Using the four dimensions of the optical field (phase and quadrature
components of the orthogonal polarization states) to encode and detect
a signal enables to design modulation formats that present a better
sensitivity than modulation formats using classical two-dimensional
constellations (QAM) combined with polarization division multiplexing
Such 4D constellations can be generated using classical polarization-
multiplexed IQ modulators combined to high-speed digital-to-analog
converters (DACs) that are required to generate the multilevel
electrical driving signals. However, for simple constellations the
use of DACs can be omitted. For instance, this is the case of
polarization-switched QPSK (PS QPSK) and its
polarization-division-multiplexed counterpart PDM QPSK, which makes
these formats attractive for high-speed low-cost solutions.
The purpose of this example is to compare the noise performance of
polarization-switched QPSK and polarization-division-multiplexed QPSK.
The performance of polarization-switched QPSK and polarization-division-multiplexed QPSK is compared for a back-to-back
configuration, where noise loading is performed in front of the receiver
The constellation diagrams of 24-Gbaud polarization-switched QPSK and polarization-division-multiplexed QPSK are displayed after phase
and frequency recovery in
for a 20-dB OSNR.
At equal baud rate (24 Gbaud), PS QPSK presents a better performance than PDM QPSK (see
but enables the coding of 3 bits per symbol only compared to 4 bits per symbol for
PDM QPSK. For a fair comparison, performance at equal bit rates should be considered.
For this, two approaches are possible: either increasing the baud rate of the PS-QPSK
signal to 40 Gbaud or keeping the same baud rate for both formats, but using the additional
bit available on the PDM-QPSK format to perform forward error correction.
At an equal raw bit rate, polarization-switched QPSK presents a slightly better performance than PDM QPSK (see
However, when using a simple Hamming (15-11) code with 27% overhead, the performance
of both formats becomes similar. When considering a more efficient code, such as a
LDPC (4161-437) code with 17% overhead combined with the MINSUM detection, the
performance of coded PDM QPSK outperforms the one of uncoded PS QPSK  (see
Keywords: Polarization Division Multiplexing (PDM), Quadrature Phase-Shift Keying (QPSK), Polarization-switched (PS), PDM QPSK, DP QPSK, PS QPSK, coded modulation, 4D modulation, FEC, BER
Similar demonstrations are available in VPItransmissionMaker Optical Systems and on the VPIphotonics Forum.
 M. Karlsson, E. Agrell, Power -Efficient Modulation Schemes, Chap. 5 in Impact of Nonlinearities on Fiber Optic Communications, Editors: Shiva Kumar, Springer, 2011
 B. Krongold et al. 'Comparison Between PS-QPSK and PDM-QPSK With Equal Rate and Bandwidth', IEEE Photonics Technology Letters, Vol. 24, No. 3, February 1, 2012, pp. 203-205