Method and apparatus of encoding and decoding data using low density parity check code in a wireless communication system
A method of encoding data using low density parity check (LDPC) code defined by a m×n parity check matrix is disclosed. More specifically, the method includes encoding input source data using the parity check matrix, wherein the parity check matrix comprises a plurality of z×z sub-matrices of which row weights and column weights are ‘0’ or ‘1’.
1. A method of encoding data in an encoder using low density parity check (LDPC) code based on a first base matrix defined for a code rate, the method comprising:
generating a parity check matrix by replacing each integer value of the first base matrix with a corresponding matrix,
wherein the first base matrix is as follows when the code rate is ⅔:
2
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1
19
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1
47
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1
48
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1
36
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1
82
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1
47
-
1
-
1
69
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1
88
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1
33
-
1
3
-
1
16
-
1
37
-
1
40
10
-
1
86
-
1
62
-
1
28
-
1
85
-
1
16
-
1
34
-
1
-
1
28
-
1
32
-
1
81
-
1
27
-
1
88
-
1
5
-
1
56
23
-
1
29
-
1
15
-
1
30
-
1
66
-
1
24
-
1
50
-
1
-
1
30
-
1
65
-
1
54
-
1
14
-
1
0
-
1
30
-
1
74
32
-
1
0
-
1
15
-
1
56
-
1
85
-
1
5
-
1
6
-
1
-
1
0
-
1
47
-
1
13
-
1
61
-
1
84
-
1
55
-
1
78
15
-
1
95
0
-
1
-
1
-
1
-
1
-
1
-
1
-
1
48
-
1
0
0
-
1
-
1
-
1
-
1
-
1
73
-
1
-
1
-
1
0
0
-
1
-
1
-
1
-
1
-
1
37
-
1
-
1
-
1
0
0
-
1
-
1
-
1
62
-
1
-
1
-
1
-
1
-
1
0
0
-
1
-
1
-
1
0
-
1
-
1
-
1
-
1
-
1
0
0
-
1
52
-
1
0
-
1
-
1
-
1
-
1
-
1
0
0
-
1
41
95
-
1
-
1
-
1
-
1
-
1
-
1
0
where “−1” indicates a zero matrix having a z max ×z max size, “0” indicates an identity matrix having the z max ×z max size, and a positive integer indicates a first permutation matrix generated by circular shifting the identity matrix by the positive integer and having the z max ×z max size; and
encoding the data using the parity check matrix.
2. The method of claim 1 , wherein z max is 96.
3. The method of claim 1 , wherein generating the parity check matrix comprises:
generating a second base matrix by replacing each first value corresponding to each element of the first base matrix with a second value corresponding to each element of the second base matrix, the second value an integer that indicates either a zero matrix or a second permutation matrix having a z×z size, wherein z is smaller than z max and each second value is determined based on z, z max , and each corresponding first value; and
replacing each second value of the second base matrix with a corresponding second permutation matrix or the zero matrix having the z×z size to generate the parity check matrix.
4. The method of claim 3 , wherein the second value corresponding to each element of the second base matrix is either a non-negative integer or “−1” and replacing each second value of the second base matrix further comprises:
replacing the second value of “−1” with the zero matrix having the z×z size;
replacing the second value of the positive integer with a second permutation matrix having the z×z size, the second permutation matrix altered from an identity matrix having the z×z size according to the positive integer; and
replacing the second value of a zero with a second permutation matrix that is the identity matrix having the z×z size.
5. The method of claim 4 , wherein altering the second permutation matrix comprises circular shifting either each entire row or each entire column of the identity matrix a number of intervals equal to the positive integer.
6. The method of claim 3 , wherein each of the first permutation matrix and second permutation matrix is defined as having a row weight and column weight of “1”.
7. The method of claim 3 , wherein the number of rows of the second base matrix is equal to the number of columns in the parity check matrix divided by z and multiplied by (1−(a coding rate)).
8. The method of claim 3 , wherein each second value is determined based on the following equation:
shift(z) =floor (shift (z max ) z/ z max ), where “shift (z max )” is the first value, “shift(z)” is the second value, and “floor (x)” denotes a nearest integer from x toward negative infinity.
9. The method of claim 3 , wherein at least two continuous integers corresponding to the first value are grouped and mapped to one second value when determining each second value.
10. The method of claim 3 , wherein generating the second base matrix further comprises replacing a first value that indicates the zero matrix having the z max ×z max size with a second value that indicates the zero matrix having the z×z size.
11. A method of decoding encoded data in a decoder using low density parity check (LDPC) code based on a first base matrix defined for a code rate, the method comprising:
generating a parity check matrix by replacing each integer value of the first base matrix with a corresponding matrix, wherein the first base matrix is as follows when the code rate is ⅔:
2
-
1
19
-
1
47
-
1
48
-
1
36
-
1
82
-
1
47
-
1
-
1
69
-
1
88
-
1
33
-
1
3
-
1
16
-
1
37
-
1
40
10
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1
86
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1
62
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1
28
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1
85
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1
16
-
1
34
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1
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1
28
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1
32
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1
81
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1
27
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1
88
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1
5
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1
56
23
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1
29
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1
15
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1
30
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1
66
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1
24
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1
50
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1
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1
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1
65
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1
54
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1
14
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1
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1
30
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1
74
32
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1
0
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1
15
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1
56
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1
85
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1
5
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1
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1
0
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1
47
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1
13
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1
61
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1
84
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1
55
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1
78
15
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1
95
0
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1
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1
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1
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1
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1
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1
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1
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1
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-
1
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1
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1
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1
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1
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1
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1
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1
-
1
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1
62
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1
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1
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1
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1
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1
52
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0
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1
41
95
-
1
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1
-
1
-
1
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1
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1
0
where “−1” indicates a zero matrix having a z max ×z max size, “0” indicates an identity matrix having the z max ×z max size, and a positive integer indicates a first permutation matrix generated by circular shifting the identity matrix by the positive integer and having the z max ×z max size; and
decoding the encoded data using the parity check matrix.
12. The method of claim 11 , wherein z max is 96.
13. The method of claim 11 , wherein generating the parity check matrix comprises:
generating a second base matrix by replacing each first value corresponding to each element of the first base matrix with a second value corresponding to each element of the second base matrix, the second value an integer that indicates either a zero matrix or a second permutation matrix having a z×z size, wherein z is smaller than z max and each second value is determined based on z, z max , and each corresponding first value; and
replacing each second value of the second base matrix with a corresponding second permutation matrix or the zero matrix having the z×z size to generate the parity check matrix.
14. The method of claim 13 , wherein the second value corresponding to each element of the second base matrix is either a non-negative integer or “−1” and replacing each second value of the second base matrix further comprises:
replacing the second value of “−1” with the zero matrix having the z×z size;
replacing the second value of the positive integer with a second permutation matrix having the z×z size, the second permutation matrix altered from an identity matrix having the z×z size according to the positive integer; and
replacing the second value of a zero with a second permutation matrix that is the identity matrix having the z×z size.
15. The method of claim 14 , wherein altering the second permutation matrix comprises circular shifting either each entire row or each entire column of the identity matrix a number of intervals equal to the positive integer.
16. The method of claim 13 , wherein each of the first permutation matrix and second permutation matrix is defined as having a row weight and column weight of “1”.
17. The method of claim 13 , wherein the number of rows of the second base matrix is equal to the number of columns in the parity check matrix divided by z and multiplied by (1−(a coding rate)).
18. The method of claim 13 , wherein each second value is determined based on the following equation:
shift(z) =floor (shift (z max ) z/ z max ), where “shift (z max )” is the first value, “shift(z)” is the second value, and “floor (x)” denotes a nearest integer from x toward negative infinity.
19. The method of claim 13 , wherein at least two continuous integers corresponding to the first value are grouped and mapped to one second value when determining each second value.
20. The method of claim 13 , wherein generating the second base matrix further comprises replacing a first value that indicates the zero matrix having the z max ×z max size with a second value that indicates the zero matrix having the z×z size.