0
−1
−1
−1
58
1
−1
−1
−1
−1
−1
−1
0
wherein −1represents an 81×81 all-zero square matrix, and all other integers represent an 81×81 identity matrix, circularly right shifted a respective number of times corresponding to the respective integers.
2. A method as defined in claim 1 , further comprising expanding the expanded parity check matrix from a base parity check matrix having a coding rate of R=⅔.
3. A method as defined in claim 2 , wherein the base parity check matrix has a size of 8×24.
4. A method as defined in claim 3 , wherein the base parity check matrix has a total weight less than or equal to 88.
5. A method as defined in claim 4 , wherein the base parity check matrix is:
1
1
1
1
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1.
6. Apparatus for low-density parity-check (LDPC) encoding data, comprising:
a processor; and
an instruction storage element operable to store instructions executable by the processor, the instructions comprising:
instructions executable to apply the following expanded parity check matrix to the data to produce encoded data with a code length of 1944:
61
75
4
63
56
−1
−1
−1
−1
−1
−1
8
−1
2
17
25
1
0
−1
−1
−1
−1
−1
−1
56
74
77
20
−1
−1
−1
64
24
4
67
−1
7
−1
−1
−1
−1
0
0
−1
−1
−1
−1
−1
28
21
68
10
7
14
65
−1
−1
−1
23
−1
−1
−1
75
−1
−1
−1
0
0
−1
−1
−1
−1
48
38
43
78
76
−1
−1
−1
−1
5
36
−1
15
72
−1
−1
−1
−1
−1
0
0
−1
−1
−1
40
2
53
25
−1
52
62
−1
20
−1
−1
44
−1
−1
−1
−1
0
−1
−1
−1
0
0
−1
−1
69
23
64
10
22
−1
21
−1
−1
−1
−1
−1
68
23
29
−1
−1
−1
−1
−1
−1
0
0
−1
12
0
68
20
55
61
−1
40
−1
−1
−1
52
−1
−1
−1
44
−1
−1
−1
−1
−1
−1
0
0
58
8
34
64
78
−1
−1
11
78
24
−1
−1
−1
−1
−1
58
1
−1
−1
−1
−1
−1
−1
0
wherein −1represents a 81×81 all-zero square matrix, and all other integers represent an 81×81 identity matrix, circularly right shifted a respective number of times corresponding to the respective integers.
7. Apparatus as defined in claim 6 , wherein the expanded base parity check matrix is expanded from a base parity check matrix having a coding rate of R=⅔.
8. Apparatus as defined in claim 7 , wherein the base parity check matrix has a size of 8×24.
9. Apparatus as defined in claim 8 , wherein the base parity check matrix has a total weight less than or equal to 88.
10. Apparatus as defined in claim 9 , wherein the base parity check matrix is:
1
1
1
1
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1.