GLDPC encoding with Reed-Muller component codes for optical communications

1. A method of encoding for optical transmission of information comprising the steps of:

encoding information with a generalized low-density parity-check (GLDPC) code for providing coding gains; and

constructing the GLDPC code with a Reed-Muller (RM)code as a component code with modular structure of generator matrix, the component code being decodable using a maximum posterior probability (MAP) decoding; and

decomposing a parity-check matrix of RM component code into a plurality of single-parity-check codes, repetition codes and first order RM codes.

2. The method of claim 1 , wherein the GLDPC code comprises a codeword length of 4096.

3. The method of claim 1 , wherein the GLDPC code comprises an information word length of 3201.

4. The method of claim 1 , wherein the GLDPC code comprises a code rate of 0.78.

5. The method of claim 1 , wherein the GLDPC code comprises a lower-bound on minimum distance of greater than or equal to 16.

6. The method of claim 1 , wherein the RM code comprises an order of 4.

7. The method of claim 1 , wherein the RM code comprises an r parameter of 6.

8. The method of claim 1 , wherein the GLDPC code comprises a codeword length of 4096, an information word length of substantially 3201, a lower-bound on minimum distance of greater than or equal to 16, a code rate of 0.78 and the RM component code comprises an order of 4 and an r parameter of 6.

9. A method of encoding for optical transmission of information comprising:

encoding information with generalized low-density parity-check (GLDPC) codes and component Reed-Muller (RM) code for providing large coding gains;

constructing the GLDPC codes with RM component codes;

transmitting the codes over an optical communication system;

decoding RM component codes by low-complexity maximum a posteriori probability (MAP) decoding algorithm;

decomposing a parity-check matrix of RM component code into a plurality of single-parity check codes, repetition codes and first order RM codes;

decoding the first order RM codes, obtained from decomposition, by fast Walsh-Hadamard transform; and

globally decoding the codes based on a sum-product technique.

10. The method of claim 9 , wherein the GLDPC codeword length is a multiple of component RM codeword length.

11. The method of claim 9 , wherein the code parity-check matrix has a row-weight that is the same as a component RM code codeword length.

12. The method of claim 9 , wherein code parity-check matrix rows are replaced with a parity-check matrix of component RM code in accordance with nonzero locations.

13. The method of claim 9 , wherein the parity-check matrix of the component RM code is obtained as a generator matrix of a corresponding dual RM code and wherein the RM generator and parity-check matrix have highly regular, modular structure.

14. The method of claim 9 , wherein component RM decoder exploits regular, modular structure of parity-check matrix of RM code by splitting the RM code into single-parity check codes, repetition codes and first order RM codes.

15. The method of claim 9 , wherein component RM decoder performs MAP decoding of decomposed RM code and wherein the MAP decoding of first order RM codes is based on fast Walsh-Hadamard transform.

16. The method of claim 9 , comprising component RM decoders that pass the reliability data to a global LDPC code.

17. The method of claim 9 , wherein a global LDPC code is a large-girth code.

18. The method of claim 9 , comprising a global LDPC decoder based on a sum-product technique, with sum-product updating rule based on MAP decoding of component RM codes.

19. The method of claim 9 , wherein extrinsic reliabilities are iterated between a global LDPC decoder and component RM codes until a GLDPC codeword is generated or until a pre-determined number of iterations has been reached.