System and method for structured LDPC code family
A low density parity check (LDPC) family of codes is constructed by: determining a protograph for a mother code for the LDPC family of codes. The protograph is lifted by a lifting factor to design code specific protograph for a code. The method also includes constructing a base matrix for the code. The base matrix is constructed by replacing each zero in the code specific protograph with a ‘−1’; and replacing each one in the code specific protograph with a corresponding value from the mother matrix. The LDPC code includes a codeword size of at least 1344, a plurality of information bits, and a plurality of parity bits. The LDPC code is based on a mother code of code length 672.
1. A method for constructing a low density parity check (LDPC) family of codes, the method comprising:
determining, by a Context-based operation Reconfigurable Instruction Set Processor (CRISP), a protograph for a mother code for the LDPC family of codes;
lifting the protograph by a lifting factor to design a code specific protograph for a code; and
constructing a base matrix for the code, the base matrix constructed by:
replacing each zero in the code specific protograph with a ‘−1’; and
replacing each one in the code specific protograph with a corresponding value from the mother matrix.
2. The method as set forth in claim 1 , wherein the mother code comprises a code length of 672.
3. The method as set forth in claim 1 , further comprising selecting circulant blocks, wherein the selecting comprises:
lifting the protograph by a lifting factor of one of 2, 3 and 4.
4. The method as set forth in claim 1 , further comprising deriving a second code from the mother code, wherein the second code comprises a second code rate that is lower than the highest code rate.
5. The method as set forth in claim 4 , wherein the second code comprises at least one of a rate-⅝ code; a rate-½ code and a rate-¾ code.
6. The method as set forth in claim 4 , wherein the second code comprises a length of at least one of 1344, 2016 and 2688.
7. The method as set forth in claim 4 , wherein the constructed codes comprise at least one of:
a same structures as the mother code;
a 4-layers decodable;
a same row and column degree distribution as the mother code; and
can be decoded by a same decoder as the mother code.
8. A Context-based operation Reconfigurable Instruction Set Processor (CRISP) decoder configured perform an error correction using a low density parity check (LDPC) code, the LDPC code comprising:
a codeword size of at least 1344;
a plurality of information bits; and
a plurality of parity bits, wherein the LDPC code is based on a mother code of code length 672, wherein the LDPC code is constructed by:
determining a protograph for a mother code for the LDPC family of codes;
lifting the protograph by a lifting factor to design a code specific protograph for a code; and
constructing a base matrix for the code, the base matrix constructed by:
replacing each zero in the code specific protograph with a ‘−1’; and
replacing each one in the code specific protograph with a corresponding value from the mother matrix.
9. The decoder as set forth in claim 8 , further comprising at least one of:
a same structures as the mother code;
a 4-layers decodable;
a same row and column degree distribution as the mother code; and
can be decoded by a same decoder as the mother code.
10. The decoder as set forth in claim 8 , wherein the construction of the LDPC code further comprises:
selecting circulant blocks, wherein the selecting comprises:
lifting the protograph by a lifting factor of one of 2, 3 and 4.
11. The decoder as set forth in claim 8 , further configured to derive a second code from the mother code, wherein the second code comprises a second code rate that is lower than the highest code rate.
12. The decoder as set forth in claim 11 , wherein the second code comprises at least one of a rate-⅝ code; a rate-½ code and a rate-¾ code.
13. The decoder as set forth in claim 11 , wherein the second code comprises a length of at least one of 1344, 2016 and 2688.
14. A method comprising:
performing, by a Context-based operation Reconfigurable Instruction Set Processor (CRISP), an error correction using a low density parity check (LDPC) code from a LDPC family of codes, the LDPC code comprising:
a codeword size of at least 1344;
a plurality of information bits; and
a plurality of parity bits, wherein the LDPC code is based on a mother code, wherein the LDPC code is constructed by:
determining a protograph for a mother code for the LDPC family of codes;
lifting the protograph by a lifting factor to design a code specific protograph for a code; and
constructing a base matrix for the code, the base matrix constructed by:
replacing each zero in the code specific protograph with a ‘−1’; and
replacing each one in the code specific protograph with a corresponding value from the mother matrix.
15. The method as set forth in claim 14 , wherein the mother code comprises a code length of 672.
16. The method as set forth in claim 14 , further comprising selecting circulant blocks, wherein the selecting comprises:
lifting the protograph by a lifting factor of one of 2, 3 and 4.
17. The method as set forth in claim 14 , further comprising deriving a second code from the mother code, wherein the second code comprises a second code rate that is lower than the highest code rate.
18. The method as set forth in claim 17 , wherein the second code comprises at least one of a rate-⅝ code; a rate-½ code and a rate-¾ code.
19. The method as set forth in claim 17 , wherein the second code comprises a length of at least one of 1344, 2016 and 2688.
20. The method as set forth in claim 17 , wherein the constructed codes comprise at least one of:
a same structures as the mother code;
a 4-layers decodable;
a same row and column degree distribution as the mother code; and
can be decoded by a same decoder as the mother code.