Encoding method using a low density parity check code with a column weight of two
A method for communicating binary data and a digital communication system are presented. According to one embodiment, the method includes encoding a message word by multiplying the message word with a generator matrix, wherein the generator matrix multiplied by the transpose of a parity check matrix for a low density parity check code yields a null set, and wherein the parity check matrix has a column weight of two. Additionally disclosed is an encoding scheme based on a three-tier Tanner graph having a girth of twelve.
1. A method for encoding binary data, comprising multiplying a message word with a generator matrix, wherein the generator matrix multiplied by the transpose of a parity check matrix for a low density parity check code yields a null set, and wherein the parity check matrix has a column weight of two and a girth of twelve.
2. The method of claim 1 , wherein the parity check matrix is structured.
3. The method of claim 2 , wherein the parity check matrix is quasi-cyclic.
4. The method of claim 3 , wherein the parity check matrix has an even number of rows.
5. The method of claim 4 , further comprising decoding the message word after encoding.
6. The method of claim 5 , wherein decoding the message includes employing soft iterative decoding.
7. A coded data system, comprising an encoder for encoding a message word by multiplying the message word with a generator matrix, wherein the generator matrix multiplied by the transpose of a parity check matrix for a low density parity check code yields a null set, and wherein the parity check matrix has a column weight of two and a girth of twelve.
8. The system of claim 7 , wherein the parity check matrix is structured.
9. The system of claim 8 , wherein the parity check matrix is quasi-cyclic.
10. The system of claim 9 , wherein the parity check matrix has an even number of rows.
11. The system of claim 7 , further comprising a decoder in communication with the encoder via a channel.
12. The system of claim 11 , wherein the decoder includes a soft iterative decoding decoder.
13. A coded data system, comprising:
an encoder for encoding a message word by multiplying the message word with a generator matrix, wherein the generator matrix multiplied by the transpose of a quasi-cyclic parity check matrix for a low density parity check code yields a null set, and wherein the parity check matrix has a column weight of two and a girth of twelve;
a decoder in communication with the encoder via a channel.
14. A coded data system, comprising:
means for encoding a message word by multiplying the message word with a generator matrix, wherein the generator matrix multiplied by the transpose of a parity check matrix for a low density parity check code yields a null set, and wherein the parity check matrix has a column weight of two and a girth of twelve; and
means for decoding the message word in communication with the means for encoding via a channel.
15. The system of claim 14 , wherein the parity check matrix is structured.
16. The system of claim 15 , wherein the parity check matrix is quasi-cyclic.
17. The system of claim 16 , wherein the means for decoding include means for soft iterative decoding of the message word.
18. A coded data system, comprising:
a first encoder for encoding a message word according to an error correction code to thereby generate a first codeword; and
a second encoder for encoding the first codeword by multiplying the first codeword with a generator matrix, wherein the generator matrix multiplied by the transpose of a parity check matrix for a low density parity check code yields a null set, and wherein the parity check matrix has a column weight of two and a girth of twelve.
19. The system of claim 18 , wherein the first encoder is for encoding the message word according to a Reed-Solomon error correction code.
20. The system of claim 19 , wherein the first encoder is for encoding the message word according to a low density parity check code having a column weight equal to or greater than three.
21. The system of claim 18 , wherein the parity check matrix is structured.
22. The system of claim 18 , wherein the parity check matrix is quasi-cyclic.
23. The system of claim 18 , further comprising:
a first decoder in communication with the second encoder via a channel; and
a second decoder in communication with the first decoder.
24. The system of claim 23 , wherein the first decoder includes a soft iterative decoding decoder.
25. A method of encoding binary data, comprising:
receiving a first message word; and
adding a first plurality of redundancy bits to the first message word to thereby generate a first codeword, wherein adding the first plurality of redundancy bits includes adding a first plurality of redundancy bits based on a three-tier Tanner graph having a girth of twelve, wherein adding the first plurality of redundancy bits based on the three-tier Tanner graph includes:
operating on the first message word at a first tier of the three-tier Tanner graph during a first time period;
operating on an output from the first tier at a second tier of the Tanner graph during a second time period; and
operating on an output from the second tier at a third tier of the Tanner graph during a third time period.
26. The method of claim 25 , further comprising:
receiving a second message word; and
adding a second plurality of redundancy bits to the second message word bits based on the three-tier Tanner graph to thereby generate a second codeword, wherein adding the second plurality of redundancy bits includes:
operating on the second message word at the first tier of the three-tier Tanner graph during the second time period;
operating on an output from the first tier at the second tier of the Tanner graph during the third time period; and
operating on an output from the second tier at the third tier of the Tanner graph during a fourth time period.