Optimum signal constellation design and mapping for few-mode fiber based LDPC-coded CO-OFDM

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;

employing one or more signal constellations obtained using an optimum signal constellation design (OSCD);

determining an optimum mapping rule by maximizing and comparing one or more cost functions of each of a plurality of mapping rules to determine a mapping that maximizes a particular cost function of each of the plurality of mapping rules;

combining one or more LDPC-coded OSCD signal constellation data streams with coherent optical-orthogonal frequency division multiplexing (CO-OFDM) coded modulation to achieve channel capacity; and

mode-multiplexing and transmitting one or more independent LDPC-coded optimum signal constellation design (OSCD) 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;

performing channel estimation based on two-dimensional (2D) orthogonal frequency division multiplexing (OFDM);

calculating 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 OSCD-based constellations are combined with LDPC codes of high girth.

4. 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).

5. The method as recited in claim 2 , wherein a pre-determined number of pre-amble OFDM symbols are employed during the channel estimation to estimate a channel, to perform compensation of mode-coupling and to perform chromatic dispersion.

6. 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.

7. The method as recited in claim 1 , further comprising employing a linear minimum mean square error (MMSE) approach to compensate for distortions introduced in a channel.

8. 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 using an optimum signal constellation design (OSCD);

an optimum mapping rule determination module configured to determine an optimum mapping rule by maximizing and comparing one or more cost functions of each of a plurality of mapping rules to determine a mapping that maximizes a particular cost function of each of the plurality of mapping rules;

a combination module configured to combine LDPC-coded OSCD signal constellation data streams with coherent optical-orthogonal frequency division multiplexing (CO-OFDM) coded modulation to achieve channel capacity; and

one or more mode-multiplexers and transmitters configured to mode-multiplex and transmit one or more independent LDPC-coded optimum signal constellation design (OSCD) data streams over a transmission medium.

9. The system as recited in claim 8 , further comprising:

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

one or more channel estimation modules configured to perform channel estimation based on two-dimensional (2D) orthogonal frequency division multiplexing (OFDM);

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

one or more LDPC decoders configured to decode LDPC coded 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.

10. The system as recited in claim 8 , wherein the OSCD-based constellations are combined with LDPC codes of high girth.

11. The system as recited in claim 8 , 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).

12. The system as recited in claim 9 , wherein a pre-determined number of pre-amble OFDM symbols are employed during the channel estimation to estimate a channel, to perform compensation of mode-coupling and to perform chromatic dispersion compensation.

13. The system as recited in claim 8 , 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.

14. The system as recited in claim 8 , further comprising employing a linear minimum mean square error (MMSE) approach to compensate for distortions introduced in a channel.