Rate-scalable, multistage quasi-cyclic LDPC coding
Encoding is performed by dividing a quasi-cyclic low-density parity-check (QC-LDPC) parity check matrix into a first sub-matrix and a second sub-matrix. The first sub-matrix includes a plurality of circulant vectors and the plurality of circulant vectors is associated with a circulant size. Input data is received having a length which is a product of an integer multiplier and the circulant size. A first stage of multi-stage LDPC encoding is performed using the input data and a subset of the plurality of circulant vectors; the number of circulant vectors in the subset equals the integer multiplier.
1. A system for encoding, comprising:
a processor configured to divide a quasi-cyclic low-density parity-check (QC-LDPC) parity check matrix into a first sub-matrix and a second sub-matrix, wherein the first sub-matrix includes a plurality of circulant vectors and the plurality of circulant vectors is associated with a circulant size;
an interface configured to receive input data having a length which is a product of an integer multiplier and the circulant size; and
an encoder configured to perform a first stage of multi-stage LDPC encoding using the input data and a subset of the plurality of circulant vectors, wherein the number of circulant vectors in the subset equals the integer multiplier.
2. The system recited in claim 1 , wherein the encoder generates LDPC encoded data and the system further includes storage configured to store the LDPC encoded data.
3. The system recited in claim 2 , wherein the storage includes one or more of the following: magnetic disk storage or Flash storage.
4. The system recited in claim 1 , wherein the plurality of circulant vectors includes at least one column of circulants.
5. The system recited in claim 1 , wherein the subset only includes circulant vectors which are contiguous to each other within the first sub-matrix.
6. The system recited in claim 1 , wherein the interface is further configured to obtain the integer multiplier, including by counting the length of the input data.
7. The system recited in claim 1 further comprising:
storage configured to store information associated with a plurality of QC-LDPC codes; and
a controller configured to:
receive a selection of one of the plurality of QC-LDPC codes; and
in response to receiving the selection: retrieve information stored in the storage associated with the selected one of the plurality of QC-LDPC codes and program the encoder with at least some of the retrieved information.
8. The system recited in claim 1 , wherein:
the parity check matrix is associated with a generator matrix which includes a plurality of circulants; and
the system further includes storage configured to store the generator matrix by storing, for at least one of the plurality of circulants, one and only one vector from said at least one of the plurality of circulants.
9. The system recited in claim 1 , wherein:
the parity check matrix includes a plurality of circulants; and
the system further includes storage configured to store the parity check matrix by storing, for at least one of the plurality of circulants, one and only one vector from said at least one of the plurality of circulants.
10. The system recited in claim 1 , wherein:
the parity check matrix includes a plurality of circulants; and
the system further includes storage configured to store the parity check matrix by storing, for at least one of the plurality of circulants, the location(s) of the 1's in one and only one vector from said at least one of the plurality of circulants.
11. The system recited in claim 10 , wherein: storing the location(s) of the 1's is performed in the event the number of 1's in the parity check matrix is less than b/(ceil(log 2 (b))) where b is the circulant size.
12. The system recited in claim 10 , wherein storing the location(s) of the 1's includes storing the location(s) in non base 2.
13. A method for encoding, comprising:
using a processor to divide a quasi-cyclic low-density parity-check (QC-LDPC) parity check matrix into a first sub-matrix and a second sub-matrix, wherein the first sub-matrix includes a plurality of circulant vectors and the plurality of circulant vectors is associated with a circulant size;
receiving input data having a length which is a product of an integer multiplier and the circulant size; and
performing a first stage of multi-stage LDPC encoding using the input data and a subset of the plurality of circulant vectors, wherein the number of circulant vectors in the subset equals the integer multiplier.
14. The method recited in claim 13 , wherein encoding generates LDPC encoded data and the method further includes storage configured to store the LDPC encoded data.
15. The method recited in claim 14 , wherein the storage includes one or more of the following: magnetic disk storage or Flash storage.
16. The method recited in claim 13 , wherein the plurality of circulant vectors includes at least one column of circulants.
17. The method recited in claim 13 , wherein the subset only includes circulant vectors which are contiguous to each other within the first sub-matrix.
18. The method recited in claim 13 , further comprising obtaining the integer multiplier, including by counting the length of the input data.
19. The method recited in claim 13 further comprising:
storing information associated with a plurality of QC-LDPC codes; and
receiving a selection of one of the plurality of QC-LDPC codes; and
in response to receiving the selection: retrieving stored information associated with the selected one of the plurality of QC-LDPC codes and programming an encoder, which performs first stage of multi-stage LDPC encoding, with at least some of the retrieved information.
20. The method recited in claim 13 , wherein:
the parity check matrix is associated with a generator matrix which includes a plurality of circulants; and
the method further includes storing the generator matrix by storing, for at least one of the plurality of circulants, one and only one vector from said at least one of the plurality of circulants.
21. The method recited in claim 13 , wherein:
the parity check matrix includes a plurality of circulants; and
the method further includes storing the parity check matrix by storing, for at least one of the plurality of circulants, one and only one vector from said at least one of the plurality of circulants.
22. The method recited in claim 13 , wherein:
the parity check matrix includes a plurality of circulants; and
the method further includes storing the parity check matrix by storing, for at least one of the plurality of circulants, the location(s) of the 1's in one and only one vector from said at least one of the plurality of circulants.
23. The method recited in claim 22 , wherein: storing the location(s) of the 1's is performed in the event the number of 1's in the parity check matrix is less than b/(ceil(log 2 (b))) where b is the circulant size.
24. The method recited in claim 22 , wherein storing the location(s) of the 1's includes storing the location(s) in non base 2.