Olga Vassilieva

Four-dimensional (4D) constellations are optimized using geometric shaping (GS) with orthant symmetry (OS) over realistic optical channel models targeting next-generation single-span systems. The optical fiber is modeled via the Manakov equation and is implemented using the split-step Fourier method (SSFM) in a Monte-Carlo based approach. Additional noise sources and losses are added making the link model relevant in practice. Constellations are optimized for different cardinalities, forward error correction code rates, and symbol rates. The SSFM-optimized constellations are reported to offer up to 4% in reach increase with respect to conventional quadrature amplitude modulation (QAM). Comparisons against existing additive white Gaussian noise (AWGN)-optimized constellations show that SSFM-optimized constellations with OS generally negligibly outperform AWGN-optimized counterparts. This somewhat unexpected result leads to the conclusion that AWGN-optimized constellations are a good choice for realistic single-span optical links.

We propose band-wise bidirectional SCLU transmission. By counterpropagating S- and U-band signals and optimizing launch powers, we achieve maximum throughput that is 1.5% lower compared to aggregate throughput of individual band transmission.

We show that subcarrier symbol rate optimization and better laser frequency stability can maximize transmission reach of super-channels. Configurations with 1.6Tb/s subcarriers achieve longer reach with benefits of smaller size/power and easier management.

We propose, simulate, and preliminarily demonstrate experimentally optically-pumped SOAs which achieve high gain, high saturation output power, and low noise figure spanning entire C+L bands.

Four dimensional geometric shell shaping (4D-GSS) is introduced as an approach for closing the nonlinearity-caused shaping gap. This format is designed at the spectral efficiency of 8 b/4D-sym and is compared against polarization-multiplexed 16QAM (PM-16QAM) and probabilistically shaped PM-16QAM (PS-PM-16QAM) in a 400ZR-compatible transmission setup with high amount of nonlinearities. Reach increase and nonlinearity tolerance are evaluated in terms of achievable information rates and post-FEC bit-error rate. Numerical simulations for a single-span, single-channel show that 4D-GSS achieves increased nonlinear tolerance and reach increase against PM-16QAM and PS-PM-16QAM when optimized for bit-metric decoding ( $\mathrm{R}_\mathrm{BMD}$ ). In terms of $\mathrm{R}_\mathrm{BMD}$ , gains are small with a reach increase of 1.7% compared to PM-16QAM. When optimizing for mutual information, a larger reach increase of 3% is achieved compared to PM-16QAM. Moreover, the introduced GSS scheme provides a scalable framework for designing well-structured 4D modulation formats with low complexity.

We discuss performance and implementation aspects of geometric and probabilistic constellation shaping, which can be optimized for different applications. We show that symbol rate optimization with probabilistic shaping can further improve reach/capacity.

Nonlinear interference (NLI) generated during the propagation of an optical waveform through the fiber depends on the fourth order standardized moment of the channel input distribution, also known as kurtosis. Probabilistically-shaped inputs optimized for the linear Gaussian channel have a Gaussian-like distribution with high kurtosis. For optical channels, this leads to an increase in NLI power and consequently, a decrease in effective signal-to-noise ratio (SNR). In this work, we propose kurtosis-limited enumerative sphere shaping (K-ESS) as an algorithm to generate low-kurtosis shaped inputs. Numerical simulations at a shaping blocklength of 108 amplitudes demonstrate that with K-ESS, it is possible to increase the effective SNRs by 0.4 dB in a single-span single-channel scenario at 400 Gbit/s. K-ESS offers also a twofold decrease in frame error rate with respect to Gaussian-channel-optimal sphere shaping.

Nonlinear interference (NLI) generated during the propagation of an optical waveform through the fiber depends on the fourth order standardized moment of the channel input distribution, also known as kurtosis. Probabilistically-shaped inputs optimized for the linear Gaussian channel have a Gaussian-like distribution with high kurtosis. For optical channels, this leads to an increase in NLI power and consequently, a decrease in effective signal-to-noise ratio (SNR). In this work, we propose kurtosis-limited enumerative sphere shaping (K-ESS) as an algorithm to generate low-kurtosis shaped inputs. Numerical simulations at a shaping blocklength of 108 amplitudes demonstrate that with K-ESS, it is possible to increase the effective SNRs by 0.4 dB in a single-span single-channel scenario at 400 Gbit/s. K-ESS offers also a twofold decrease in frame error rate with respect to Gaussian-channel-optimal sphere shaping.

We demonstrate how optimization of information rates and symbol rates in flexible transponders utilizing Probabilistic Constellation Shaping (PCS) can maximize transmission reach and SE x reach product for high speed optical transmission networks.