Probabilistic Constellation Shaping of Multi-Dimensional Symbols for Improved Tolerance to Nonlinear Impairments

An optical transmitter device comprising:

• a digital signal processor (DSP) comprising digital hardware, the DSP operative
• to generate shaped bits from a first set of information bits;
• to apply a systematic forward error correction (FEC) scheme to encode the shaped bits and a second set of information bits, where the first set of information bits and the second set of information bits are disjoint sets;
• to select a collection based on a value of at least one of the shaped bits, where a Cartesian product of a constellation has been partitioned into disjoint collections;
• to use some of the shaped bits to select symbols from the selected collection;
• and
• to map symbols including the selected symbols to physical dimensions,
• wherein each unshaped bit is either one of the second set of information bits or one of multiple parity bits resulting from the FEC encoding.

A method comprising:

• generating shaped bits from a first set of information bits;
• applying a systematic forward error correction (FEC) scheme to encode the shaped bits and a second set of information bits, where the first set of information bits and the second set of information bits are disjoint sets;
• and
• for multiple pairs of groups, each pair consisting of a first group and a second group, each first group consisting of a first unshaped bit and a first shaped bit and each second group consisting of a second unshaped bit and second shaped bit
• mapping the first unshaped bit and the first shaped bit to a first quadrature phase shift keying (QPSK) symbol according to a labeling scheme;
• mapping the second unshaped bit and the second one of the shaped bits to a second QPSK symbol according to the labeling scheme;
• and
• mapping the first QPSK symbol and the second QPSK symbol to four physical dimensions,
• wherein each unshaped bit is either one of the second set of information bits or one of multiple parity bits resulting from the FEC encoding;
• and
• wherein either the least significant bit in all groups is always one of the shaped bits or the most significant bit in all groups is always one of the shaped bits.

A method comprising:

• generating shaped bits from a first set of information bits;
• applying a systematic forward error correction (FEC) scheme to encode the shaped bits and a second set of information bits, where the first set of information bits and the second set of information bits are disjoint sets;
• and
• for multiple groups, each group consisting of K unshaped bits and one shaped bit,
• selecting one of two constellations based on a value of the shaped bit, where all symbols of one of the two constellations have an amplitude A, all symbols of the other of the two constellations have an amplitude B, A and B are real positive numbers, B<A, and a sum of squares of the amplitudes A2+B2 is equal to 1 or differs slightly from 1,
• using the K unshaped bits to select a first symbol from a first of the two constellations and a second symbol from a second of the two constellations;
• where the first of the two constellations is selected, mapping the first symbol to two physical dimensions of an optical carrier component that is polarized in a first polarization and mapping the second symbol to two physical dimensions of an optical carrier component that is polarized in a second polarization that is orthogonal to the first polarization;
• and
• where the second of the two constellations is selected, mapping the second symbol to the two physical dimensions of the optical carrier component that is polarized in the first polarization and mapping the first symbol to the two physical dimensions of the optical carrier component that is polarized in the second polarization,
• wherein each of the K unshaped bits is either one of the second set of information bits or one of multiple parity bits resulting from the FEC encoding, and K is a positive integer greater than three.