Methods and apparatus for optical communications via pulse amplitude modulation (PAM) in dense wavelength-division multiplexing (DWDM) systems

1. A method, comprising:

modulating a digital signal via pulse amplitude modulation (PAM) to generate a modulated digital signal;

applying, to the modulated digital signal, a forward correction code (FEC) including a low-density parity-check (LDPC) code to produce a coded digital signal;

applying Nyquist shaping to the coded digital signal to generate a filtered digital signal;

converting the filtered digital signal into an analog signal; and

transmitting the analog signal in an optical communication channel via a dense wavelength division multiplexing (DWDM) scheme.

2. The method of claim 1 , wherein the PAM includes an N-ary PAM, where N is an integer equal to or greater than 4.

3. The method of claim 1 , wherein applying the Nyquist shaping to the coded digital signal includes transmitting the coded digital signal through a square-root raised cosine filter.

4. The method of claim 1 , wherein applying the Nyquist shaping to the coded digital signal includes applying the Nyquist shaping at a roll-off factor (ROF) substantially equal to or less than 0.5.

5. The method of claim 1 , further comprising:

before applying the Nyquist shaping, applying to the digital signal with probabilistic shaping that includes at least one of a Maxwell-Boltzmann distribution or an exponential distribution.

6. The method of claim 1 , further comprising:

measuring at least one attribute of the optical communication channel during transmission of the analog signal, the at least one attribute of the optical communication channel including an optical signal to noise ratio (OSNR) or a chromatic dispersion level; and

changing an ROF of the Nyquist shaping applied to the coded digital signal based on the at least one attribute of the optical communication channel.

7. The method of claim 1 , further comprising:

transmitting the digital signal through a distribution matcher (DM) configured to apply probabilistic shaping to the digital signal;

measuring at least one attribute of the optical communication channel during transmission of the analog signal, the at least one attribute of the optical communication channel including an optical signal to noise ratio (OSNR) or a chromatic dispersion level; and

changing a number of bits per symbol in the digital signal using the DM based on the at least one attribute of the optical communication channel.

8. The method of claim 1 , further comprising:

transmitting the digital signal through a distribution matcher (DM) configured to apply probabilistic shaping to the digital signal;

measuring at least one attribute of the optical communication channel during transmission of the analog signal, the at least one attribute of the optical communication channel including an optical signal to noise ratio (OSNR) or a chromatic dispersion level; and

changing at least one of a number of bits per symbol in the digital signal using the DM, a code rate of the LDPC code, or an ROF of the Nyquist shaping based on the at least one attribute of the optical communication channel.

9. An apparatus, comprising:

a modulator configured to encode binary data into a digital signal via pulse amplitude modulation (PAM);

a distribution matcher (DM) operatively coupled to the modulator, the DM configured to apply probabilistic shaping to the digital signal;

a digital filter operatively coupled to the DM and configured to apply Nyquist shaping to the digital signal after the DM applies probabilistic shaping to the digital signal; and

a digital to analog converter (DAC) operatively coupled to the modulator and the digital filter, the DAC configured to convert the digital signal to an analog signal and send the analog signal into an optical communication channel using a dense wavelength division multiplexing (DWDM) scheme.

10. The apparatus of claim 9 , wherein the modulator is configured to encode the binary data using an N-ary PAM, where N is an integer equal to or greater than 4.

11. The apparatus of claim 9 , wherein the digital filter includes a square-root raised cosine filter.

12. The apparatus of claim 9 , wherein the filter is configured to apply the Nyquist shaping at a roll-off factor (ROF) substantially equal to or less than 0.5.

13. The apparatus of claim 9 , wherein the filter has an adjustable ROF.

14. The apparatus of claim 9 , wherein:

the probabilistic shaping including at least one of a Maxwell-Boltzmann distribution or an exponential distribution.

15. The apparatus of claim 9 , further comprising:

an encoder operatively coupled to the modulator and configured to apply a density parity-check (LDPC) code to the digital signal before the digital filter.

16. The apparatus of claim 9 , further comprising:

a controller operatively coupled to the digital filter, the controller configured to receive information representing an optical signal to noise ratio (OSNR) or a chromatic dispersion level of the optical communication channel measured during transmission of the analog signal, the controller further configured to cause the digital filter to change an ROF of the Nyquist shaping based on the information.

17. The apparatus of claim 9 , further comprising:

a controller operatively coupled to the DM, the controller configured to receive information representing an OSNR or a chromatic dispersion level of the optical communication channel measured during transmission of the analog signal, the controller further configured to cause the DM to change a number of bits per symbol in the digital signal based on the information.

18. The apparatus of claim 9 , further comprising:

an encoder operatively coupled to the modulator and the digital filter, the encoder configured to apply a density parity-check (LDPC) code to the digital signal before the digital filter and after the DM; and

a controller operatively coupled to the DM and the digital filter, the controller configured to receive information representing an OSNR or a chromatic dispersion level of the optical communication channel measured during transmission of the analog signal, the controller further configured to: cause the DM to change a number of bits per symbol in the digital signal, cause the digital filter to change an ROF of the Nyquist shaping, or cause the encoder to change a code rate of the LDPC code, based on the information.

19. A method, comprising:

modulating a digital signal via pulse amplitude modulation (PAM);

applying Nyquist shaping the digital signal to generate a filtered digital signal;

converting the filtered digital signal into an analog signal;

transmitting the analog signal in an optical communication channel via a dense wavelength division multiplexing (DWDM) scheme;

measuring at least one attribute of the optical communication channel during transmitting of the analog signal, the at least one attribute of the optical communication channel including an optical signal to noise ratio (OSNR) or a chromatic dispersion level; and

changing a roll-off factor (ROF) of the Nyquist shaping applied to the digital signal based on the at least one attribute of the optical communication channel.

20. The method of claim 19 , further comprising:

before applying the Nyquist shaping, applying to the digital signal with probabilistic shaping that includes at least one of a Maxwell-Boltzmann distribution or an exponential distribution.