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Optical transmitter and transmission method

11496221 · 2022-11-08

Assignee

Inventors

Cpc classification

International classification

Abstract

An optical transmitter, having an encoder and modulator, transmits a data signal. The encoder maps information bits of the data signal to a symbol in eight-dimensional (8D) constellation space spanned by vectors IXT1, QXT1, IYT1, QYT1, IXT2, QXT2, IYT2, QYT2, wherein I and Q are in-phase and quadrature components of an optical carrier, X and Y are orthogonal polarizations of the optical carrier, and T1 and T2 are two consecutive transmission time slots, by selecting the symbol from a set of constellation points in the 8D space. The modulator uses the symbol in the two consecutive transmission time slots to modulate two carrier waves, and to transmit the two carrier waves over the orthogonal polarizations of the optical carrier. The set of constellation points do not include any constellation point with parallel Stokes vectors in the two consecutive transmission time slots but comprise constellation points with orthogonal Stokes vectors.

Claims

1. An optical transmitter for transmitting a data signal, the optical transmitter comprising: an encoder configured to map a number of information bits of the data signal to a symbol in an eight-dimensional constellation space spanned by vectors IXT1, QXT1, IYT1, QYT1, IXT2, QXT2, IYT2, QYT2, wherein I and Q are in-phase and quadrature components of an optical carrier, X and Y are orthogonal polarizations of the optical carrier, and T1 and T2 are two consecutive transmission time slots, by selecting the symbol from a set of constellation points in the eight-dimensional constellation space; and a modulator configured to use the selected symbol in the two consecutive transmission time slots T1 and T2 to modulate a first carrier wave and a second carrier wave, and to transmit the first carrier wave and the second carrier wave over the orthogonal polarizations X and Y of the optical carrier; wherein the set of constellation points does not comprise any constellation point with parallel Stokes vectors in the two consecutive transmission time slots T1 and T2 and comprises one or more constellation points with orthogonal Stokes vectors in the two consecutive transmission time slots T1 and T2.

2. The optical transmitter according to claim 1, wherein each constellation point in the set of constellation points comprises, for each of the two consecutive transmission time slots T1 and T2, a first symbol for modulating the first carrier wave and a second symbol for modulating the second carrier wave.

3. The optical transmitter according to claim 2, wherein the first symbol for modulating the first carrier wave and the second symbol for modulating the second carrier wave are from a quadrature phase shift keying (QPSK) base constellation.

4. The optical transmitter according to claim 1, wherein the modulator is configured to modulate an in-phase component and a quadrature component of each of the first carrier wave and the second carrier wave.

5. The optical transmitter according to claim 1, wherein the set of constellation points further comprises one or more constellation points with anti-parallel Stokes vectors in the two consecutive transmission time slots T1 and T2.

6. The optical transmitter according to claim 1, wherein the encoder is configured to map the information bits to the symbol in the eight-dimensional constellation space by: generating a number of overhead bits from the information bits; and mapping a bit sequence that comprises the information bits and the overhead bits to the symbol in the eight-dimensional constellation space.

7. The optical transmitter according to claim 6, wherein the encoder is configured to generate the overhead bits from the information bits by using Boolean equations.

8. The optical transmitter according to claim 7, wherein the encoder is configured to perform at least one Boolean operation based on at least two of the information bits to obtain at least one of the overhead bits of the bit sequence.

9. The optical transmitter according to claim 6, wherein the optical transmitter is configured to transmit the data signal with a spectral efficiency of 2.5 bits per transmission time slot.

10. The optical transmitter according to claim 9, wherein symbol polarization states in each of the transmission time slots take one of at least four distinct polarizations states.

11. The optical transmitter according to claim 9, wherein the information bits are five bits b1 . . . b5, wherein the overhead bits are three overhead bits b1′, b2′, b3′ wherein the bit sequence comprises the eight bits b1 . . . b5, b1′, b2′, b3′, and wherein the three overhead bits b1′, b2′, b3′ are generated according to:
b1′=b3 XOR b4 XOR b5
b2′=b2 XOR b4 XOR b5
b3′=b1 XOR b4 XOR b5.

12. The optical transmitter according to claim 11, wherein for the two consecutive transmission time slots T1 and T2, for the orthogonal polarizations X and Y of the optical carrier, and for a set of four QPSK symbols denoted −1−1i, −1+1i, 1−1i and 1+1i, the encoder is configured to select the symbol in the eight-dimensional constellation space based on the information bits according to the following labelling: TABLE-US-00013 Labelling (from left to right) 5 bits b1 . . . b5, Time slot T.sub.1 Time slot T.sub.2 and 3 overhead X Y X Y bits b1’, polar- polar- polar- polar- b2’, b3’ ization ization ization ization 0 0 0 0 0 0 1 1 −1−1i −1−1i −1−1i  1+1i 0 0 0 0 1 1 0 0 −1−1i −1−1i  1+1i −1−1i 0 0 0 1 0 1 0 0 −1−1i −1+1i −1+1i −1−1i 0 0 0 1 1 0 1 1 −1−1i −1+1i  1−1i  1+1i 0 0 1 0 0 1 1 1 −1−1i  1−1i −1+1i  1+1i 0 0 1 0 1 0 0 0 −1−1i  1−1i  1−1i −1−1i 0 0 1 1 0 0 0 0 −1−1i  1+1i −1−1i −1−1i 0 0 1 1 1 1 1 1 −1−1i  1+1i  1+1i  1+1i 0 1 0 0 0 0 0 1 −1+1i −1−1i −1−1i −1+1i 0 1 0 0 1 1 1 0 −1+1i −1−1i  1+1i  1−1i 0 1 0 1 0 1 1 0 −1+1i −1+1i −1+1i  1−1i 0 1 0 1 1 0 0 1 −1+1i −1+1i  1−1i −1+1i 0 1 1 0 0 1 0 1 −1+1i  1−1i −1+1i −1+1i 0 1 1 0 1 0 1 0 −1+1i  1−1i  1−1i  1−1i 0 1 1 1 0 0 1 0 −1+1i  1+1i −1−1i  1−1i 0 1 1 1 1 1 0 1 −1+1i  1+1i  1+1i −1+1i 1 0 0 0 0 0 1 0  1−1i −1−1i −1−1i  1−1i 1 0 0 0 1 1 0 1  1−1i −1−1i  1+1i −1+1i 1 0 0 1 0 1 0 1  1−1i −1+1i −1+1i −1+1i 1 0 0 1 1 0 1 0  1−1i −1+1i  1−1i  1−1i 1 0 1 0 0 1 1 0  1−1i  1−1i −1+1i  1−1i 1 0 1 0 1 0 0 1  1−1i  1−1i  1−1i −1+1i 1 0 1 1 0 0 0 1  1−1i  1+1i −1−1i −1+1i 1 0 1 1 1 1 1 0  1−1i  1+1i  1+1i  1−1i 1 1 0 0 0 0 0 0  1+1i −1−1i −1−1i −1−1i 1 1 0 0 1 1 1 1  1+1i −1−1i  1+1i  1+1i 1 1 0 1 0 1 1 1  1+1i −1+1i −1+1i  1+1i 1 1 0 1 1 0 0 0  1+1i −1+1i  1−1i −1−1i 1 1 1 0 0 1 0 0  1+1i  1−1i −1+1i −1−1i 1 1 1 0 1 0 1 1  1+1i  1−1i  1−1i  1+1i 1 1 1 1 0 0 1 1  1+1i  1+1i −1−1i  1+1i 1 1 1 1 1 1 0 0  1+1i  1+1i  1+1i  −1−1i.

13. The optical transmitter according to claim 6, wherein the optical transmitter is configured to transmit the data signal with a spectral efficiency of 3.5 bits per transmission time slot.

14. The optical transmitter according to claim 13, wherein symbols in at least a subset of the consecutive transmission time slots have orthogonal polarization states.

15. The optical transmitter according to claim 13, wherein the information bits are seven bits b1 . . . b7, wherein the overhead bit is bit b′, wherein the bit sequence comprises eight the bits b1 . . . b7, b′, and wherein the overhead bit b′ is generated according to:
b1′=b1 XOR b4 XOR b6 XOR
(b1 XOR b2)AND(b3 XOR b4 XOR b5 XOR b6)XOR
(b3 XOR b4)AND(b5 XOR b6).

16. The optical transmitter according to claim 15, wherein for the two consecutive transmission time slots T1 and T2, for the orthogonal polarizations X and Y of the optical carrier, and for a set of four QPSK symbols denoted −1−1i, −1+1i, 1−1i and 1+1i, the encoder is configured to select the symbol in the eight-dimensional constellation space based on the information bits according to the following labelling: TABLE-US-00014 Labelling (from left to right) Time slot T.sub.1 Time slot T.sub.2 7 bits b1 . . . b7, X Y X Y and 1 polar- polar- polar- polar- overhead bit b’ ization ization ization ization 0 0 0 0 0 0 0 1 −1−1i −1−1i −1−1i −1+1i 0 0 0 0 0 0 1 1 −1−1i −1−1i −1−1i  1+1i 0 0 0 0 0 1 0 0 −1−1i −1−1i −1+1i −1−1i 0 0 0 0 0 1 1 0 −1−1i −1−1i −1+1i  1−1i 0 0 0 0 1 0 0 1 −1−1i −1−1i  1−1i −1+1i 0 0 0 0 1 0 1 1 −1−1i −1−1i  1−1i  1+1i 0 0 0 0 1 1 0 0 −1−1i −1−1i  1+1i −1−1i 0 0 0 0 1 1 1 0 −1−1i −1−1i  1+1i  1−1i 0 0 0 1 0 0 0 0 −1−1i −1+1i −1−1i −1−1i 0 0 0 1 0 0 1 0 −1−1i −1+1i −1−1i  1−1i 0 0 0 1 0 1 0 0 −1−1i −1+1i −1+1i −1−1i 0 0 0 1 0 1 1 0 −1−1i −1+1i −1+1i  1−1i 0 0 0 1 1 0 0 1 −1−1i −1+1i  1−1i −1+1i 0 0 0 1 1 0 1 1 −1−1i −1+1i  1−1i  1+1i 0 0 0 1 1 1 0 1 −1−1i −1+1i  1+1i −1+1i 0 0 0 1 1 1 1 1 −1−1i −1+1i  1+1i  1+1i 0 0 1 0 0 0 0 1 −1−1i  1−1i −1−1i −1+1i 0 0 1 0 0 0 1 1 −1−1i  1−1i −1−1i  1+1i 0 0 1 0 0 1 0 1 −1−1i  1−1i −1+1i −1+1i 0 0 1 0 0 1 1 1 −1−1i  1−1i −1+1i  1+1i 0 0 1 0 1 0 0 0 −1−1i  1−1i  1−1i −1−1i 0 0 1 0 1 0 1 0 −1−1i  1−1i  1−1i  1−1i 0 0 1 0 1 1 0 0 −1−1i  1−1i  1+1i −1−1i 0 0 1 0 1 1 1 0 −1−1i  1−1i  1+1i  1−1i 0 0 1 1 0 0 0 0 −1−1i  1+1i −1−1i −1−1i 0 0 1 1 0 0 1 0 −1−1i  1+1i −1−1i  1−1i 0 0 1 1 0 1 0 1 −1−1i  1+1i −1+1i −1+1i 0 0 1 1 0 1 1 1 −1−1i  1+1i −1+1i  1+1i 0 0 1 1 1 0 0 0 −1−1i  1+1i  1−1i −1−1i 0 0 1 1 1 0 1 0 −1−1i  1+1i  1−1i  1−1i 0 0 1 1 1 1 0 1 −1−1i  1+1i  1+1i −1+1i 0 0 1 1 1 1 1 1 −1−1i  1+1i  1+1i  1+1i 0 1 0 0 0 0 0 1 −1+1i −1−1i −1−1i −1+1i 0 1 0 0 0 0 1 1 −1+1i −1−1i −1−1i  1+1i 0 1 0 0 0 1 0 1 −1+1i −1−1i −1+1i −1+1i 0 1 0 0 0 1 1 1 −1+1i −1−1i −1+1i  1+1i 0 1 0 0 1 0 0 0 −1+1i −1−1i  1−1i −1−1i 0 1 0 0 1 0 1 0 −1+1i −1−1i  1−1i  1−1i 0 1 0 0 1 1 0 0 −1+1i −1−1i  1+1i −1−1i 0 1 0 0 1 1 1 0 −1+1i −1−1i  1+1i  1−1i 0 1 0 1 0 0 0 1 −1+1i −1+1i −1−1i −1+1i 0 1 0 1 0 0 1 1 −1+1i −1+1i −1−1i  1+1i 0 1 0 1 0 1 0 0 −1+1i −1+1i −1+1i −1−1i 0 1 0 1 0 1 1 0 −1+1i −1+1i −1+1i  1−1i 0 1 0 1 1 0 0 1 −1+1i −1+1i  1−1i −1+1i 0 1 0 1 1 0 1 1 −1+1i −1+1i  1−1i  1+1i 0 1 0 1 1 1 0 0 −1+1i −1+1i  1+1i −1−1i 0 1 0 1 1 1 1 0 −1+1i −1+1i  1+1i  1−1i 0 1 1 0 0 0 0 0 −1+1i  1−1i −1−1i −1−1i 0 1 1 0 0 0 1 0 −1+1i  1−1i −1−1i  1−1i 0 1 1 0 0 1 0 1 −1+1i  1−1i −1+1i −1+1i 0 1 1 0 0 1 1 1 −1+1i  1−1i −1+1i  1+1i 0 1 1 0 1 0 0 0 −1+1i  1−1i  1−1i −1−1i 0 1 1 0 1 0 1 0 −1+1i  1−1i  1−1i  1−1i 0 1 1 0 1 1 0 1 −1+1i  1−1i  1+1i −1+1i 0 1 1 0 1 1 1 1 −1+1i  1−1i  1+1i  1+1i 0 1 1 1 0 0 0 0 −1+1i  1+1i −1−1i −1−1i 0 1 1 1 0 0 1 0 −1+1i  1+1i −1−1i  1−1i 0 1 1 1 0 1 0 0 −1+1i  1+1i −1+1i −1−1i 0 1 1 1 0 1 1 0 −1+1i  1+1i −1+1i  1−1i 0 1 1 1 1 0 0 1 −1+1i  1+1i  1−1i −1+1i 0 1 1 1 1 0 1 1 −1+1i  1+1i  1−1i  1+1i 0 1 1 1 1 1 0 1 −1+1i  1+1i  1+1i −1+1i 0 1 1 1 1 1 1 1 −1+1i  1+1i  1+1i  1+1i 1 0 0 0 0 0 0 0  1−1i −1−1i −1−1i −1−1i 1 0 0 0 0 0 1 0  1−1i −1−1i −1−1i  1−1i 1 0 0 0 0 1 0 0  1−1i −1−1i −1+1i −1−1i 1 0 0 0 0 1 1 0  1−1i −1−1i −1+1i  1−1i 1 0 0 0 1 0 0 1  1−1i −1−1i  1−1i −1+1i 1 0 0 0 1 0 1 1  1−1i −1−1i  1−1i  1+1i 1 0 0 0 1 1 0 1  1−1i −1−1i  1+1i −1+1i 1 0 0 0 1 1 1 1  1−1i −1−1i  1+1i  1+1i 1 0 0 1 0 0 0 0  1−1i −1+1i −1−1i −1−1i 1 0 0 1 0 0 1 0  1−1i −1+1i −1−1i  1−1i 1 0 0 1 0 1 0 1  1−1i −1+1i −1+1i −1+1i 1 0 0 1 0 1 1 1  1−1i −1+1i −1+1i  1+1i 1 0 0 1 1 0 0 0  1−1i −1+1i  1−1i −1−1i 1 0 0 1 1 0 1 0  1−1i −1+1i  1−1i  1−1i 1 0 0 1 1 1 0 1  1−1i −1+1i  1+1i −1+1i 1 0 0 1 1 1 1 1  1−1i −1+1i  1+1i  1+1i 1 0 1 0 0 0 0 1  1−1i  1−1i −1−1i −1+1i 1 0 1 0 0 0 1 1  1−1i  1−1i −1−1i  1+1i 1 0 1 0 0 1 0 0  1−1i  1−1i −1+1i −1−1i 1 0 1 0 0 1 1 0  1−1i  1−1i −1+1i  1−1i 1 0 1 0 1 0 0 1  1−1i  1−1i  1−1i −1+1i 1 0 1 0 1 0 1 1  1−1i  1−1i  1−1i  1+1i 1 0 1 0 1 1 0 0  1−1i  1−1i  1+1i −1−1i 1 0 1 0 1 1 1 0  1−1i  1−1i  1+1i  1−1i 1 0 1 1 0 0 0 1  1−1i  1+1i −1−1i −1+1i 1 0 1 1 0 0 1 1  1−1i  1+1i −1−1i  1+1i 1 0 1 1 0 1 0 1  1−1i  1+1i −1+1i −1+1i 1 0 1 1 0 1 1 1  1−1i  1+1i −1+1i  1+1i 1 0 1 1 1 0 0 0  1−1i  1+1i  1−1i −1−1i 1 0 1 1 1 0 1 0  1−1i  1+1i  1−1i  1−1i 1 0 1 1 1 1 0 0  1−1i  1+1i  1+1i −1−1i 1 0 1 1 1 1 1 0  1−1i  1+1i  1+1i  1−1i 1 1 0 0 0 0 0 0  1+1i −1−1i −1−1i −1−1i 1 1 0 0 0 0 1 0  1+1i −1−1i −1−1i  1−1i 1 1 0 0 0 1 0 1  1+1i −1−1i −1+1i −1+1i 1 1 0 0 0 1 1 1  1+1i −1−1i −1+1i  1+1i 1 1 0 0 1 0 0 0  1+1i −1−1i  1−1i −1−1i 1 1 0 0 1 0 1 0  1+1i −1−1i  1−1i  1−1i 1 1 0 0 1 1 0 1  1+1i −1−1i  1+1i −1+1i 1 1 0 0 1 1 1 1  1+1i −1−1i  1+1i  1+1i 1 1 0 1 0 0 0 1  1+1i −1+1i −1−1i −1+1i 1 1 0 1 0 0 1 1  1+1i −1+1i −1−1i  1+1i 1 1 0 1 0 1 0 1  1+1i −1+1i −1+1i −1+1i 1 1 0 1 0 1 1 1  1+1i −1+1i −1+1i  1+1i 1 1 0 1 1 0 0 0  1+1i −1+1i  1−1i −1−1i 1 1 0 1 1 0 1 0  1+1i −1+1i  1−1i  1−1i 1 1 0 1 1 1 0 0  1+1i −1+1i  1+1i −1−1i 1 1 0 1 1 1 1 0  1+1i −1+1i  1+1i  1−1i 1 1 1 0 0 0 0 0  1+1i  1−1i −1−1i −1−1i 1 1 1 0 0 0 1 0  1+1i  1−1i −1−1i  1−1i 1 1 1 0 0 1 0 0  1+1i  1−1i −1+1i −1−1i 1 1 1 0 0 1 1 0  1+1i  1−1i −1+1i  1−1i 1 1 1 0 1 0 0 1  1+1i  1−1i  1−1i −1+1i 1 1 1 0 1 0 1 1  1+1i  1−1i  1−1i  1+1i 1 1 1 0 1 1 0 1  1+1i  1−1i  1+1i −1+1i 1 1 1 0 1 1 1 1  1+1i  1−1i  1+1i  1+1i 1 1 1 1 0 0 0 1  1+1i  1+1i −1−1i −1+1i 1 1 1 1 0 0 1 1  1+1i  1+1i −1−1i  1+1i 1 1 1 1 0 1 0 0  1+1i  1+1i −1+1i −1−1i 1 1 1 1 0 1 1 0  1+1i  1+1i −1+1i  1−1i 1 1 1 1 1 0 0 1  1+1i  1+1i  1−1i −1+1i 1 1 1 1 1 0 1 1  1+1i  1+1i  1−1i  1+1i 1 1 1 1 1 1 0 0  1+1i  1+1i  1+1i −1−1i 1 1 1 1 1 1 1 0  1+1i  1+1i  1+1i   1−1i .

17. The optical transmitter according to claim 6, wherein the optical transmitter is configured to transmit the data signal with a spectral efficiency of 2 bits per transmission time slot.

18. The optical transmitter according to claim 17, wherein the symbol polarization states in each of the transmission time slots take one of at least four distinct polarization states.

19. The optical transmitter according to claim 17, wherein the information bits are four bits b1 . . . b4, wherein the overhead bits comprise bits b1′, b2′, b3′, b4′, wherein the bit sequence comprises the eight bits b1 . . . b3, b1′, b4, b2′ . . . b4′, and wherein the overhead bits b1′, b2′, b3′, b4′ are generated according to:
b1′=b1 XOR b2 XOR b3
b2′=b1 XOR b2 XOR b5
b3′=b1 XOR b3 XOR b5
b4′=b2 XOR b3 XOR b5.

20. The optical transmitter according to claim 19, wherein for the two of the consecutive transmission time slots T1 and T2, for the orthogonal polarizations X and Y of the optical carrier, and for a set of four QPSK symbols denoted −1−1i, −1+1i, 1−1i, 1+1i, the encoder is configured to select the symbol in the eight-dimensional constellation space based on the information bits according to the following labelling: TABLE-US-00015 Labelling (from the left to the right: 3 information Time slot T.sub.1 Time slot T.sub.2 bits, 1 parity bit, 1 X Y X Y information bit, 3 parity bits) polarization polarization polarization polarization 00000011 −1−1i −1−1i −1−1i +1+1i 00001100 −1−1i −1−1i +1+1i −1−1i 00110000 −1−1i +1+1i −1−1i −1−1i 00111111 −1−1i +1+1i +1+1i +1+1i 01010110 −1+1i −1+1i −1+1i +1−1i 01011001 −1+1i −1+1i +1−1i −1+1i 01100101 −1+1i +1−1i −1+1i −1+1i 01101010 −1+1i +1−1i +1−1i +1−1i 10010101 +1−1i −1+1i −1+1i −1+1i 10011010 +1−1i −1+1i +1−1i +1−1i 10100110 +1−1i +1−1i −1+1i +1−1i 10101001 +1−1i +1−1i +1−1i −1+1i 11000000 +1+1i −1−1i −1−1i −1−1i 11001111 +1+1i −1−1i +1+1i +1+1i 11110011 +1+1i +1+1i −1−1i +1+1i 11111100 +1+1i +1+1i +1+1i  −1−1i.

21. The optical transmitter according to claim 6, wherein the optical transmitter is configured to transmit the data signal with a spectral efficiency of 3 bits per transmission time slot.

22. The optical transmitter according to claim 21, wherein symbols in at least a subset of the consecutive transmission time slots have orthogonal polarization states.

23. The optical transmitter according to claim 21, wherein the information bits are six bits b1 . . . b6, wherein the overhead bits comprise bits b1′, b2′, wherein the bit sequence comprises the eight bits b1 . . . b6, b1′, b2′, and wherein the bits b1′, b2; are generated according to:
b1′=b2 XOR b3 XOR b5 XOR(b1 XOR b2)AND(b3 XOR b4 XOR b5 XOR b6)XOR(b3 XOR b4)AND(b5 XOR b6)
b2′=b1XOR b4 XOR b6 XOR(b1 XOR b2)AND(b3 XOR b4 XOR b5 XOR b6)XOR(b3 XOR b4)AND(b5 XOR b6).

24. The optical transmitter according to claim 23, wherein for the two consecutive transmission time slots T1 and T2, for the orthogonal polarizations X and Y of the optical carrier, and for a set of four QPSK symbols denoted −1−1i, −1+1i, 1−1i and 1+1i, the encoder is configured to select the symbol in the eight-dimensional constellation space based on the information bits according to the following labelling: TABLE-US-00016 Labelling (from the Time slot T1 Time slot T2 left to the right: 6 information X Y X Y bits and 2 parity bit) polarization polarization polarization polarization 00000011 −1−1i −1−1i −1−1i +1+1i 00000110 −1−1i −1−1i −1+1i +1−1i 00001001 −1−1i −1−1i +1−1i −1+1i 00001100 −1−1i −1−1i +1+1i −1−1i 00010010 −1−1i −1+1i −1−1i +1−1i 00010100 −1−1i −1+1i −1+1i −1−1i 00011011 −1−1i −1+1i +1−1i +1+1i 00011101 −1−1i −1+1i +1+1i −1+1i 00100001 −1−1i +1−1i −1−1i −1+1i 00100111 −1−1i +1−1i −1+1i +1+1i 00101000 −1−1i +1−1i +1−1i −1−1i 00101110 −1−1i +1−1i +1+1i +1−1i 00110000 −1−1i +1+1i −1−1i −1−1i 00110101 −1−1i +1+1i −1+1i −1+1i 00111010 −1−1i +1+1i +1−1i +1−1i 00111111 −1−1i +1+1i +1+1i +1+1i 01000001 −1+1i −1−1i −1−1i −1+1i 01000111 −1+1i −1−1i −1+1i +1+1i 01001000 −1+1i −1−1i +1−1i −1−1i 01001110 −1+1i −1−1i +1+1i +1−1i 01010011 −1+1i −1+1i −1−1i +1+1i 01010110 −1+1i −1+1i −1+1i +1−1i 01011001 −1+1i −1+1i +1−1i −1+1i 01011100 −1+1i −1+1i +1+1i −1−1i 01100000 −1+1i +1−1i −1−1i −1−1i 01100101 −1+1i +1−1i −1+1i −1+1i 01101010 −1+1i +1−1i +1−1i +1−1i 01101111 −1+1i +1−1i +1+1i +1+1i 01110010 −1+1i +1+1i −1−1i +1−1i 01110100 −1+1i +1+1i −1+1i −1−1i 01111011 −1+1i +1+1i +1−1i +1+1i 01111101 −1+1i +1+1i +1+1i −1+1i 10000010 +1−1i −1−1i −1−1i +1−1i 10000100 +1−1i −1−1i −1+1i −1−1i 10001011 +1−1i −1−1i +1−1i +1+1i 10001101 +1−1i −1−1i +1+1i −1+1i 10010000 +1−1i −1+1i −1−1i −1−1i 10010101 +1−1i −1+1i −1+1i −1+1i 10011010 +1−1i −1+1i +1−1i +1−1i 10011111 +1−1i −1+1i +1+1i +1+1i 10100011 +1−1i +1−1i −1−1i +1+1i 10100110 +1−1i +1−1i −1+1i +1−1i 10101001 +1−1i +1−1i +1−1i −1+1i 10101100 +1−1i +1−1i +1+1i −1−1i 10110001 +1−1i +1+1i −1−1i −1+1i 10110111 +1−1i +1+1i −1+1i +1+1i 10111000 +1−1i +1+1i +1−1i −1−1i 10111110 +1−1i +1+1i +1+1i +1−1i 11000000 +1+1i −1−1i −1−1i −1−1i 11000101 +1+1i −1−1i −1+1i −1+1i 11001010 +1+1i −1−1i +1−1i +1−1i 11001111 +1+1i −1−1i +1+1i +1+1i 11010001 +1+1i −1+1i −1−1i −1+1i 11010111 +1+1i −1+1i −1+1i +1+1i 11011000 +1+1i −1+1i +1−1i −1−1i 11011110 +1+1i −1+1i +1+1i +1−1i 11100010 +1+1i +1−1i −1−1i +1−1i 11100100 +1+1i +1−1i −1+1i −1−1i 11101011 +1+1i +1−1i +1−1i +1+1i 11101101 +1+1i +1−1i +1+1i −1+1i 11110011 +1+1i +1+1i −1−1i +1+1i 11110110 +1+1i +1+1i −1+1i +1−1i 11111001 +1+1i +1+1i +1−1i −1+1i 11111100 +1+1i +1+1i +1+1i  −1−1i.

25. A method of optically transmitting a data signal, the method comprising: mapping a number of information bits of the data signal to a symbol in an eight-dimensional constellation space spanned by vectors IXT1, QXT1, IYT1, QYT1, IXT2, QXT2, IYT2, QYT2, wherein I and Q are in-phase and quadrature components of an optical carrier, X and Y are orthogonal polarizations of the optical carrier, and T1 and T2 are two consecutive transmission time slots, by selecting the symbol from a set of constellation points in the eight-dimensional constellation space; using the selected symbol in the two consecutive transmission time slots T1 and T2 to modulate a first carrier wave and a second carrier wave; and transmitting the first carrier wave and the second carrier wave over the orthogonal polarizations X and Y of the optical carrier; wherein the set of constellation points does not comprise any constellation point with parallel Stokes vectors in the two consecutive transmission time slots T1 and T2 and comprises one or more constellation points with orthogonal Stokes vectors in the two consecutive transmission time slots T1 and T2.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The above described aspects and implementation forms of the disclosure will be explained in the following description of exemplary embodiments in relation to the enclosed drawings, in which:

(2) FIG. 1 shows an optical transmitter according to an exemplary embodiment of the present disclosure.

(3) FIG. 2 shows a set of four symbols, in particular a QPSK constellation and labelling.

(4) FIG. 3 shows an optical transmission system according to an exemplary embodiment of the present disclosure including an optical transmitter according to an embodiment of the present disclosure.

(5) FIG. 4 shows an example encoder of an optical transmitter according to an exemplary embodiment of the present disclosure.

(6) FIG. 5 shows a method according to an exemplary embodiment of the present disclosure.

DETAILED DESCRIPTION OF THE EMBODIMENTS

(7) The disclosure presents an optical transmitter 100, an optical transmission system, and a method 500, which use modulation formats obtained by set-partitioning of a constellation whose projection onto an interval is the PDM-QPSK constellation. The following constraints were applied for designing the modulation formats: Symbols must not have identical (parallel) states of polarization in two consecutive time slots. If possible, symbols have opposite (antiparallel) states of polarization in two consecutive time slots. If there are not enough symbols to reach the desired spectral efficiency, then missing symbols are chosen from the set of symbols with the polarization alternating property (not identical polarization states). The overall set of symbols are chosen to have preferably a high symmetry. More specifically, for each symbol of a given modulation format, the Euclidean distances to its neighbors is preferably chosen to be the highest possible one, with respect to what the whole PDM-QPSK constellation offers.

(8) The modulation formats used by the optical transmitter 100, the transmission system, and the method 500 according to embodiments of the present disclosure, respectively, differ from the known modulation formats (at the same spectral efficiency) at least in that: The modulation formats are derived from the same base constellation of a set of four symbols. The modulation formats have the same modulus in each of the dimensions separately (this is in fact a consequence of the previous point). The modulation formats may contain symbols with the polarization alternating property. The modulation formats have at least four distinct polarization states.

(9) FIG. 1 shows an optical transmitter 100 according to an exemplary embodiment of the present disclosure. The optical transmitter 100 is configured to transmit a data signal 101, which comprises a sequence of bits, over an optical link like an optical carrier 104. The optical transmitter 100 comprises an encoder 102 for encoding the data signal 101, and a modulator 103 for modulating and transmitting the data signal 101 on the optical carrier 104. For instance, the optical carrier 104 may be an optical fiber.

(10) In particular, the encoder 102 is configured to encode the data signal 101 by selecting, based on a bit sequence, a first symbol and a second symbol from a set 200 of four symbols 201-204 (see FIG. 2), for each one of at least two transmission time slots. Notably, the bit sequence may be the bits of the data signal 101 itself or may be a bit sequence 401 derived from the data signal 101.

(11) The modulator 103 is configured to use, in each transmission time slot, the first symbol to modulate a first carrier wave and the second symbol to modulate a second carrier wave. Further, the modulator 103 is configured to transmit the two carrier waves over orthogonal polarizations of the optical carrier 104.

(12) Symbols 201-204 in consecutive transmission time slots have non-identical polarization states, i.e. they follow the above-described ‘polarization alternating’ concept. The modulation symbols 201-204 for a given polarization and time slot are preferably taken from the QPSK constellation shown in FIG. 2, providing the set 200 of four symbols 201-204. The set 200 shown in FIG. 2 includes specifically the four QPSK symbols denoted as −1−1i (symbol 201), −1+1i (symbol 203), 1−1i (symbol 202) and 1+1i (symbols 204).

(13) FIG. 3 shows an optical communication or transmission system according to an exemplary embodiment of the disclosure, in which the modulation formats may be implemented. The transmission system comprises an optical transmitter 100 according to an embodiment of the present disclosure, particularly the optical transmitter 100 shown in FIG. 1, an optical (coherent) receiver 300 for receiving the data signal 101, and an optical link (i.e. the optical carrier 104) between the transmitter 100 and receiver 300. The optical receiver 300 is particularly configured to receive and decode the modulated carrier waves of the optical carrier 104, in order to obtain the data signal 101.

(14) In the optical transmitter 100, the encoder 102 encodes the data signal 101 and may generally generate a sequence of M drive signals from an M=4N-dimensional constellation, where N is the number of time slots. The drive signals from the encoder 102 in turn are used to drive the modulator 103, which modulates the respective dimensions onto the (X and Y) polarizations of the optical carrier 104. The modulator 103 and a laser 105 of the optical transmitter 100 may be implemented using devices known in the art.

(15) The optical receiver 300 is preferably a coherent receiver, which includes an optical beam splitter 301 to separate the received carrier waves into X and Y polarizations. The two obtained signals are mixed separately with a local oscillator 302 and a set of photodetectors 304 detects the optical power of each of the mixed signals for each polarization generated by an optical hybrid 302. An analog to digital converter 305 (ADC) samples each current of the photodetectors 304. The sample streams, which each represent one of the modulated dimensions of the optical carrier 104, are processed in a digital signal processing 306 (DSP), which may include dispersion compensation and possibly other equalization techniques and down-sampling. The processed sample stream is further processed in a decoder 307, such that samples corresponding to the same multi-dimensional constellation symbol 201-204 are processed jointly to recover the transmitted data signal 101. Specifically, the decoder 307 in the receiver 300 performs the inverse operation of the encoder 102 in the transmitter 100.

(16) The modulation formats detailed in the present disclosure are implemented in the encoder 102 of the transmitter 100. An example for such an encoder 102 is shown in FIG. 4. In the encoder 102, a number of input bits, namely information bits of the data signal 101 to be transmitter, is preferably mapped to a number of output bits of a bit sequence 401. This bit sequence 401 includes a number of overhead bits 402 generated through arithmetic operations from the input bits. The output bits are then mapped to multi-dimensional output symbols 201-204 according to the labeling of the constellation points.

(17) In the following, two refined embodiments are specifically described as examples. These embodiments define the encoder 103 and decoder 307 and correspond to two different modulation formats in 8D with spectral efficiencies of 2.5 and 3.5 bit/transmission time slot, respectively. The two modulation formats both achieve the 8D through: I and Q, two orthogonal polarizations referred to as X and Y, and two consecutive time slots referred to as T.sub.1 and T.sub.2. For a given polarization and time slot, the symbols 201-204 are chosen from the set of four symbols 200, preferably from the points in the I-Q-plane shown in FIG. 2.

(18) In the first exemplary embodiment, the modulation format is defined in 8D: I, Q, polarization and two consecutive time-slots. The encoder 103 (as shown in FIG. 4) maps 5 information bits of the data signal 101, referred to as [b.sub.1, b.sub.2, b.sub.3, b.sub.4, b.sub.5] to eight output bits of the bit sequence 401. Three parity or overhead bits 402, referred to as b.sub.1′, b.sub.2′ and b.sub.3′, are defined using the following equations:
b1′=b3 XOR b4 XOR b5
b2′=b2 XOR b4 XOR b5
b3′=b1 XOR b4 XOR b5

(19) Thus, the set of [b.sub.1 b.sub.2 b.sub.3 b.sub.4 b.sub.5 b.sub.1′ b.sub.2′ b.sub.3′] is finally obtained. The first two bits [b.sub.1 b.sub.2] are used to choose a symbol 201-204 from the set 200 shown in FIG. 2. These symbols 201-204 represent the 2 dimensions I and Q of the X polarization on the time slot T.sub.1. Then, the next two bits [b.sub.3 b.sub.4] are used to choose a symbol 201-204 from the set 200 of FIG. 2, which symbols 201-204 represents the 2 dimensions I and Q of the Y polarization on the time slot T.sub.1. The same approach is used for the bits [b.sub.5 b.sub.1′] and [b.sub.2′ b.sub.3′], respectively, selecting symbols 201-204 that represent the 2 dimensions I and Q on the time slot T2 of both X and Y polarizations, respectively. At the end, a spectral efficiency of 2.5 bits/transmission time slot (5 bits in 8 dimensions) is reached in this embodiment, and all obtained symbols 201-204 are listed in the table below. The labelling of the constellation points (the mapping from information bits of the data signal 101 to complex symbols 201-204) determines the linear channel performance.

(20) TABLE-US-00005 Labelling (from left to right) Time slot T.sub.1 Time slot T.sub.2 5 bits b1 . . . b5, and X Y X Y 3 overhead bits polar- polar- polar- polar- b1’, b2’, b3’ ization ization ization ization 0 0 0 0 0 0 1 1 −1−1i −1−1i −1−1i  1+1i 0 0 0 0 1 1 0 0 −1−1i −1−1i  1+1i −1−1i 0 0 0 1 0 1 0 0 −1−1i −1+1i −1+1i −1−1i 0 0 0 1 1 0 1 1 −1−1i −1+1i  1−1i  1+1i 0 0 1 0 0 1 1 1 −1−1i  1−1i −1+1i  1+1i 0 0 1 0 1 0 0 0 −1−1i  1−1i  1−1i −1−1i 0 0 1 1 0 0 0 0 −1−1i  1+1i −1−1i −1−1i 0 0 1 1 1 1 1 1 −1−1i  1+1i  1+1i  1+1i 0 1 0 0 0 0 0 1 −1+1i −1−1i −1−1i −1+1i 0 1 0 0 1 1 1 0 −1+1i −1−1i  1+1i  1−1i 0 1 0 1 0 1 1 0 −1+1i −1+1i −1+1i  1−1i 0 1 0 1 1 0 0 1 −1+1i −1+1i  1−1i −1+1i 0 1 1 0 0 1 0 1 −1+1i  1−1i −1+1i −1+1i 0 1 1 0 1 0 1 0 −1+1i  1−1i  1−1i  1−1i 0 1 1 1 0 0 1 0 −1+1i  1+1i −1−1i  1−1i 0 1 1 1 1 1 0 1 −1+1i  1+1i  1+1i −1+1i 1 0 0 0 0 0 1 0  1−1i −1−1i −1−1i  1−1i 1 0 0 0 1 1 0 1  1−1i −1−1i  1+1i −1+1i 1 0 0 1 0 1 0 1  1−1i −1+1i −1+1i −1+1i 1 0 0 1 1 0 1 0  1−1i −1+1i  1−1i  1−1i 1 0 1 0 0 1 1 0  1−1i  1−1i −1+1i  1−1i 1 0 1 0 1 0 0 1  1−1i  1−1i  1−1i −1+1i 1 0 1 1 0 0 0 1  1−1i  1+1i −1−1i −1+1i 1 0 1 1 1 1 1 0  1−1i  1+1i  1+1i  1−1i 1 1 0 0 0 0 0 0  1+1i −1−1i −1−1i −1−1i 1 1 0 0 1 1 1 1  1+1i −1−1i  1+1i  1+1i 1 1 0 1 0 1 1 1  1+1i −1+1i −1+1i  1+1i 1 1 0 1 1 0 0 0  1+1i −1+1i  1−1i −1−1i 1 1 1 0 0 1 0 0  1+1i  1−1i −1+1i −1−1i 1 1 1 0 1 0 1 1  1+1i  1−1i  1−1i  1+1i 1 1 1 1 0 0 1 1  1+1i  1+1i −1−1i  1+1i 1 1 1 1 1 1 0 0  1+1i  1+1i  1+1i −1−1i

(21) These symbols 201-204 have an overall of 4 possible states of polarization with the condition that the state of polarization in T.sub.2 is opposite to the one of T.sub.1. The constellation has a high symmetry. The structure is such that the each constellation point has the same number of neighbors. The neighbors are located at 4 different Euclidean distances, as shown on the following table.

(22) TABLE-US-00006 Euclidean Distance Number of neighboring symbols 2.82 4 4 22 4.89 4 5.65 1

(23) The above table shows that every point of the constellation has 4, 22, 4 and 1 symbols at Euclidean distances of 2.82, 4, 4.89 and 5.65, respectively.

(24) In the second exemplary embodiment, the modulation format is defined in 8D: I, Q, polarization and two consecutive time slots. To map bits into symbols 201-204, the following approach is used: from 7 information bits of the data signal 101, referred to as [b.sub.1, b.sub.2, b.sub.3, b.sub.4, b.sub.5, b.sub.6, b.sub.7], one overhead bit (b′) is obtained using the following equation:
b1′=b1 XOR b4 XOR b6 XOR(b1 XOR b2)AND(b3 XOR b4 XOR b5 XOR b6)XOR(b3 XOR b4)AND(b5 XOR b6)

(25) Thus, the set of [b.sub.1, b.sub.2, b.sub.3, b.sub.4, b.sub.5, b.sub.6, b.sub.7, b′] is obtained. The mapping is then done as follows. The first two bits [b.sub.1 b.sub.2] are used to select a symbol 201-204 from the set 200 (QPSK constellation) shown in FIG. 2. These symbols represents the 2 dimensions I and Q of the X polarization on the time slot T.sub.1. Using the same approach, I and Q symbols of Y polarization on T.sub.1, X polarization on T.sub.2 and finally Y polarization on T.sub.2 are obtained using the bits [b.sub.3 b.sub.4], [b.sub.5 b.sub.6] and finally [.sub.b7 b′], respectively. At the end, a spectral efficiency of 3.5 bits/transmission time slot (7 bits in 8 dimensions) is reached, and all obtained symbols 201-204 are given in the following table. The labelling (mapping from bits to symbols 201-204) of each symbol 201-204 is given in the table as well, because as mentioned before, different labelling may result on different linear channel performance (except for equivalent constellations related by symmetry).

(26) TABLE-US-00007 Labelling (from left to right) Time slot T.sub.1 Time slot T.sub.2 7 bits b1 . . . b7, X Y X Y and 1 over- polar- polar- polar- polar- head bit b’ ization ization ization ization 0 0 0 0 0 0 0 1 −1−1i −1−1i −1−1i −1+1i 0 0 0 0 0 0 1 1 −1−1i −1−1i −1−1i  1+1i 0 0 0 0 0 1 0 0 −1−1i −1−1i −1+1i −1−1i 0 0 0 0 0 1 1 0 −1−1i −1−1i −1+1i  1−1i 0 0 0 0 1 0 0 1 −1−1i −1−1i  1−1i −1+1i 0 0 0 0 1 0 1 1 −1−1i −1−1i  1−1i  1+1i 0 0 0 0 1 1 0 0 −1−1i −1−1i  1+1i −1−1i 0 0 0 0 1 1 1 0 −1−1i −1−1i  1+1i  1−1i 0 0 0 1 0 0 0 0 −1−1i −1+1i −1−1i −1−1i 0 0 0 1 0 0 1 0 −1−1i −1+1i −1−1i  1−1i 0 0 0 1 0 1 0 0 −1−1i −1+1i −1+1i −1−1i 0 0 0 1 0 1 1 0 −1−1i −1+1i −1+1i  1−1i 0 0 0 1 1 0 0 1 −1−1i −1+1i  1−1i −1+1i 0 0 0 1 1 0 1 1 −1−1i −1+1i  1−1i  1+1i 0 0 0 1 1 1 0 1 −1−1i −1+1i  1+1i −1+1i 0 0 0 1 1 1 1 1 −1−1i −1+1i  1+1i  1+1i 0 0 1 0 0 0 0 1 −1−1i  1−1i −1−1i −1+1i 0 0 1 0 0 0 1 1 −1−1i  1−1i −1−1i  1+1i 0 0 1 0 0 1 0 1 −1−1i  1−1i −1+1i −1+1i 0 0 1 0 0 1 1 1 −1−1i  1−1i −1+1i  1+1i 0 0 1 0 1 0 0 0 −1−1i  1−1i  1−1i −1−1i 0 0 1 0 1 0 1 0 −1−1i  1−1i  1−1i  1−1i 0 0 1 0 1 1 0 0 −1−1i  1−1i  1+1i −1−1i 0 0 1 0 1 1 1 0 −1−1i  1−1i  1+1i  1−1i 0 0 1 1 0 0 0 0 −1−1i  1+1i −1−1i −1−1i 0 0 1 1 0 0 1 0 −1−1i  1+1i −1−1i  1−1i 0 0 1 1 0 1 0 1 −1−1i  1+1i −1+1i −1+1i 0 0 1 1 0 1 1 1 −1−1i  1+1i −1+1i  1+1i 0 0 1 1 1 0 0 0 −1−1i  1+1i  1−1i −1−1i 0 0 1 1 1 0 1 0 −1−1i  1+1i  1−1i  1−1i 0 0 1 1 1 1 0 1 −1−1i  1+1i  1+1i −1+1i 0 0 1 1 1 1 1 1 −1−1i  1+1i  1+1i  1+1i 0 1 0 0 0 0 0 1 −1+1i −1−1i −1−1i −1+1i 0 1 0 0 0 0 1 1 −1+1i −1−1i −1−1i  1+1i 0 1 0 0 0 1 0 1 −1+1i −1−1i −1+1i −1+1i 0 1 0 0 0 1 1 1 −1+1i −1−1i −1+1i  1+1i 0 1 0 0 1 0 0 0 −1+1i −1−1i  1−1i −1−1i 0 1 0 0 1 0 1 0 −1+1i −1−1i  1−1i  1−1i 0 1 0 0 1 1 0 0 −1+1i −1−1i  1+1i −1−1i 0 1 0 0 1 1 1 0 −1+1i −1−1i  1+1i  1−1i 0 1 0 1 0 0 0 1 −1+1i −1+1i −1−1i −1+1i 0 1 0 1 0 0 1 1 −1+1i −1+1i −1−1i  1+1i 0 1 0 1 0 1 0 0 −1+1i −1+1i −1+1i −1−1i 0 1 0 1 0 1 1 0 −1+1i −1+1i −1+1i  1−1i 0 1 0 1 1 0 0 1 −1+1i −1+1i  1−1i −1+1i 0 1 0 1 1 0 1 1 −1+1i −1+1i  1−1i  1+1i 0 1 0 1 1 1 0 0 −1+1i −1+1i  1+1i −1−1i 0 1 0 1 1 1 1 0 −1+1i −1+1i  1+1i  1−1i 0 1 1 0 0 0 0 0 −1+1i  1−1i −1−1i −1−1i 0 1 1 0 0 0 1 0 −1+1i  1−1i −1−1i  1−1i 0 1 1 0 0 1 0 1 −1+1i  1−1i −1+1i −1+1i 0 1 1 0 0 1 1 1 −1+1i  1−1i −1+1i  1+1i 0 1 1 0 1 0 0 0 −1+1i  1−1i  1−1i −1−1i 0 1 1 0 1 0 1 0 −1+1i  1−1i  1−1i  1−1i 0 1 1 0 1 1 0 1 −1+1i  1−1i  1+1i −1+1i 0 1 1 0 1 1 1 1 −1+1i  1−1i  1+1i  1+1i 0 1 1 1 0 0 0 0 −1+1i  1+1i −1−1i −1−1i 0 1 1 1 0 0 1 0 −1+1i  1+1i −1−1i  1−1i 0 1 1 1 0 1 0 0 −1+1i  1+1i −1+1i −1−1i 0 1 1 1 0 1 1 0 −1+1i  1+1i −1+1i  1−1i 0 1 1 1 1 0 0 1 −1+1i  1+1i  1−1i −1+1i 0 1 1 1 1 0 1 1 −1+1i  1+1i  1−1i  1+1i 0 1 1 1 1 1 0 1 −1+1i  1+1i  1+1i −1+1i 0 1 1 1 1 1 1 1 −1+1i  1+1i  1+1i  1+1i 1 0 0 0 0 0 0 0  1−1i −1−1i −1−1i −1−1i 1 0 0 0 0 0 1 0  1−1i −1−1i −1−1i  1−1i 1 0 0 0 0 1 0 0  1−1i −1−1i −1+1i −1−1i 1 0 0 0 0 1 1 0  1−1i −1−1i −1+1i  1−1i 1 0 0 0 1 0 0 1  1−1i −1−1i  1−1i −1+1i 1 0 0 0 1 0 1 1  1−1i −1−1i  1−1i  1+1i 1 0 0 0 1 1 0 1  1−1i −1−1i  1+1i −1+1i 1 0 0 0 1 1 1 1  1−1i −1−1i  1+1i  1+1i 1 0 0 1 0 0 0 0  1−1i −1+1i −1−1i −1−1i 1 0 0 1 0 0 1 0  1−1i −1+1i −1−1i  1−1i 1 0 0 1 0 1 0 1  1−1i −1+1i −1+1i −1+1i 1 0 0 1 0 1 1 1  1−1i −1+1i −1+1i  1+1i 1 0 0 1 1 0 0 0  1−1i −1+1i  1−1i −1−1i 1 0 0 1 1 0 1 0  1−1i −1+1i  1−1i  1−1i 1 0 0 1 1 1 0 1  1−1i −1+1i  1+1i −1+1i 1 0 0 1 1 1 1 1  1−1i −1+1i  1+1i  1+1i 1 0 1 0 0 0 0 1  1−1i  1−1i −1−1i −1+1i 1 0 1 0 0 0 1 1  1−1i  1−1i −1−1i  1+1i 1 0 1 0 0 1 0 0  1−1i  1−1i −1+1i −1−1i 1 0 1 0 0 1 1 0  1−1i  1−1i −1+1i  1−1i 1 0 1 0 1 0 0 1  1−1i  1−1i  1−1i −1+1i 1 0 1 0 1 0 1 1  1−1i  1−1i  1−1i  1+1i 1 0 1 0 1 1 0 0  1−1i  1−1i  1+1i −1−1i 1 0 1 0 1 1 1 0  1−1i  1−1i  1+1i  1−1i 1 0 1 1 0 0 0 1  1−1i  1+1i −1−1i −1+1i 1 0 1 1 0 0 1 1  1−1i  1+1i −1−1i  1+1i 1 0 1 1 0 1 0 1  1−1i  1+1i −1+1i −1+1i 1 0 1 1 0 1 1 1  1−1i  1+1i −1+1i  1+1i 1 0 1 1 1 0 0 0  1−1i  1+1i  1−1i −1−1i 1 0 1 1 1 0 1 0  1−1i  1+1i  1−1i  1−1i 1 0 1 1 1 1 0 0  1−1i  1+1i  1+1i −1−1i 1 0 1 1 1 1 1 0  1−1i  1+1i  1+1i  1−1i 1 1 0 0 0 0 0 0  1+1i −1−1i −1−1i −1−1i 1 1 0 0 0 0 1 0  1+1i −1−1i −1−1i  1−1i 1 1 0 0 0 1 0 1  1+1i −1−1i −1+1i −1+1i 1 1 0 0 0 1 1 1  1+1i −1−1i −1+1i  1+1i 1 1 0 0 1 0 0 0  1+1i −1−1i  1−1i −1−1i 1 1 0 0 1 0 1 0  1+1i −1−1i  1−1i  1−1i 1 1 0 0 1 1 0 1  1+1i −1−1i  1+1i −1+1i 1 1 0 0 1 1 1 1  1+1i −1−1i  1+1i  1+1i 1 1 0 1 0 0 0 1  1+1i −1+1i −1−1i −1+1i 1 1 0 1 0 0 1 1  1+1i −1+1i −1−1i  1+1i 1 1 0 1 0 1 0 1  1+1i −1+1i −1+1i −1+1i 1 1 0 1 0 1 1 1  1+1i −1+1i −1+1i  1+1i 1 1 0 1 1 0 0 0  1+1i −1+1i  1−1i −1−1i 1 1 0 1 1 0 1 0  1+1i −1+1i  1−1i  1−1i 1 1 0 1 1 1 0 0  1+1i −1+1i  1+1i −1−1i 1 1 0 1 1 1 1 0  1+1i −1+1i  1+1i  1−1i 1 1 1 0 0 0 0 0  1+1i  1−1i −1−1i −1−1i 1 1 1 0 0 0 1 0  1+1i  1−1i −1−1i  1−1i 1 1 1 0 0 1 0 0  1+1i  1−1i −1+1i −1−1i 1 1 1 0 0 1 1 0  1+1i  1−1i −1+1i  1−1i 1 1 1 0 1 0 0 1  1+1i  1−1i  1−1i −1+1i 1 1 1 0 1 0 1 1  1+1i  1−1i  1−1i  1+1i 1 1 1 0 1 1 0 1  1+1i  1−1i  1+1i −1+1i 1 1 1 0 1 1 1 1  1+1i  1−1i  1+1i  1+1i 1 1 1 1 0 0 0 1  1+1i  1+1i −1−1i −1+1i 1 1 1 1 0 0 1 1  1+1i  1+1i −1−1i  1+1i 1 1 1 1 0 1 0 0  1+1i  1+1i −1+1i −1−1i 1 1 1 1 0 1 1 0  1+1i  1+1i −1+1i  1−1i 1 1 1 1 1 0 0 1  1+1i  1+1i  1−1i −1+1i 1 1 1 1 1 0 1 1  1+1i  1+1i  1−1i  1+1i 1 1 1 1 1 1 0 0  1+1i  1+1i  1+1i −1−1i 1 1 1 1 1 1 1 0  1+1i  1+1i  1+1i  1−1i

(27) These symbols have 4 possible states of polarization with the condition that the state of polarization on T.sub.2 is either opposite to or different from the state of polarization on T.sub.1. The constellation has a high symmetry. The structure is such that the each constellation point has the same number of neighbors. The neighbors are located at 8 different Euclidean distances, as shown on the following table.

(28) TABLE-US-00008 Euclidean Number of Distance neighboring symbols 2 4 2.82 12 3.46 28 4 38 4.47 28 4.89 12 5.29 4 5.65 1

(29) Basically, every point of the constellation has 8 symbols at Euclidean distance of 2, 12 symbols at an Euclidean distance of 2.82, and so on. As for the modulation format of the previous embodiment, this structure is highly symmetrical, which yields good linear channel performance.

(30) In the third exemplary embodiment, the modulation format is defined in 8D: I, Q, polarization and two consecutive time slots. To map bits into symbols 201-204, the following approach is used: from 4 information bits of the data signal 101, referred to as [b.sub.1, b.sub.2, b.sub.3, b.sub.4], four overhead bits [b′.sub.1, b′.sub.2, b′.sub.3, b′.sub.4] are obtained using the following equation:
b1′=b1 XOR b2 XOR b3
b2′=b1 XOR b2 XOR b5
b3′=b1 XOR b3 XOR b5
b4′=b2 XOR b3 XOR b5

(31) Thus, the set of [b.sub.1, b.sub.2, b.sub.3, b′.sub.1, b.sub.4, b′.sub.2, b′.sub.3, b′.sub.4] is obtained. The mapping is then done as follows. The first two bits [b.sub.1 b.sub.2] are used to select a symbol 201-204 from the set 200 (QPSK constellation) shown in FIG. 2. These symbols represents the 2 dimensions I and Q of the X polarization on the time slot T.sub.1. Using the same approach, I and Q symbols of Y polarization on T.sub.1, X polarization on T.sub.2 and finally Y polarization on T.sub.2 are obtained using the bits [b.sub.3 b′.sub.1], [b.sub.4 b′.sub.2] and finally [b′.sub.3 b′.sub.4], respectively. At the end, a spectral efficiency of 2 bits/transmission time slot (4 bits in 8 dimensions) is reached, and all obtained symbols 201-204 are given in the following table. The labelling (mapping from bits to symbols 201-204) of each symbol 201-204 is given in the table as well, because as mentioned before, different labelling may result on different linear channel performance (except for equivalent constellations related by symmetry).

(32) TABLE-US-00009 Labelling (from the left to the right: 3 information bits, 1 Time slot T.sub.1 Time slot T.sub.2 parity bit, 1 information bit, 3 X Y X Y parity bits) polarization polarization polarization polarization 00000011 −1−1i −1−1i −1−1i +1+1i 00001100 −1−1i −1−1i +1+1i −1−1i 00110000 −1−1i +1+1i −1−1i −1−1i 00111111 −1−1i +1+1i +1+1i +1+1i 01010110 −1+1i −1+1i −1+1i +1−1i 01011001 −1+1i −1+1i +1−1i −1+1i 01100101 −1+1i +1−1i −1+1i −1+1i 01101010 −1+1i +1−1i +1−1i +1−1i 10010101 +1−1i −1+1i −1+1i −1+1i 10011010 +1−1i −1+1i +1−1i +1−1i 10100110 +1−1i +1−1i −1+1i +1−1i 10101001 +1−1i +1−1i +1−1i −1+1i 11000000 +1+1i −1−1i −1−1i −1−1i 11001111 +1+1i −1−1i +1+1i +1+1i 11110011 +1+1i +1+1i −1−1i +1+1i 11111100 +1+1i +1+1i +1+1i −1−1i

(33) These symbols have 4 possible states of polarization with the condition that the state of polarization on T.sub.2 is opposite to the state of polarization on T.sub.1. The constellation has a high symmetry. The structure is such that the each constellation point has the same number of neighbors. The neighbors are located at 2 different Euclidean distances, as shown on the following table.

(34) TABLE-US-00010 Euclidean Number Distance of neighboring symbols 4 14 5.65 1

(35) Basically, every point of the constellation has 14 symbols at Euclidean distance of 4 and one symbol at an Euclidean distance of 5.65. As for the modulation format of the previous embodiment, this structure is highly symmetrical, which yields good linear channel performance.

(36) In the fourth exemplary embodiment, the modulation format is defined in 8D: I, Q, polarization and two consecutive time slots. To map bits into symbols 201-204, the following approach is used: from 6 information bits of the data signal 101, referred to as [b.sub.1, b.sub.2, b.sub.3, b.sub.4, b.sub.5, b.sub.6], two overhead bits [b′.sub.1, b′.sub.2] are obtained using the following equation:
b1′=b2 XOR b3 XOR b5 XOR(b1 XOR b2)AND(b3 XOR b4 XOR b5 XOR b6)XOR(b3 XOR b4)AND(b5 XOR b6)
b2′=b1 XOR b4 XOR b6 XOR(b1 XOR b2)AND(b3 XOR b4 XOR b5 XOR b6)XOR(b3 XOR b4)AND(b5 XOR b6)

(37) Thus, the set of [b.sub.1, b.sub.2, b.sub.3, b.sub.4, b.sub.5, b.sub.6, b′.sub.1, b′.sub.2] is obtained. The mapping is then done as follows. The first two bits [b.sub.1 b.sub.2] are used to select a symbol 201-204 from the set 200 (QPSK constellation) shown in FIG. 2. These symbols represents the 2 dimensions I and Q of the X polarization on the time slot T.sub.1. Using the same approach, I and Q symbols of Y polarization on T.sub.1, X polarization on T.sub.2 and finally Y polarization on T.sub.2 are obtained using the bits [b.sub.3 b.sub.4], [b.sub.5 b.sub.6] and finally [b′.sub.1 b′.sub.2], respectively. At the end, a spectral efficiency of 3 bits/transmission time slot (6 bits in 8 dimensions) is reached, and all obtained symbols 201-204 are given in the following table. The labelling (mapping from bits to symbols 201-204) of each symbol 201-204 is given in the table as well, because as mentioned before, different labelling may result on different linear channel performance (except for equivalent constellations related by symmetry).

(38) TABLE-US-00011 Labelling (from the Time slot T.sub.1 Time slot T.sub.2 left to the right: 6 X Y X Y information bits polar- polar- polar- polar- and 2 parity bit) ization ization ization ization 00000011 −1−1i −1−1i −1−1i +1+1i 00000110 −1−1i −1−1i −1+1i +1−1i 00001001 −1−1i −1−1i +1−1i −1+1i 00001100 −1−1i −1−1i +1+1i −1−1i 00010010 −1−1i −1+1i −1−1i +1−1i 00010100 −1−1i −1+1i −1+1i −1−1i 00011011 −1−1i −1+1i +1−1i +1+1i 00011101 −1−1i −1+1i +1+1i −1+1i 00100001 −1−1i +1−1i −1−1i −1+1i 00100111 −1−1i +1−1i −1+1i +1+1i 00101000 −1−1i +1−1i +1−1i −1−1i 00101110 −1−1i +1−1i +1+1i +1−1i 00110000 −1−1i +1+1i −1−1i −1−1i 00110101 −1−1i +1+1i −1+1i −1+1i 00111010 −1−1i +1+1i +1−1i +1−1i 00111111 −1−1i +1+1i +1+1i +1+1i 01000001 −1+1i −1−1i −1−1i −1+1i 01000111 −1+1i −1−1i −1+1i +1+1i 01001000 −1+1i −1−1i +1−1i −1−1i 01001110 −1+1i −1−1i +1+1i +1−1i 01010011 −1+1i −1+1i −1−1i +1+1i 01010110 −1+1i −1+1i −1+1i +1−1i 01011001 −1+1i −1+1i +1−1i −1+1i 01011100 −1+1i −1+1i +1+1i −1−1i 01100000 −1+1i +1−1i −1−1i −1−1i 01100101 −1+1i +1−1i −1+1i −1+1i 01101010 −1+1i +1−1i +1−1i +1−1i 01101111 −1+1i +1−1i +1+1i +1+1i 01110010 −1+1i +1+1i −1−1i +1−1i 01110100 −1+1i +1+1i −1+1i −1−1i 01111011 −1+1i +1+1i +1−1i +1+1i 01111101 −1+1i +1+1i +1+1i −1+1i 10000010 +1−1i −1−1i −1−1i +1−1i 10000100 +1−1i −1−1i −1+1i −1−1i 10001011 +1−1i −1−1i +1−1i +1+1i 10001101 +1−1i −1−1i +1+1i −1+1i 10010000 +1−1i −1+1i −1−1i −1−1i 10010101 +1−1i −1+1i −1+1i −1+1i 10011010 +1−1i −1+1i +1−1i +1−1i 10011111 +1−1i −1+1i +1+1i +1+1i 10100011 +1−1i +1−1i −1−1i +1+1i 10100110 +1−1i +1−1i −1+1i +1−1i 10101001 +1−1i +1−1i +1−1i −1+1i 10101100 +1−1i +1−1i +1+1i −1−1i 10110001 +1−1i +1+1i −1−1i −1+1i 10110111 +1−1i +1+1i −1+1i +1+1i 10111000 +1−1i +1+1i +1−1i −1−1i 10111110 +1−1i +1+1i +1+1i +1−1i 11000000 +1+1i −1−1i −1−1i −1−1i 11000101 +1+1i −1−1i −1+1i −1+1i 11001010 +1+1i −1−1i +1−1i +1−1i 11001111 +1+1i −1−1i +1+1i +1+1i 11010001 +1+1i −1+1i −1−1i −1+1i 11010111 +1+1i −1+1i −1+1i +1+1i 11011000 +1+1i −1+1i +1−1i −1−1i 11011110 +1+1i −1+1i +1+1i +1−1i 11100010 +1+1i +1−1i −1−1i +1−1i 11100100 +1+1i +1−1i −1+1i −1−1i 11101011 +1+1i +1−1i +1−1i +1+1i 11101101 +1+1i +1−1i +1+1i −1+1i 11110011 +1+1i +1+1i −1−1i +1+1i 11110110 +1+1i +1+1i −1+1i +1−1i 11111001 +1+1i +1+1i +1−1i −1+1i 11111100 +1+1i +1+1i +1+1i −1−1i

(39) These symbols have 4 possible states of polarization with the condition that the state of polarization on T.sub.2 is opposite to the state of polarization on T.sub.1. The constellation has a high symmetry. The structure is such that the each constellation point has the same number of neighbors. The neighbors are located at 4 different Euclidean distances, as shown on the following table.

(40) TABLE-US-00012 Euclidean Number of Distance neighboring symbols 2.82 12 4 38 4.89 12 5.65 1

(41) Basically, every point of the constellation has 12 symbols at Euclidean distance of 2.82, 38 symbols at an Euclidean distance of 4, and so on. As for the modulation format of the previous embodiment, this structure is highly symmetrical, which yields good linear channel performance.

(42) The four exemplary modulation formats presented above, provide the optical transmitter 100 with a linear and nonlinear channel performance that exceeds the state of the art. In particular, the exemplary modulation format with a spectral efficiency of 2.5 bit/transmission time slot has a better nonlinear performance (found to be 0.35 dB higher in Q2 factor) than the one of a corresponding conventional solution, even though the linear performance is the same. The modulation format with spectral efficiency of 3.5 bit/transmission time slot has better linear and nonlinear performance. This is because the set 200 of symbols 201-0204 (base constellation) has a higher Euclidian distance, which gives better linear performance. As mentioned above, this can be achieved because the polarization-balance criterion is relaxed to polarization alternating. This allows using the base constellation as for example shown in FIG. 2. Modulation formats of spectral efficiencies of 2 and 3 bit/transmission time slot have the same performance of the state-of-the-art but are generated using Boolean equations, which simplify the mapper and demapper and allow low complexity implementation, which results on low power consuming solution.

(43) FIG. 5 shows a method 500 of optically transmitting a data signal 101. The method 500 may be performed by the optical transmitter 100. The method comprises a step 501 of encoding 501 the data signal 101 by selecting based on a bit sequence a first symbol and a second symbol from a set 200 of four symbols 201-204 for each one of at least two transmission time slots. This step 501 may be performed by the encoder 102. The method 500 further comprises a step 502 of using in each transmission time slot the first symbol to modulate a first carrier wave and the second symbol to modulate a second carrier wave, and transmitting the two carrier waves over orthogonal polarizations of an optical carrier 104. This step 501 may be performed by the modulator 103. Symbols 201-204 in consecutive transmission time slots have non-identical polarization states.

(44) The present invention has been described in conjunction with various embodiments as examples as well as implementations. However, other variations can be understood and effected by those persons skilled in the art and practicing the claimed invention, from the studies of the drawings, this disclosure and the independent claims. In the claims as well as in the description the word “comprising” does not exclude other elements or steps and the indefinite article “a” or “an” does not exclude a plurality. A single element or other unit may fulfill the functions of several entities or items recited in the claims. The mere fact that certain measures are recited in the mutual different dependent claims does not indicate that a combination of these measures cannot be used in an advantageous implementation.