Constellation Shaping for WDM Systems Using 256QAM/1024QAM With Probabilistic Optimization

Abstract

In this paper, probabilistic shaping is numerically and experimentally investigated for increasing the transmission reach of wavelength division multiplexed (WDM) optical communication systems employing quadrature amplitude modulation (QAM). An optimized probability mass function (PMF) of the QAM symbols is first found from a modified Blahut-Arimoto algorithm for the optical channel. A turbo coded bit interleaved coded modulation system is then applied, which relies on manyto-one labeling to achieve the desired PMF, thereby achieving shaping gains. Pilot symbols at rate at most 2% are used for synchronization and equalization, making it possible to receive input constellations as large as 1024QAM. The system is evaluated experimentally on a 10 GBaud, 5 channels WDM setup. The maximum system reach is increased w.r.t. standard 1024QAM by 20% at input data rate of 4.65 bits/symbol and up to 75% at 5.46 bits/symbol. It is shown that rate adaptation does not require changing of the modulation format. The performance of the proposed 1024QAM shaped system is validated on all 5 channels of the WDM signal for selected distances and rates. Finally, it is shown via EXIT charts and BER analysis that iterative demapping, while generally beneficial to the system, is not a requirement for achieving the shaping gain.

Digital signal processing for fiber nonlinearities [Invited]

“…In order to achieve the non-uniform PMF of the output, a many-to-one bit-to-symbol labeling was proposed in a combination with a convolutional turbo code. It was shown in [63], that this optimization slightly outperforms the MB family, which for two constellation symbols x i and x j has the restriction of p(x i ) > p(x j ) for |x i | < |x j |. However, similar experimental gains were achieved as in [60], suggesting that the specific PMF shape is non-consequential in practice under the constraint of independent symbols in each time slot.…”

“…It was demonstrated in [61,63], that pilot symbols can be used at a rate of 1-2% for both purposes. This technique also improves the tolerance to phase slips, allows for adaptive equalization, and can potentially be used for frequency and clock recovery.…”

Temporal Probabilistic Shaping for Mitigation of Nonlinearities in Optical Fiber Systems

“…In particular, probabilistic shaping of quadrature amplitude modulation (QAM) constellations is gathering popularity due to its simple integration with standard digital signal processing techniques. As recently demonstrated [1]- [4], probabilistic shaping can be integrated into coded modulation schemes with powerful forward error correcting codes, thus allowing for increased link distance while also approaching the high data rate demand that the fiber systems face. Most such systems operate based on a memoryless channel assumption due to the reduced complexity of the receiver.…”

Link-Placement Characterization of Optical Phase Conjugation for Nonlinearity Compensation

“…Polarization dependence below 0.4 dB is achieved. The total input signal power has been optimized to 2 dBm, as a trade-off between optical signal-to-noise ratio (OSNR) degradation and nonlinear distortion [10]. The input and output spectra for the 5×WDM channels after 322-km transmission are shown in Fig.…”

“…Negligible OSNR penalty (< 0.2 dB) is introduced by the conversion as seen comparing input signal to output idler after amplification and optical bandpass filtering (OBPF). Finally, the use of a high-quality (10-kHz linewidth) pump laser further ensures a negligible penalty due to pump phase noise transfer [10].…”