Modified orthogonal polynomials based hybrid coded-modulation for multi-Tb/second optical transport

1. A method for transmitting data, comprising:

encoding one or more streams of input data using one or more Low Density Parity Check (LDPC) encoders;

generating one or more signal constellations;

modulating one or more signals using hybrid multidimensional coded modulation;

applying modified orthogonal polynomials as electrical basis functions and spatial Modes as optical basis functions; and

mode-multiplexing and transmitting one or more LDPC-coded data streams over a transmission medium.

2. The method as recited in claim 1 , further comprising:

receiving and mode-demultiplexing the one or more data streams;

calculating optimum signal constellation design OSCD symbol reliabilities using one or more a posteriori probability (APP) demappers;

LDPC decoding data using one or more LDPC decoders; and

iterating extrinsic information between LDPC decoders and APP demappers until convergence or a predetermined number of iterations has been reached.

3. The method as recited in claim 1 , wherein the hybrid multidimensional coded modulation employs both electrical and optical degrees of freedom.

4. The method as recited in claim 1 , wherein the modified orthogonal polynomials are employed in both in-phase and quadrature channels in combination with two orthogonal polarization states and N orthogonal spatial modes.

5. The method as recited in claim 1 , wherein the transmission medium is one or more of single-mode fiber (SMF), few-mode fiber (FMF), few-core fiber (FCF), and few-mode-few-core fiber (FMFCF).

6. The method as recited in claim 1 , wherein the one or more signal constellations are decomposed into two sub-constellations, corresponding to in-phase and quadrature channels, for each of the one or more signal constellations.

7. The method as recited in claim 6 , wherein corresponding points of each of the one or more signal sub-constellations do not overlap in constellation space.

8. The method as recited in claim 1 , wherein the one or more signal constellations include one or more signal constellations with constellation sizes that are not a power of two to improve the tolerance to in-phase/quadrature (IQ) imbalance and the tolerance to polarization crosstalk from imperfectly compensated polarization-mode dispersion (PMD).

9. The method as recited in claim 1 , wherein the one or more signal constellations are generated using optimum signal constellation design (OSCD).

10. The method as recited in claim 1 , wherein the one or more signal constellations are generated using one of Cartesian products of existing 1-D and 2-D constellations or a sphere packing method.

11. A system for transmitting data, comprising:

one or more Low Density Parity Check (LDPC) encoders configured to encode one or more streams of input data;

a signal constellation generation module configured to generate one or more signal constellations;

one or more modulators configured to generate one or more signals using hybrid multidimensional coded modulation;

a modified orthogonal polynomial generation module configured to generate modified orthogonal polynomials for use as electrical basis functions; and

one or more mode-multiplexers and transmitters configured to mode-multiplex and transmit one or more LDPC-coded data streams over a transmission medium.

12. The system as recited in claim 11 , further comprising:

one or more receivers and mode-demultiplexers configured to receive and mode-demultiplex the one or more data streams;

one or more a posteriori probability (APP) demappers configured to calculate OSCD symbol reliabilities;

one or more LDPC decoders configured to LDPC decode data; and

a feedback loop configured to iterate extrinsic information between LDPC decoders and APP demappers until convergence or a predetermined number of iterations has been reached.

13. The system as recited in claim 11 , wherein the hybrid multidimensional coded modulation employs both electrical and optical degrees of freedom.

14. The system as recited in claim 11 , wherein the modified orthogonal polynomials are employed in both in-phase and quadrature channels in combination with two orthogonal polarization states and N orthogonal spatial modes.

15. The system as recited in claim 11 , wherein the transmission medium is one or more of single-mode fiber (SMF), few-mode fiber (FMF), few-core fiber (FCF), and few-mode-few-core fiber (FMFCF).

16. The system as recited in claim 11 , wherein the one or more signal constellations are decomposed into two sub-constellations, corresponding to in-phase and quadrature channels, for each of the one or more signal constellations.

17. The system as recited in claim 16 , wherein corresponding points of each of the one or more signal sub-constellations do not overlap.

18. The system as recited in claim 11 , wherein the one or more signal constellations employed include one or more signal constellations with constellation sizes that are not a power of two to improve the tolerance to in-phase/quadrature (IQ) imbalance and the tolerance to polarization crosstalk from imperfectly compensated polarization-mode dispersion (PMD).

19. The system as recited in claim 11 , wherein the one or more signal constellations are generated using optimum signal constellation design (OSCD).

20. The system as recited in claim 11 , wherein the one or more signal constellations are generated using one of Cartesian products of existing 1-D and 2-D constellations and a sphere packing method.