Probabilistic constellation shaping using set-partitioned M-QAM

1. A method for constellation shaping of M-QAM modulation formats in optical transport networks, the method comprising:

receiving binary data to be transmitted as an optical signal;

partitioning symbols of an M-QAM constellation in the complex plane into two non-overlapping subsets of symbols, the two subsets of symbols collectively including all symbols of the M-QAM constellation;

assigning respective probabilities to each symbol in a first one of the two subsets of symbols dependent on a target probability distribution for the first subset of symbols;

mapping at least a portion of the received binary data to the symbols in the first subset, the mapping including generating a respective codeword for each symbol in the first subset; and

in a first symbol period:

providing data representing the respective codewords mapped to the symbols in the first subset to an optical modulator for transmission; and

refraining from providing any data representing codewords mapped to the symbols in the second subset to the optical modulator.

2. The method of claim 1 , wherein the symbols in the first subset are mirror images of the symbols in the second subset with respect to the I axis or the Q axis in the complex plane.

3. The method of claim 1 , wherein:

each of the codewords comprises a same number of bits; and

the respective codewords for neighboring symbols in the first subset differ from each other in only one bit position.

4. The method of claim 3 , wherein the value in the one bit position represents an error correction encoding.

5. The method of claim 1 , further comprising:

determining a respective codeword for each symbol in the second subset; and

in a second symbol period, providing the respective codewords for the symbols in the second subset to the optical modulator for transmission.

6. The method of claim 5 , wherein, within alternating odd and even time slots, the first symbol period represents an odd time slot and the second symbol period represents an even time slot.

7. The method of claim 5 , wherein:

generating a respective codeword for each symbol in the first subset comprises generating the codeword at a matcher element of a transmitter; and

determining a respective codeword for each symbol in the second subset comprises re-mapping a codeword generated for a given symbol in the first subset to a given symbol in the second subset that mirrors the given symbol in the first subset with respect to the I axis or the Q axis in the complex plane.

8. The method of claim 5 , wherein:

generating a respective codeword for each symbol in the first subset comprises generating the codeword at a first matcher element of a transmitter; and

generating a respective codeword for each symbol in the first subset comprises generating the codeword at a second matcher element of the transmitter.

9. The method of claim 1 , further comprising:

receiving, at a coherent receiver in a third symbol period, codewords for the first subset;

receiving, at the coherent receiver in a fourth symbol period, codewords for the second subset;

re-mapping the codewords for the first subset to symbols in the second subset that mirror the symbols in the first subset with respect to the I axis or the Q axis in the complex plane; and

performing one or more of de-mapping, decoding, and de-matching the codewords for the first subset and the second subset to recover the at least a portion of the binary data.

10. The method of claim 1 , further comprising:

receiving, at a coherent receiver in a third symbol period, an optical signal representing codewords for the first subset;

receiving, at the coherent receiver in a fourth symbol period, an optical signal representing codewords for the second subset;

directing the codewords for the first subset to a first processing path and the codewords from the second subset to a second processing path;

performing, by elements of the first processing path and the second processing path, one or more of de-mapping, decoding, and de-matching the codewords for the first subset and the codewords for the second subset, respectively; and

combining outputs of the first processing path and the second processing path to recover the at least a portion of the binary data.

11. An optical transport network for constellation shaping of M-QAM modulation formats, the optical transport network comprising:

an optical transmission path, including an optical transmitter and an optical receiver, the optical transmitter configured to:

receive binary data to be transmitted as an optical signal;

partition symbols of an M-QAM constellation of a given M-QAM modulation format in the complex plane into two non-overlapping subsets of symbols, the two subsets of symbols collectively including all symbols of the M-QAM constellation;

assign, by a matcher element, respective probabilities to each symbol in a first one of the two subsets of symbols dependent on a target probability distribution for the first subset of symbols;

map, by a mapper element, at least a portion of the received binary data to the symbols in the first subset, the mapping including generating a respective codeword for each symbol in the first subset; and

in a first symbol period:

provide data representing the respective codewords mapped to the symbols in the first subset to an optical modulator for transmission over the optical channel; and

refrain from providing any data representing codewords mapped to the symbols in the second subset to the optical modulator.

12. The optical transport network of claim 11 , wherein the symbols in the first subset are mirror images of the symbols in the second subset with respect to the I axis or the Q axis in the complex plane.

13. The optical transport network of claim 11 , wherein:

each of the codewords comprises a same number of bits;

the respective codewords for neighboring symbols in the first subset differ from each other in only one bit position; and

the value in the one bit position represents an error correction encoding.

14. The optical transport network of claim 11 , wherein the optical transmitter is further configured to:

determine a respective codeword for each symbol in the second subset; and

in a second symbol period, provide the respective codewords for the symbols in the second subset to the optical modulator for transmission.

15. The optical transport network of claim 14 , wherein, within alternating odd and even time slots, the first symbol period represents an odd time slot and the second symbol period represents an even time slot.

16. The optical transport network of claim 14 , wherein:

the optical transmitter comprises a matcher element configured to generate the respective codeword for each symbol in the first subset; and

to determine the respective codeword for each symbol in the second subset, the optical transmitter comprises a re-mapping element configured to re-map a codeword generated for a given symbol in the first subset to a given symbol in the second subset that mirrors the given symbol in the first subset with respect to the I axis or the Q axis in the complex plane.

17. The optical transport network of claim 14 , wherein the optical transmitter comprises:

a first matcher element configured to generate the respective codeword for each symbol in the first subset; and

a second matcher element configured to generate the respective codeword for each symbol in the second subset.

18. The optical transport network of claim 11 , wherein the optical receiver is configured to:

receive, in a third symbol period, codewords for the first subset;

receive, in a fourth symbol period, codewords for the second subset;

re-map the codewords for the first subset to symbols in the second subset that mirror the symbols in the first subset with respect to the I axis or the Q axis in the complex plane; and

perform one or more of de-mapping, decoding, and de-matching the codewords for the first subset and the second subset to recover the at least a portion of the binary data.

19. The optical transport network of claim 11 , wherein the optical receiver is configured to:

receive, in a third symbol period, an optical signal representing codewords for the first subset;

receive, in a fourth symbol period, an optical signal representing codewords for the second subset;

direct the codewords for the first subset to a first processing path of the optical receiver and the codewords from the second subset to a second processing path of the optical receiver;

perform, by elements of the first processing path and the second processing path, one or more of de-mapping, decoding, and de-matching the codewords for the first subset and the codewords for the second subset, respectively; and

combine outputs of the first processing path and the second processing path to recover the at least a portion of the binary data.

20. The optical transport network of claim 11 , further comprising a network management system configured to:

send a first command to the optical transmitter to use the given M-QAM modulation format for an optical channel transmitted over the optical transmission path and to activate constellation shaping using set partitioning for the optical channel; and

send a second command to the optical receiver to use the given M-QAM modulation format for the optical channel and to activate constellation shaping using set partitioning for the optical channel.