High-rate long LDPC codes
Methods and devices for encoding source words and decoding codewords wherein encoding a source word includes: receiving a 1×K source word row vector ū; and generating a 1×N codeword vector c =ū·G, wherein G is a K×N generator matrix derived from a parity check matrix H I ; and wherein the parity check matrix H I is derived from a base parity check matrix H by applying an optimized lifting matrix to the base parity check matrix H.
1. A method for encoding a source word, comprising:
receiving a 1×K source word row vector ū; and
generating a 1×N codeword vector c =ū·G, wherein
G is a K×N generator matrix derived from a parity check matrix H I ; and
wherein H I is derived from a base parity check matrix H by applying an optimized lifting matrix to the base parity check matrix H, the optimized lifting matrix being either:
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
or
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1.
2. The method of claim 1 wherein different rows in the base parity check matrix are summed to obtain H I .
3. The method of claim 2 wherein rows 1 and 3 of the intermediate base parity check matrix are summed.
4. The method of claim 2 wherein rows 2 and 4 of the intermediate base parity check matrix are summed.
5. The method of claim 1 wherein H I is:
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41
18
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40
11
41
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6
20
6
32
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18
35
37
19
31
18
41
23
22
11
40
21
41
6
39
6
20
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32
9
25
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30
22
0
4
34
8
31
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3
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14
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4
4
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25
22
30
4
0
8
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31
22
3
17
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4
15
27
4
28
9
12
17
3
29
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0
13
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17
12
29
3
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0
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24
13
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18
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13
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13
22
24.
6. A system, comprising:
a processor
a non-transitory memory connected to the processor and storing instructions configuring the processor to cause the system to perform the method of:
receiving a 1×K source word row vector ū; and
generating a 1×N codeword vector c =ū·G, wherein
G is a K×N generator matrix derived from a parity check matrix H I ; and
wherein H I is derived from a base parity check matrix H by applying an optimized lifting matrix to the base parity check matrix H I the optimized lifting matrix being either:
1
1
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0
0
1
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1
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1
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0
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0
or:
0
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0
0
1
1
0
0
0
1
0
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1
1
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1