Geometric Shaping of 2-D Constellations in the Presence of Laser Phase Noise

In this article, we propose a geometric shaping (GS) strategy to design 8, 16, 32, and 64 -ary modulation formats for the optical fibre channel impaired by both additive white Gaussian (AWGN) and phase noise. The constellations were optimised to maximise generalised mutual information (GMI) using a mismatched channel model. The presented formats demonstrate an enhanced signal-to-noise ratio (SNR) tolerance in high phase noise regimes when compared with their quadrature amplitude modulation (QAM) or AWGN-optimised counterparts. By putting the optimisation results in the context of the 400ZR implementation agreement, we show that GS alone can either relax the laser linewidth (LW) or carrier phase estimation (CPE) requirements of 400 Gbit/s transmission links and beyond. Following the GMI validation, the performance of the presented formats was examined in terms of post forward error correction (FEC) bit-error-rate (BER) for a soft decision (SD) extended Hamming code (128, 120), implemented as per the 400ZR implementation agreement. We demonstrate gains of up to 1.2 dB when compared to the 64 -ary AWGN shaped formats

The Partially-Coherent AWGN Channel: Transceiver Strategies for Low-Complexity Fibre Links

Carrier phase estimation (CPE) is one of the key requirements to perform intradyne coherent detection in optical communication systems. Residual errors in the phase estimation at the receiver, also known as residual phase noise (RPN), follow the so-called Tikhonov distribution. In the digital domain, a channel where the phase has already been estimated by the CPE is generally known as a partially-coherent additive white Gaussian noise (PCAWGN) channel. Herein, we present a joint strategy to modulate and demodulate a 2-dimensional (2D) signal in a PCAWGN channel. Using a low-complexity demapper, we geometrically shape (GS) 8- to 64- ary modulation formats for a PCAWGN channel. Through numerical simulations, we then assess the bit-wise achievable information rates (AIRs) and post forward error correction (FEC) bit error rates (BER) of the presented constellations with the: theoretical optimum model, Euclidean model and the low-complexity PCAWGN model. The resulting constellations are shown to be tolerant to a significant amount of RPN and are therefore applicable to coherent optical communication systems using high linewidth lasers (e.g., >500 kHz) and/or lower symbol rates. Moreover, we demonstrate that shaped PCAWGN constellations combined with a low-complexity demapper can either significantly relax laser linewidth (LW) or carrier phase estimation (CPE) requirements. Assuming a rate-9/10 LDPC scheme, we demonstrate post-FEC BER shaping gains of up to 2.59 dB and 2.19 dB versus uniform 64QAM and 64-ary constellations shaped for the purely AWGN channel, respectively

Packet Timescale Wavelength Switching Enabled by Regression Optimisation

A linear regression algorithm is applied to a digital-supermode distributed Bragg reflector laser to optimise wavelength switching times. The algorithm uses the output of a digital coherent receiver as feedback to update the pre-emphasis weights applied to the laser section currents. This permits in-situ calculation without manual weight adjustments. The application of this optimiser to a representative subsection of channels indicates this commercially available laser can rapidly reconfigure over 6.05 THz, supporting 122 channels, in less than 10 ns

Performance of momentum-based frequency-domain MIMO equalizer in the presence of feedback delay

A frequency-domain multiple-input multiple-output (FD-MIMO) equalizer employing a momentum-based gradient descent update algorithm is proposed for polarization multiplexing coherent receivers. Its performance in operation with dynamically varying optical channels is investigated and the impact of filter update delays, arising from the latency of the fast Fourier transforms (FFTs) and other digital signal processing (DSP) operations in the feedback loop, is assessed. We show that the proposed momentum-based gradient descent algorithm used to control the equalizer response has significantly greater tolerance to feedback delay than the conventional gradient descent algorithm. We considered a 92 Gbaud dual-polarization 64 QAM receiver, with DSP operating at two samples per symbol, and with the equalizer operating on blocks of 512 and 1024 samples (i.e., 512/1024-point FFT). We found that at an optical signal-to-noise power ratio (OSNR) of 35 dB, the momentum-based gradient descent algorithm can successfully track state-of-polarization (SOP) rotation at frequencies of up to 50 kHz and with filter update delays of up to 14 blocks (39 ns). In comparison, using the conventional gradient descent algorithm in an otherwise identical receiver, the equalizer performance starts to deteriorate at SOP rotation frequencies above 20 kHz

Damage modelling: the current state and the latest progress on the development of creep damage constitutive equations for high Cr steels

This paper reviews the fundamentals of the development of creep damage constitutive equations for high Cr steels including (1) a concise summary of the characteristics of creep deformation and creep damage evolution and their dependence on the stress level and the importance of cavitation for the final fracture; (2) a critical review of the state of art of creep damage equation for high Cr steels; (3) some discussion and comments on the various approaches; (4) consideration and suggestion for future work. It emphasises the need for better understanding the nucleation, cavity growth and coalesces and the theory for coupling method between creep cavity damage and brittle fracture and generalisatio

Selection for Replicases in Protocells

PMCID: PMC3649988This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

Extending Phase Noise Tolerance in UDWDM Access Networks

Geometrically shaped constellations, designed for improved AWGN channel performance, are combined with enhanced symbol decision metrics for low symbol rate/high linewidth applications, e.g., ultra-dense wavelength division multiplexed passive optical networks (UDWDM-PON). The improved metric enables 32-ary constellation transmission with robustness to AWGN and phase noise

Nanostructuring Germanium Nanowires by In Situ TEM Ion Irradiation

Once nanomaterials have been synthesized, inducing further structural modifications is challenging. However, being able to do so in a controlled manner is crucial. In this context, germanium nanowires are irradiated in situ within a transmission electron microscope (TEM) by a 300 keV xenon ion beam at temperatures ranging from room temperature (RT) to 500 °C. The ion irradiation is performed in situ and the evolution of nanowires during irradiation is monitored. At 300 °C and below, where the temperature is low enough to allow amorphization, the ion beam causes the formation of nanostructures within the nanowires. Formation of nanopores and swelling of nanowires is observed for a very low fluence of 2.2 × 1014 and up to 4.2 × 1015 ions cm−2. At higher fluences, the thickness of the nanowires decreases, the nanowires lose their wire-like cylindrical shape and the nanostructuring caused by the ion beam becomes more complex. The nanostructures are observed to be stable upon crystallization when the nanowires are annealed at 530 °C. Furthermore, in situ imaging allows the growth of nanopores during irradiation to be followed at RT and at 300 °C providing valuable insights into the mechanism responsible for the nanostructuring