Construction of irregular LDPC (low density parity check) codes using RS (Reed-Solomon) codes or GRS (generalized Reed-Solomon) code

1. A computer implemented method for constructing a parity check matrix that corresponds to a GRS (Generalized Reed-Solomon)-based irregular LDPC (Low Density Parity Check) code, the method comprising:

choosing a plurality of possible bit degree distributions for an LDPC code block;

selecting a bit degree distribution from among the plurality of possible bit degree distributions, wherein the selected bit degree distribution has a best performance threshold among the plurality of possible bit degree distributions;

decomposing a parity check matrix that corresponds to a GRS-based regular LDPC code into a plurality of partial-matrices based on the selected bit degree distribution, wherein each partial-matrix of the plurality of partial-matrices has a corresponding bit degree and each partial-matrix of the plurality of partial-matrices has a corresponding plurality of permutation matrices; and

replacing at least one permutation matrix within at least one partial-matrix of the plurality of partial-matrices with a zero matrix thereby generating a parity check matrix that corresponds to a GRS-based irregular LDPC code; and

decoding an LDPC coded signal, that has been encoded using the GRS-based irregular LDPC code, using the parity check matrix that corresponds to the GRS-based irregular LDPC code, thereby making a best estimate of at least one information bit encoded within the LDPC coded signal.

2. The method of claim 1 , further comprising:

performing a density evolution method analysis to each bit degree distribution of the plurality of possible bit degree distributions thereby generating a plurality of corresponding density evolution method analysis resultants; and

selecting the bit degree distribution from among the plurality of possible bit degree distributions by comparing the density evolution method analysis resultants.

3. The method of claim 1 , wherein:

the plurality of partial-matrices comprises three partial-matrices.

4. The method of claim 1 , further comprising:

replacing at least one permutation matrix within a first partial-matrix of the three partial-matrices with a zero matrix; and

replacing at least one permutation matrix within a second partial-matrix of the three partial-matrices with a zero matrix.

5. The method of claim 1 , further comprising:

generating at least one additional parity check matrix that corresponds to at least one additional GRS-based irregular LDPC code;

determining a first performance, in terms of BLER (Block Error Rate) as a function of SNR (Signal to Noise Ratio), corresponding to the GRS-based irregular LDPC code as applied to a communication channel;

determining a second performance, in terms of BLER as a function of SNR, corresponding to the at least one additional GRS-based irregular LDPC code as applied to the communication channel; and

selecting the GRS-based irregular LDPC code when the first performance has a lower error floor than the second performance; and

selecting the at least one additional GRS-based irregular LDPC code when the second performance has a lower error floor than the first performance.

6. The method of claim 1 , wherein:

the selected bit degree distribution from among the plurality of possible bit degree distributions comprises three bit degrees.

7. The method of claim 1 , wherein:

each permutation matrix of each corresponding plurality of permutation matrices is an 81×81 matrix.

8. The method of claim 1 , wherein:

the zero matrix is an 81×81 matrix having all 0 valued entries.

9. The method of claim 1 , wherein:

the GRS-based regular LDPC code has a minimum distance; and

the GRS-based irregular LDPC code also has the minimum distance.

10. The method of claim 1 , wherein:

each loop of an LDPC bipartite graph that corresponds to the GRS-based irregular LDPC code is at least a size of 6.

11. The method of claim 1 , further comprising:

constructing a generator matrix that corresponds to the parity check matrix that corresponds to the GRS-based irregular LDPC code; and

encoding at least one information bit using the generator matrix thereby generating at least one LDPC codeword of at least one additional LDPC coded signal.

12. The method of claim 1 , wherein:

the method is performed within a communication device; and

the communication device is implemented within at least one of a satellite communication system, a wireless communication system, a wired communication system, and a fiber-optic communication system.

13. A computer implemented method for selecting a GRS (Generalized Reed-Solomon)-based irregular LDPC (Low Density Parity Check) code, the method comprising:

constructing a plurality of parity check matrices that corresponds to a plurality of GRS-based irregular LDPC codes;

determining a plurality of performances, in terms of BLER (Block Error Rate) as a function of SNR (Signal to Noise Ratio), that corresponds to each GRS-based irregular LDPC code of the plurality of GRS-based irregular LDPC codes as applied to a communication channel; and

selecting a GRS-based irregular LDPC code, having a corresponding parity check matrix, from among the plurality of GRS-based irregular LDPC codes having a lowest error floor as determined from the plurality of performances.

14. The method of claim 13 , further comprising:

considering a complexity of a first decoder to be implemented to decode signals coded according to a first GRS-based irregular LDPC code of the plurality of GRS-based irregular LDPC codes;

considering a complexity of a second decoder to be implemented to decode signals coded according to a second GRS-based irregular LDPC code of the plurality of GRS-based irregular LDPC codes

selecting the first GRS-based irregular LDPC code when the complexity of the first decoder is less than the complexity of the second decoder; and

selecting the second GRS-based irregular LDPC code when the complexity of the second decoder is less than the complexity of the first decoder.

15. The method of claim 13 , wherein:

a parity check matrix of the plurality of parity check matrices comprises a first partial-matrix and a second partial-matrix; and

at least one permutation matrix within the second partial-matrix is replaced with a zero matrix.

16. The method of claim 13 , wherein:

a first parity check matrix of the plurality of parity check matrices is formed from a parity check matrix that corresponds to GRS-based regular LDPC code,

a second parity check matrix of the plurality of parity check matrices is also formed from the parity check matrix that corresponds to GRS-based regular LDPC code,

the parity check matrix that corresponds to GRS-based regular LDPC code comprises a first partial-matrix and a second partial-matrix, and each of the first partial-matrix and the second partial-matrix comprises a corresponding plurality of permutation matrices;

at least one permutation matrix within the first partial-matrix is replaced with a zero matrix thereby generating the first parity check matrix of the plurality of parity check matrices; and

at least one permutation matrix within the second partial-matrix is replaced with a zero matrix thereby generating the second parity check matrix of the plurality of parity check matrices.

17. The method of claim 13 , wherein:

each parity check matrix of the plurality of parity check matrices is formed from a parity check matrix that corresponds to GRS-based regular LDPC code;

the GRS-based regular LDPC code has a minimum distance;

each GRS-based irregular LDPC code of the plurality of GRS-based irregular LDPC codes also has the minimum distance.

18. The method of claim 13 , wherein:

each loop of an LDPC bipartite graph that corresponds to a GRS-based irregular LDPC code of the plurality of GRS-based irregular LDPC codes is at least a size of 6.

19. The method of claim 13 , further comprising:

constructing a generator matrix that corresponds to the parity check matrix that corresponds to the selected GRS-based irregular LDPC code; and

encoding at least one information bit using the generator matrix thereby generating at least one LDPC codeword of at least one additional LDPC coded signal.

20. The method of claim 13 , further comprising:

the method is performed within a communication device; and

the communication device is implemented within at least one of a satellite communication system, a wireless communication system, a wired communication system, and a fiber-optic communication system.

21. A computer implemented method for constructing a parity check matrix that corresponds to a GRS (Generalized Reed-Solomon)-based irregular LDPC (Low Density Parity Check) code, the method comprising:

decomposing a parity check matrix that corresponds to a GRS-based regular LDPC code into a plurality of partial-matrices based on a bit degree distribution, wherein each partial-matrix of the plurality of partial-matrices has a corresponding bit degree and each partial-matrix of the plurality of partial-matrices has a corresponding plurality of permutation matrices; and

replacing at least one permutation matrix within at least one partial-matrix of the plurality of partial-matrices with a zero matrix thereby generating a parity check matrix that corresponds to a GRS-based irregular LDPC code; and

decoding an LDPC coded signal, that has been encoded using the GRS- based irregular LDPC code, using the parity check matrix that corresponds to the GRS-based irregular LDPC code, thereby making a best estimate of at least one information bit encoded within the LDPC coded signal.

22. The method of claim 21 , further comprising:

choosing a plurality of possible bit degree distributions for an LDPC code block;

selecting the bit degree distribution from among the plurality of possible bit degree distributions, wherein the selected bit degree distribution has a best performance threshold among the plurality of possible bit degree distributions; and wherein:

the GRS-based regular LDPC code has a minimum distance; and

the GRS-based irregular LDPC code also has the minimum distance.

23. The method of claim 21 , wherein:

each loop of an LDPC bipartite graph that corresponds to the GRS-based irregular LDPC code is at least a size of 6.

24. The method of claim 21 , further comprising:

generating at least one additional parity check matrix that corresponds to at least one additional GRS-based irregular LDPC code;

determining a first performance, in terms of BLER (Block Error Rate) as a function of SNR (Signal to Noise Ratio), corresponding to the GRS-based irregular LDPC code as applied to a communication channel;

determining a second performance, in terms of BLER as a function of SNR, corresponding to the at least one additional GRS-based irregular LDPC code as applied to the communication channel; and

selecting the GRS-based irregular LDPC code when the first performance has a lower error floor than the second performance; and

selecting the at least one additional GRS-based irregular LDPC code when the second performance has a lower error floor than the first performance.

25. The method of claim 21 , further comprising:

constructing a generator matrix that corresponds to the parity check matrix that corresponds to the GRS-based irregular LDPC code; and

encoding at least one information bit using the generator matrix thereby generating at least one LDPC codeword of at least one additional LDPC coded signal.

26. The method of claim 21 , wherein:

the method is performed within a communication device; and

the communication device is implemented within at least one of a satellite communication system, a wireless communcation system, a wired communication system, and a fiber-optic communication system.