Nonlinear tolerant super-Gaussian distribution for probabilistic shaping modulation
Consistent with the present disclosure, codewords indicative of a super Gaussian distribution may be encoded and decoded using the encoders and decoders disclosed herein. Based on such codewords, symbols may be transmitted in accordance or in conformance with a super Gaussian distribution to tailor the SE of an optical signal or subcarrier for a given link having non-linear degradations and shaping gain. Such tailed SE may not be achievable with a Gaussian symbol transmission probability distribution.
1. An apparatus, comprising:
a transmitter, the transmitter including:
a laser;
an encoder block that outputs a sequence of symbols, each symbol in the sequence of symbols corresponding to one of a plurality of constellation points in an in-phase-quadrature (IQ) plane having I and Q axes, a distribution of the plurality of constellation points conforming to a super gaussian distribution;
a driver circuit that supplies drive signals based on the sequence of symbols;
a modulator, the modulator receiving light output from the laser and the drive signals, the modulator outputting modulated optical signals based on the drive signals; and
a combiner that receives the modulated optical signals and combines the optical signals to provide a polarization multiplexed optical signal having a first polarization component and a second polarization component.
2. An apparatus in accordance with claim 1 , wherein the super gaussian distribution, p(x), satisfies:
p ( x )= e −Kx 2
where x is an amplitude associated with each of the plurality of constellation points taken along one of the I and Q axes, K is a constant, and P is a real number other than 2.
3. An apparatus in accordance with claim 2 , wherein P is greater than 2 and less than or equal to 6.
4. An apparatus in accordance with claim 1 , wherein the modulated optical signals includes a plurality of Nyquist subcarriers.
5. An apparatus in accordance with claim 4 , wherein one of the plurality of Nyquist subcarriers carries the sequence of symbols.
6. An apparatus in accordance with claim 5 , wherein said one of the plurality of Nyquist subcarriers is a first one of the Nyquist subcarriers, and the sequence of symbols is a first sequence of symbols, a second one of the plurality of Nyquist subcarriers carrying a second sequence of symbols.
7. An apparatus in accordance with claim 6 , wherein the super gaussian distribution is a first super gaussian distribution and the plurality of constellation points is a plurality of first constellation points, the encoder block outputting the second sequence of symbols, each of which corresponding to a respective one of a plurality of second constellation points in the IQ plane, a distribution of the plurality of second constellation points conforms to a second super gaussian distribution.
8. An apparatus in accordance with claim 7 , wherein the first super gaussian distribution, p1(x1), satisfies:
p 1( x 1)= e −K1x1 P1
where x1 is an amplitude associated with each of the plurality of first constellation points taken along one of the I and Q axes, K1 is a first constant, and P1 is a real number other than 2,
wherein the second super gaussian distribution, p2(x2), satisfies:
p 2( x 2)= e −K2x2 P2
where x2 is an amplitude associated with each of the plurality of second constellation points taken along one of the I and Q axes, K2 is a second constant, and P2 is a real number other than 2.
9. An apparatus in accordance with claim 8 , wherein P1 is greater than 2 and less than or equal to 6, and P2 is greater than 2 and less than or equal to 6, P1 being different than P2.
10. An apparatus in accordance with claim 1 , wherein the transmitter is a first transmitter, the laser is a first laser, the driver circuit is a first driver circuit, the drive signals are first drive signals, the modulator is a first modulator, the modulated optical signal is a first modulated optical signal, the sequence of symbols is a first sequence of symbols, and the super gaussian distribution is a first upper gaussian distribution, the apparatus further including:
a second transmitter, the second transmitter including:
a second laser;
a second driver circuit;
a second modulator, the second modulator receiving light output from the second laser and second drive signals from the second driver circuit, the second drive signals being based on a second sequence of symbols output from the encoder circuit, the second sequence of symbols conforms to a second super gaussian distribution, each of the symbols of the second sequence is represented by a corresponding one of a plurality of second constellation points in the inphase-quadrature (IQ) plane.
11. An apparatus in accordance with claim 10 , wherein the first super gaussian distribution, p1(x1), satisfies:
p 1( x 1)= e −K1x1 P1
where x1 is an amplitude associated with each of the plurality of first constellation points taken along one of the I and Q axes, K1 is a first constant, and P1 is a real number other than 2,
wherein the second super gaussian distribution, p2(x2), satisfies:
p 2( x 2)= e −K2x2 P2
where x2 is an amplitude associated with each of the plurality of second constellation points taken along one of the I and Q axes, K2 is a second constant, and P2 is a real number other than 2.
12. An apparatus in accordance with claim 2 , wherein P1 is greater than 2 and less than or equal to 6 and P2 is greater than 2 and less than or equal to 6, P1 is different than P2.
13. A transmitter comprising:
a laser;
an encoder block that outputs a sequence of symbols, each symbol in the sequence of symbols corresponding to one of a plurality of constellation points in an in-phase-quadrature (IQ) plane having I and Q axes, a distribution of the plurality of constellation points conforming to a super gaussian distribution;
a driver circuit that supplies drive signals based on the sequence of symbols;
a modulator, the modulator receiving light output from the laser and the drive signals, the modulator outputting a modulated optical based on the drive signals.
14. An transmitter in accordance with claim 13 , wherein the super gaussian distribution, p(x), satisfies:
p ( x )= e −Kx 2
where x is an amplitude associated with each of the plurality of constellation points taken along one of the I and Q axes, K is a constant, and P is a real number other than 2.
15. A transmitter in accordance with claim 14 , wherein P is greater than 2 and less than or equal to 6.
16. A transmitter in accordance with claim 13 , wherein the modulated optical signal includes a plurality of Nyquist subcarriers.
17. A transmitter in accordance with claim 16 , wherein one of the plurality of Nyquist subcarriers carries the sequence of symbols.
18. A transmitter in accordance with claim 17 , wherein said one of the plurality of Nyquist subcarriers is a first one of the Nyquist subcarriers, and the sequence of symbols is a first sequence of symbols, a second one of the plurality of Nyquist subcarriers carrying a second sequence of symbols.
19. A transmitter in accordance with claim 18 , wherein the super gaussian distribution is a first super gaussian distribution and the plurality of constellation points is a plurality of first constellation points, the encoder block outputting the second sequence of symbols, each of which corresponding to a respective one of a plurality of second constellation points in the IQ plane, a distribution of the plurality of second constellation points conforms to a second super gaussian distribution.
20. An transmitter in accordance with claim 19 , wherein the first super gaussian distribution, p1(x1), satisfies:
p 1( x 1)= e −K1x1 P1
where x1 is an amplitude associated with each of the plurality of first constellation points taken along one of the I and Q axes, K1 is a first constant, and P1 is a real number other than 2,
wherein the second super gaussian distribution, p2(x2), satisfies:
p 2( x 2)= e −K2x2 P2
where x2 is an amplitude associated with each of the plurality of second constellation points taken along one of the I and Q axes, K2 is a second constant, and P2 is a real number other than 2.
21. A transmitter in accordance with claim 20 , wherein P1 is greater than 2 and less than or equal to 6, and P2 is greater than 2 and less than or equal to 6, P1 being different than P2.
22. An transmitter in accordance with claim 13 , wherein the transmitter is a first transmitter, the laser is a first laser, the driver circuit is a first driver circuit, the drive signals are first drive signals, the modulator is a first modulator, the modulated optical signal is a first modulated optical signal, the sequence of symbols is a first sequence of symbols, and the super gaussian distribution is a first upper gaussian distribution, the apparatus further including:
a second transmitter, the second transmitter including:
a second laser;
a second driver circuit;
a second modulator, the second modulator receiving light output from the second laser and second drive signals from the second driver circuit, the second drive signals being based on a second sequence of symbols output from the encoder circuit, the second sequence of symbols conforms to a second super gaussian distribution, each of the symbols of the second sequence is represented by a corresponding one of a plurality of second constellation points in the inphase-quadrature (IQ) plane.
23. An transmitter in accordance with claim 22 , wherein the first super gaussian distribution, p1(x1), satisfies:
p 1( x 1)= e −K1x1 P1
where x1 is an amplitude associated with each of the plurality of first constellation points taken along one of the I and Q axes, K1 is a first constant, and P1 is a real number other than 2,
wherein the second super gaussian distribution, p2(x2), satisfies:
p 2( x 2)= e −K2x2 P2
where x2 is an amplitude associated with each of the plurality of second constellation points taken along one of the I and Q axes, K2 is a second constant, and P2 is a real number other than 2.
24. A transmitter in accordance with claim 23 , wherein P1 is greater than 2 and less than or equal to 6 and P2 is greater than 2 and less than or equal to 6, P1 is different than P2.