Probabilistic shaping on eight-dimensional super-symbols

1. A method for probabilistic shaping of an eight-dimensional super-symbol in optical transport networks, the method comprising:

receiving binary data to be transmitted as an optical signal;

mapping at least a portion of the binary data to symbols of a M-QAM constellation;

generating a first four-dimensional symbol of the M-QAM constellation for a first symbol period, including applying probabilistic shaping to the first four-dimensional symbol;

generating a second four-dimensional symbol of the M-QAM constellation for a second symbol period, the second symbol period consecutive to the first symbol period, wherein the first and the second four-dimensional symbols have i) an equal symbol energy and ii) a one-to-one relationship;

time interleaving the first symbol period and the second symbol period to generate an eight-dimensional super-symbol; and

transmitting the eight-dimension super-symbol over the optical transport network.

2. The method of claim 1 , wherein generating the second four-dimensional symbol comprises:

identifying, via a look-up table (LUT), multiple four-dimensional symbols of the M-QAM constellation for the second symbol period, wherein each combination of the first four-dimensional symbol and each of identified multiple four-dimensional symbols have i) an equal symbol energy and iii) a one-to-one relationship; and

identifying the second four-dimensional symbol from the multiple four-dimensional symbols based on a maximization of Euclidean distance of the eight-dimensional super-symbol.

3. The method of claim 2 , wherein identifying the multiple four-dimensional symbols of the M-QAM constellation for the second symbol period further comprises:

concatenating binary bits from the first four-dimensional symbol;

converting the concatenation to a decimal super-symbol index;

identifying a symbol index that corresponds to the decimal super-symbol index;

converting symbols of the symbol index that correspond to the second four-dimensional symbol to binary bits; and

interleaving the binary bits of the first and the second four-dimensional symbols.

4. The method of claim 1 , wherein the second four-dimensional symbol included probabilistic shaping based on i) the one-to-one relationship between the first and the second four-dimensional symbol and ii) the probabilistic shaping of the first four-dimensional symbol.

5. The method of claim 1 , wherein the probabilistic shaping is applied only to the first four-dimensional symbol.

6. The method of claim 1 , further comprising applying a log-likelihood ratio to the eight-dimensional super-symbol.

7. A system for probabilistic shaping of an eight-dimension super-symbol in optical networks, the system comprising a processor having access to memory media storing instructions executable by the processor to:

receive binary data to be transmitted as an optical signal;

map at least a portion of the binary data to symbols of a M-QAM constellation;

generate a first four-dimensional symbol of the M-QAM constellation for a first symbol period, including applying probabilistic shaping to the first four-dimensional symbol;

generate a second four-dimensional symbol of the M-QAM constellation for a second symbol period, the second symbol period consecutive to the first symbol period, wherein the first and the second four-dimensional symbols have i) an equal symbol energy and ii) a one-to-one relationship;

time interleave the first symbol period and the second symbol period to generate an eight-dimensional super-symbol; and

transmitting the eight-dimension super-symbol over the optical transport network.

8. The system of claim 7 , wherein generating the second four-dimensional symbol comprises:

identifying, via a look-up table (LUT), multiple four-dimensional symbols of the M-QAM constellation for the second symbol period, wherein each combination of the first four-dimensional symbol and each of identified multiple four-dimensional symbols have i) an equal symbol energy and iii) a one-to-one relationship; and

identifying the second four-dimensional symbol from the multiple four-dimensional symbols based on a maximization of Euclidean distance of the eight-dimensional super-symbol.

9. The system of claim 8 , wherein identifying the multiple four-dimensional symbols of the M-QAM constellation for the second symbol period further comprises:

concatenating binary bits from the first four-dimensional symbol;

converting the concatenation to a decimal super-symbol index;

identifying a symbol index that corresponds to the decimal super-symbol index;

converting symbols of the symbol index that correspond to the second four-dimensional symbol to binary bits; and

interleaving the binary bits of the first and the second four-dimensional symbols.

10. The system of claim 7 , wherein probabilistic shaping is applied to the second four-dimensional symbol based on i) the one-to-one relationship between the first and the second four-dimensional symbol and ii) the probabilistic shaping of the first four-dimensional symbol.

11. The system of claim 7 , wherein the probabilistic shaping is applied only to the first four-dimensional symbol.

12. The system of claim 7 , the instructions further comprising applying a log-likelihood ratio to the eight-dimensional super-symbol.