Tobias Fehenberger

On achievable rates for long-haul fiber-optic communications.

Lower bounds on mutual information (MI) of long-haul optical fiber systems for hard-decision and soft-decision decoding are studied. Ready-to-use expressions to calculate the MI are presented. Extensive numerical simulations are used to quantify how changes in the optical transmitter, receiver, and channel affect the achievable transmission rates of the system. Special emphasis is put to the use of different quadrature amplitude modulation formats, channel spacings, digital back-propagation schemes and probabilistic shaping. The advantages of using MI over the prevailing Q-factor as a figure of merit of coded optical systems are also highlighted.

Comparison of the nonlinear transmission performance of quasi-Nyquist WDM and reduced guard interval OFDM

The nonlinear transmission performance of quasi-Nyquist wavelength-division multiplexing (qN-WDM) and reduced guard interval orthogonal frequency-division multiplexing (RGI-OFDM) using polarization-division multiplexing quadrature phase-shift-keying (PDM-QPSK) and quadrature amplitude modulation (PDM-QAM-8 and PDM-QAM-16) with high information spectral densities have been compared for the first time, both by simulations and analytically. The results show that both systems are able to reach similar maximum transmission distances of approximately 6700km, 2600km and 1100km over standard single-mode fibre for the spectral efficiencies of 3.43 bits/s/Hz, 5.25 bits/s/Hz and 7 bits/s/Hz respectively.

On Probabilistic Shaping of Quadrature Amplitude Modulation for the Nonlinear Fiber Channel

Different aspects of probabilistic shaping for a multispan optical communication system are studied. First, a numerical analysis of the additive white Gaussian noise (AWGN) channel investigates the effect of using a small number of input probability mass functions (PMFs) for a range of signal-to-noise ratios (SNRs), instead of optimizing the constellation shaping for each SNR. It is shown that if a small penalty of at most 0.1 dB SNR to the full shaping gain is acceptable, just two shaped PMFs are required per quadrature amplitude modulation (QAM) over a large SNR range. For a multispan wavelength division multiplexing optical fiber system with 64QAM input, it is shown that just one PMF is required to achieve large gains over uniform input for distances from 1400 to 3000 km. Using recently developed theoretical models that extend the Gaussian noise (GN) model and full-field split-step simulations, we illustrate the ramifications of probabilistic shaping on the effective SNR after fiber propagation. Our results show that, for a fixed average optical launch power, a shaping gain is obtained for the noise contributions from fiber amplifiers and modulation-independent nonlinear interference (NLI), whereas shaping simultaneously causes a penalty as it leads to an increased NLI. However, this nonlinear shaping loss is found to have a relatively minor impact, and optimizing the shaped PMF with a modulation-dependent GN model confirms that the PMF found for AWGN is also a good choice for a multi-span fiber system.

LDPC coded modulation with probabilistic shaping for optical fiber systems

An LDPC coded modulation scheme with probabilistic shaping, optimized interleavers and noniterative demapping is proposed. Full-field simulations show an increase in transmission distance by 8% compared to uniformly distributed input.

Sensitivity Gains by Mismatched Probabilistic Shaping for Optical Communication Systems

Probabilistic shaping of quadrature amplitude modulation (QAM) is used to enhance the sensitivity of an optical communication system. Sensitivity gains of 0.43 and 0.8 dB are demonstrated in back-to-back experiments by the shaping of 16QAM and 64QAM, respectively. Furthermore, numerical simulations are used to prove the robustness of probabilistic shaping to a mismatch between the constellation used and the signal-to-noise ratio (SNR) of the channel. It is found that, accepting a 0.1-dB SNR penalty, only four shaping distributions are required to support these gains for 64QAM.

Low-Complexity Tracking of Laser and Nonlinear Phase Noise in WDM Optical Fiber Systems

In this paper, the wavelength division multiplexed (WDM) fiber optic channel is considered. It is shown that for ideal distributed Raman amplification (IDRA), the Wiener process model is suitable for the non-linear phase noise due to cross phase modulation from neighboring channels. Based on this model, a phase noise tracking algorithm is presented. We approximate the distribution of the phase noise at each time instant by a mixture of Tikhonov distributions, and derive a closed form expression for the posterior probabilities of the input symbols. This reduces the complexity dramatically compared to previous trellis-based approaches, which require numerical integration. Further, the proposed method performs very well in low-to-moderate signal-to-noise ratio (SNR), where standard decision directed (DD) methods, especially for high-order modulation, fail. The proposed algorithm does not rely on averaging, and therefore does not experience high error floors at high SNR in severe phase noise scenarios. The laser linewidth (LLW) tolerance is thereby increased for the entire SNR region compared to previous DD methods. In IDRA WDM links, the algorithm is shown to effectively combat the combined effect of both laser phase noise and non-linear phase noise, which cannot be neglected in such scenarios. In a more practical lumped amplification scheme, we show near-optimal performance for 16 QAM, 64 QAM, and 256 QAM with LLW up to 100 kHz, and reasonable performance for LLW of 1 MHz for 16 QAM and 64 QAM, at the moderate received SNR region. The performance in these cases is close to the information rate achieved by the above mentioned trellis processing.

Compensation of XPM interference by blind tracking of the nonlinear phase in WDM systems with QAM input

Exploiting temporal correlations in the phase, achievable rates are studied and a blind trellis-based receiver is presented. Gains of 0.5 bit per symbol are found in point-to-point links irrespective of the symbol rate. These gains disappear in network configurations.

On the impact of carrier phase estimation on phase correlations in coherent fiber transmission

Carrier phase estimation (CPE) is an integral part of the digital signal processing (DSP) of coherent optical communication systems as it compensates laser phase noise (LPN) introduced by free-running transmitter and local oscillating (LO) lasers. Nonlinear interactions during propagation are another source of correlated phase noise. In this paper, we show through simulations and in experiments that blind decision-directed (DD) CPE with regular block lengths removes a large portion of the memory. This makes it virtually impossible in practice to quantify correlations that come from propagation effects, or to obtain rate gains by exploiting the nonlinear phase noise (NLPN). Larger CPE block lengths leave the memory partly intact. This, however, comes at the expense of reduced information rates. We are able to fully recover this rate loss in simulations by using idealized processing of phase distortions. In experiments with full DSP, an almost full rate recovery is reported.

Digital Back-Propagation of a Superchannel: Achievable Rates and Adaption of the GN Model

The impact of back-propagating an entire superchannel and sub-channels thereof is quantified by evaluating mutual information. We report a 50 Gb/s per channel increase in data rate. Additionally, the Gaussian Noise model is adapted to take into account back-propagation.

Improved achievable information rates by optimized four-dimensional demappers in optical transmission experiments

We experimentally study different four-dimensional demappers in a dispersion-managed fiber system. The proposed blind algorithm is shown to offer gains of 0.2 bits per 4D symbol for DP-16QAM.