Probabilistic constellation shaping of multi-dimensional symbols for improved tolerance to nonlinear impairments
An optical transmitter device includes a digital signal processor (DSP) having digital hardware. The DSP is operative to generate shaped bits from a first set of information bits, and 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. Unshaped bits and the shaped bits are mapped to selected symbols or are used to select symbols from one or more constellations. The selected symbols are mapped to physical dimensions. Each unshaped bit is either one of the second set of information bits or one of multiple parity bits resulting from the FEC encoding. In this manner, a target spectral efficiency is achieved.
1 . 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; and
for multiple groups, each group consisting of 6 unshaped bits and one shaped bit,
to select one of two 8 phase shift keying (8PSK) constellations based on a value of the shaped bit, where all symbols of one of the two 8PSK constellations have an amplitude A, all symbols of the other of the two 8PSK constellations have an amplitude B, A and B are real positive numbers, B<A, and a sum of squares of the amplitudes A 2 +B 2 is equal to 1 or differs slightly from 1,
to use the 6 unshaped bits to select a first symbol from a first of the two 8PSK constellations and a second symbol from a second of the two 8PSK constellations;
where the first of the two 8PSK constellations is selected, to map the first symbol to two physical dimensions of an optical carrier component that is polarized in a first polarization and to map 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 8PSK constellations is selected, to map the second symbol to the two physical dimensions of the optical carrier component that is polarized in the first polarization and to map the first symbol to the two physical dimensions of the optical carrier component that is polarized in the second polarization,
wherein each of the 6 unshaped bits is either one of the second set of information bits or one of multiple parity bits resulting from the FEC encoding.
2 . The optical transmitter device recited in claim 1 , further comprising
a first modulator operative to modulate the optical carrier component that is polarized in the first polarization to convey the symbol that is mapped to the two physical dimensions of the optical carrier that is polarized in the first polarization; and
a second modulator operative to modulate the optical carrier component that is polarized in the second polarization to convey the symbol that is mapped to the two physical dimensions of the optical carrier that is polarized in the second polarization.
3 . The optical transmitter device recited in claim 1 , wherein the DSP is operative to apply any arbitrary shaping algorithm to the first set of information bits to generate the shaped bits.
4 . The optical transmitter device recited in claim 1 , wherein the DSP is operative to apply a tree encoding structure to the first set of information bits to generate the shaped bits, the tree encoding structure having look-up tables that were programmed to achieve particular probabilities of the shaped bits.
5 . The optical transmitter device recited in claim 1 , wherein the DSP is operative to apply a tree encoding structure to the first set of information bits to generate the shaped bits, the tree encoding structure having look-up tables that were programmed according to different pseudo-energies that were assigned to points of a two-point constellation.
6 . 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 6 unshaped bits and one shaped bit,
selecting one of two 8 phase shift keying (8PSK) constellations based on a value of the shaped bit, where all symbols of one of the two 8PSK constellations have an amplitude A, all symbols of the other of the two 8PSK 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 6 unshaped bits to select a first symbol from a first of the two 8PSK constellations and a second symbol from a second of the two 8PSK constellations;
where the first of the two 8PSK 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 8PSK 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 6 unshaped bits is either one of the second set of information bits or one of multiple parity bits resulting from the FEC encoding.
7 . The method recited in claim 6 , further comprising
modulating the optical carrier component that is polarized in the first polarization to convey the symbol that is mapped to the two physical dimensions of the optical carrier component that is polarized in the first polarization; and
modulating the optical carrier component that is polarized in the second polarization to convey the symbol that is mapped to the two physical dimensions of the optical carrier component that is polarized in the second polarization.
8 . The method recited in claim 6 , further comprising applying any arbitrary shaping algorithm to the first set of information bits to generate the shaped bits.
9 . The method recited in claim 6 , further comprising applying a tree encoding structure to the first set of information bits to generate the shaped bits, the tree encoding structure having look-up tables that were programmed to achieve particular probabilities of the shaped bits.
10 . The method recited in claim 6 , further comprising applying a tree encoding structure to the first set of information bits to generate the shaped bits, the tree encoding structure having look-up tables that were programmed according to different pseudo-energies that were assigned to points of a two-point constellation.
11 . 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;
selecting 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 and the selected collection is one of the disjoint collections;
using some of the shaped bits to select symbols from the selected collection; and
mapping 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.
12 . The method recited in claim 11 , wherein the symbols mapped to the physical dimensions are of constant symbol energy.
13 . The method recited in claim 11 , wherein the symbols mapped to the physical dimensions are polarization-balanced.
14 . The method recited in claim 11 , further comprising applying any arbitrary shaping algorithm to the first set of information bits to generate the shaped bits.
15 . The method recited in claim 11 , further comprising applying a tree encoding structure to the first set of information bits to generate the shaped bits, the tree encoding structure having look-up tables that were programmed to achieve particular probabilities of the shaped bits.
16 . The method recited in claim 11 , further comprising applying a tree encoding structure to the first set of information bits to generate the shaped bits, the tree encoding structure having look-up tables that were programmed according to different pseudo-energies that were assigned to points of a two-point constellation.
17 . The method recited in claim 11 , wherein selecting the collection, selecting symbols from the selected collection, and mapping symbols including the selected symbols to physical dimensions comprises
for multiple groups, each group consisting of K unshaped bits and L of the shaped bits
selecting one of 2 L collections based on a value of the L shaped bits in the group, where a Cartesian product of a quadrature phase shift keying (QPSK) constellation has been partitioned into the 2 L disjoint collections;
using the K unshaped bits to select an ordered N-tuple of QPSK symbols from the selected collection; and
mapping four QPSK symbols including QPSK symbols of the selected ordered N-tuple to eight 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 K, L, and N are positive integers.
18 . The method recited in claim 17 , wherein the K unshaped bits are used to select an ordered triplet of QPSK symbols from the selected collection, wherein the four QPSK symbols mapped to the eight physical dimensions include the three QPSK symbols of the selected ordered triplet, denoted X 1 , Y 1 , and X 2 , respectively, and a fourth QPSK symbol denoted Y 2 that satisfies a condition X 1 Y 1 *+X 2 Y 2 *=0, where asterisk (*) denotes complex conjugate.
19 . The method recited in claim 17 , wherein K equals 7, L equals 1, and N equals 4.
20 . The method recited in claim 17 , wherein K equals 6, L equals 1, and N equals 3.