For transmitting data via an optical transmission signal it is a prominent approach to modulate the phase of the optical signal in dependence on the transmission data. One such approach of phase modulation is that of binary phase shift keying (BPSK), in which the phase of the optical signal may take on two distinct different states and wherein each of these two states represents either a 0 or a 1 of a transmission data bit. A further approach of phase modulation is that of quaternary phase shift keying (QPSK), in which the phase of the transmission signal may take on one out of four distinct different states and wherein each of such states represents two data bits of the transmission data. Thus, in QPSK the data transmission bits are mapped as sets of two transmission bits per set onto the different transmission symbols. Each of such of the four symbols is represented by a constellation point of a QPSK constellation scheme.
In order to increase the data rate of the optical transmission method it is a further prominent approach to also apply the concept of polarization division multiplexing (PDM). In PDM, a first optical transmission signal of a specific wavelength may be modulated in accordance to a QPSK modulation method and in dependence on first transmission data, wherein this first transmission signal has a first polarization state. Furthermore, a further optical transmission signal of the same wavelength, but of a polarization state that is orthogonal to the first polarization state may be modulated in accordance to a QPSK modulation method and in dependence on further transmission data. At a receiving side, the resulting overall optical transmission signal containing both of the previously mentioned transmission signals may be decomposed into two received transmission signals by taking into account polarization properties of the different optical transmission signals.
When relying on data transmission using PDM and QPSK in conjunction as previously described above, this may be conceived as a so-called four dimensional (4D) modulation format, wherein two dimensions are given by the real and the imaginary part of the QPSK symbol of the first optical signal and further two dimensions are given by the real and the imaginary part of the QPSK symbol of the second optical signal. A further prominent technique that may also be applied in addition to PDM and QPSK modulation is that of set partitioning. In set partitioning, not all the different possible states for the two combined rank symbols are used, but only a subset out of the possible states are chosen. For example, the first optical signal may take on any of the four possible symbols (or constellation points) of the QPSK constellation scheme, while the second optical signal may take on only two of the four possible symbols (or constellation points) of the QPSK constellation scheme. In other words, while a state is defined by a combination of the two chosen QPSK symbols, the number of states is reduced by allowing one of the QPSK symbols to take on only a subset of possible symbol values.
Such choice of subsets different constellation points as set partitioning on the one hand reduces the overall data rate in comparison to not applying set partitioning, since the first QPSK symbol may be used to transmit two bits per symbol via the different four constellation points of the QPSK constellation scheme, while the second QPSK symbol may be used to transmit only one bit per symbol, since the second QPSK symbol may take on only two out of the four different possible symbol values of the QPSK constellation scheme. On the other hand, such set partitioning allows to make a data transmission more robust, since the different QPSK symbol values (or constellation points) of the different QPSK symbols may be chosen, such that the Euclidean distance of the chosen QPSK symbol values to each other is maximized; thus, the QPSK symbol values or QPSK constellation points resulting from set partitioning have an overall distance to each other that is greater than when not performing set partitioning.
When transmitting data via a phase modulation method such as QPSK, the phase of the transmitted data symbol is estimated at the receiving side after a phase estimation and then corrected in a step of phase correction. Such phase correction may cause a so-called cycle-slip, also called phase-slip, wherein such a cycle-slip may results for a QPSK modulation method in a rotation of the constellation scheme by the angle of a multiple of π/2, thus causing data errors at the receiving side for the duration of the cycle-slip.