Regular perturbation on the group-velocity dispersion parameter for nonlinear fibre-optical communications.

Communication using the optical fibre channel can be challenging due to nonlinear effects that arise in the optical propagation. These effects represent physical processes that originate from light propagation in optical fibres. To obtain fundamental understandings of these processes, mathematical models are typically used. These models are based on approximations of the nonlinear Schrödinger equation, the differential equation that governs the propagation in an optical fibre. All available models in the literature are restricted to certain regimes of operation. Here, we present an approximate model for the nonlinear optical fibre channel in the weak-dispersion regime, in a noiseless scenario. The approximation is obtained by applying regular perturbation theory on the group-velocity dispersion parameter of the nonlinear Schrödinger equation. The proposed model is compared with three other models using the normalized square deviation metric and shown to be significantly more accurate for links with high nonlinearities and weak dispersion.

Accuracy Assessment of Nondispersive Optical Perturbative Models through Capacity Analysis.

A number of simplified models, based on perturbation theory, have been proposed for the fiber-optical channel and have been extensively used in the literature. Although these models are mainly developed for the low-power regime, they are used at moderate or high powers as well. It remains unclear to what extent the capacity of these models is affected by the simplifying assumptions under which they are derived. In this paper, we consider single-channel data transmission based on three continuous-time optical models: (i) a regular perturbative channel, (ii) a logarithmic perturbative channel, and (iii) the stochastic nonlinear Schrödinger (NLS) channel. To obtain analytically tractable discrete-time models, we consider zero-dispersion fibers and a sampling receiver. We investigate the per-sample capacity of these models. Specifically, (i) we establish tight bounds on the capacity of the regular perturbative channel; (ii) we obtain the capacity of the logarithmic perturbative channel; and (iii) we present a novel upper bound on the capacity of the zero-dispersion NLS channel. Our results illustrate that the capacity of these models departs from each other at high powers because these models yield different capacity pre-logs. Since all three models are based on the same physical channel, our results highlight that care must be exercised in using simplified channel models in the high-power regime.

Multi-channel collision-free reception for optical interconnects.

A multi-channel reception scheme that allows each node to receive an arbitrary set of wavelengths simultaneously (i.e., collision-free) is proposed for optical interconnects. The proposed scheme only needs to use a few receivers and fixed-wavelength filters that are designed based on error-control coding theory. Experiments with up to four channel collision-free reception units are carried out to demonstrate the feasibility of the proposed scheme.

On the limits of digital back-propagation in the presence of transceiver noise.

This paper investigates the impact of transceiver noise on the performance of digital back-propagation (DBP). A generalized expression to estimate the signal-to-noise ratio (SNR) obtained using DBP in the presence of transceiver noise is described. This new expression correctly accounts for the nonlinear beating between the transceiver noise and the signal in the optical fiber transmission link. The transceiver noise-signal nonlinear beating has been identified as the main reason for the discrepancy between predicted and practical performance of DBP; which has not been previously suggested. This nonlinear beating has been included in the GN model, allowing DBP gains in practical systems to be predicted analytically. Experiments and split-step simulations with and without polarization-mode dispersion (PMD) in the transmission link have been performed. The results show that the impact of transceiver noise greatly outweighs that of PMD, and the analytical expressions are confirmed by the numerical simulations.

Digital backpropagation accounting for polarization-mode dispersion.

Digital backpropagation (DBP) is a promising digital-domain technique to mitigate Kerr-induced nonlinear interference. While it successfully removes deterministic signal-signal interactions, the performance of ideal DBP is limited by stochastic effects, such as polarization-mode dispersion (PMD). In this paper, we consider an ideal full-field DBP implementation and modify it to additionally account for PMD; reversing the PMD effects in the backward propagation by passing the reverse propagated signal also through PMD sections, which concatenated equal the inverse of the PMD in the forward propagation. These PMD sections are calculated analytically at the receiver based on the total accumulated PMD of the link estimated from channel equalizers. Numerical simulations show that, accounting for nonlinear polarization-related interactions in the modified DBP algorithm, additional signal-to-noise ratio gains of 1.1 dB are obtained for transmission over 1000 km.

Polarization Drift Channel Model for Coherent Fibre-Optic Systems.

A theoretical framework is introduced to model the dynamical changes of the state of polarization during transmission in coherent fibre-optic systems. The model generalizes the one-dimensional phase noise random walk to higher dimensions, accounting for random polarization drifts, emulating a random walk on the Poincaré sphere, which has been successfully verified using experimental data. The model is described in the Jones, Stokes and real four-dimensional formalisms, and the mapping between them is derived. Such a model will be increasingly important in simulating and optimizing future systems, where polarization-multiplexed transmission and sophisticated digital signal processing will be natural parts. The proposed polarization drift model is the first of its kind as prior work either models polarization drift as a deterministic process or focuses on polarization-mode dispersion in systems where the state of polarization does not affect the receiver performance. We expect the model to be useful in a wide-range of photonics applications where stochastic polarization fluctuation is an issue.

Implications of information theory in optical fibre communications.

Recent decades have witnessed steady improvements in our ability to harness the information-carrying capability of optical fibres. Will this process continue, or will progress eventually stall? Information theory predicts that all channels have a limited capacity depending on the available transmission resources, and thus it is inevitable that the pace of improvements will slow. However, information theory also provides insights into how transmission resources should, in principle, best be exploited, and thus may serve as a guide for where to look for better ways to squeeze more out of a precious resource. This tutorial paper reviews the basic concepts of information theory and their application in fibre-optic communications.

Single parity check-coded 16QAM over spatial superchannels in multicore fiber transmission.

We experimentally investigate single-parity check (SPC) coded spatial superchannels based on polarization-multiplexed 16-ary quadrature amplitude modulation (PM-16QAM) for multicore fiber transmission systems, using a 7-core fiber. We investigate SPC over 1, 2, 4, 5 or 7 cores in a back-to-back configuration and compare the sensitivity to uncoded PM-16QAM, showing that at symbol rates of 20 Gbaud and at a bit-error-rate (BER) of 10-3, the SPC superchannels exhibit sensitivity improvements of 2.7 dB, 2.0 dB, 1.7 dB, 1.3 dB, and 1.1 dB, respectively. We perform both single channel and wavelength division multiplexed (WDM) transmission experiments with 22 GHz channel spacing and 20 Gbaud channel symbol rate for SPC over 1, 3 and 7 cores and compare the results to PM-16QAM with the same spacing and symbol rate. We show that in WDM signals, SPC over hl1 core can achieve more than double the transmission distance compared to PM-16QAM at the cost of 0.91 bit/s/Hz/core in spectral efficiency (SE). When sharing the parity-bit over 7 cores, the loss in SE becomes only 0.13 bit/s/Hz/core while the increase in transmission reach over PM-16QAM is 44 %.

Improving soft FEC performance for higher-order modulations via optimized bit channel mappings.

Soft forward error correction with higher-order modulations is often implemented in practice via the pragmatic bit-interleaved coded modulation paradigm, where a single binary code is mapped to a nonbinary modulation. In this paper, we study the optimization of the mapping of the coded bits to the modulation bits for a polarization-multiplexed fiber-optical system without optical inline dispersion compensation. Our focus is on protograph-based low-density parity-check (LDPC) codes which allow for an efficient hardware implementation, suitable for high-speed optical communications. The optimization is applied to the AR4JA protograph family, and further extended to protograph-based spatially coupled LDPC codes assuming a windowed decoder. Full field simulations via the split-step Fourier method are used to verify the analysis. The results show performance gains of up to 0.25 dB, which translate into a possible extension of the transmission reach by roughly up to 8%, without significantly increasing the system complexity.

On nonlinearly-induced noise in single-channel optical links with digital backpropagation.

In this paper, we investigate the performance limits of electronic chromatic dispersion compensation (EDC) and digital backpropagation (DBP) for a single-channel non-dispersion-managed fiber-optical link. A known analytical method to derive the performance of the system with EDC is extended to derive a first-order approximation for the performance of the system with DBP. In contrast to the cubic growth of the variance of the nonlinear noise-like interference, often called nonlinear noise, with input power for EDC, a quadratic growth is observed with DBP using this approximation. Finally, we provide numerical results to verify the accuracy of the proposed approach and compare it with existing analytical models.

Comparison of 128-SP-QAM with PM-16-QAM.

In this paper we investigate an interesting modulation format for fiber optic communications, set-partitioning 128 polarization-multiplexed 16-QAM (128-SP-QAM), which consists of the symbols with even parity from the symbol alphabet of polarization-multiplexed 16-QAM (PM-16-QAM). We compare 128-SP-QAM and PM-16-QAM using numerical simulations in long-haul transmission scenarios at bit rates of 112 Gbit/s and 224 Gbit/s, and at the same symbol rates (14 and 28 Gbaud). The transmission link is made up of standard single-mode fiber with 60, 80 or 100 km amplifier spacing and both single channel and WDM transmission (25- and 50 GHz-spaced) is investigated. The results show that 128-SP-QAM achieves more than 40% increase in transmission reach compared to PM-16-QAM at the same data rate for all cases studied for a bit error rate of 10⁻³. In addition, we find that in single channel transmission there is, as expected, an advantage in terms of transmission distance when using a data rate of 112 Gbit/s as compared to 224 Gbit/s. However, when comparing the two different WDM systems with the same aggregate data rates, the reach is similar due to the smaller impact of nonlinear crosstalk between the WDM channels in the systems with 50 GHz spacing. We also discuss decoding and phase estimation of 128-SP-QAM and implement differential coding, which avoids error bursts due to cycle slips in the phase estimation. Simulations including laser phase noise show that the phase noise tolerance is similar for the two formats, with 0.5 dB OSNR penalty compared to the case with zero phase noise for a laser linewidth to symbol rate ratio of 10⁻4.

Experimental comparison of modulation formats in IM/DD links.

We present an experimental comparison of modulation formats for optical intensity modulated links with direct detection. Specifically, we compare OOK, QPSK on an electrical subcarrier and a new modulation format named OOPSK. The OOPSK modulation format is shown to have better sensitivity than the other modulation formats, in agreement with theoretical predictions. The impact of propagation in multimode fiber is also studied and the results show that all modulation formats have similar sensitivity penalties, with respect to the fibre length.

Modified constant modulus algorithm for polarization-switched QPSK.

By using a generalized cost function, a modified constant modulus algorithm (CMA) that allows polarization demultiplexing and equalization of polarization-switched QPSK is found. An implementation that allows easy switching between the conventional and the modified CMA is described. Using numerical simulations, the suggested algorithm is shown to have similar performance for polarization-switched QPSK as CMA has for polarization-multiplexed QPSK.

30 Gbps 4-PAM transmission over 200 m of MMF using an 850 nm VCSEL.

We present high speed real time, error free 4-PAM transmission for short range optical links based on a VCSEL operating at 850 nm, a multimode fibre and a simple intensity detector. Transmission speeds of 25 Gbps and 30 Gbps are demonstrated, and the maximum fibre reaches were 300 m and 200 m, respectively. The 4-PAM is also compared with OOK transmission at 25 Gbps, and we find that at this bit rate 4-PAM increases the error free transmission distance in the multimode fibre by 100 m, compared to OOK.

Multilevel pulse-position modulation for optical power-efficient communication.

A family of modulation formats is derived by combining pulse-position modulation (PPM) with multilevel dual-polarization signal constellations. With 16-PPM, gains of up to 5.4 dB are obtained over dual-polarization QPSK, at the cost of reduced spectral efficiency.

Power efficient subcarrier modulation for intensity modulated channels.

We compare formats for optical intensity modulation limited by thermal noise with the assumption of having ideal devices. At the same bitrate and bandwidth, a hitherto unknown format turns out to be more power efficient than known formats. This new modulation, which is a hybrid between on-off keying and phase-shift keying, belongs to the subcarrier modulation family. At asymptotically high signal-to-noise ratios, this hybrid scheme has a 1.2 dB average electrical power gain and 0.6 dB average optical power gain compared to OOK, while it has a 3.0 dB average electrical power gain and 2.1 dB average optical power gain compared to subcarrier QPSK.

Which is the most power-efficient modulation format in optical links?

By exploiting the electromagnetic wave's four-dimensional signal space, we find that for the additive white Gaussian noise channel, the modulation format with best sensitivity to be an 8-level format with 1.76 dB asymptotic gain over BPSK, for uncoded optical transmission with coherent detection. Low-complexity modulators are presented for the format, as well as an interpretation in terms of quantum-limited sensitivity.

Fiber communications using convolutional coding and bandwidth-efficient modulation.

In this paper we evaluate numerically the advantage of combining convolutional coding and bandwidth-efficient modulation. We compare different multilevel modulation formats, line codes, and hard/soft decision decoding. Compared with DPSK modulation (with the same bandwidth and information transmission rate), an improvement of almost 5 dB is observed for bit error rates around 10-8. We also study the robustness to intersymbol interference in the form of chromatic dispersion, and find that the improvement of the coded transmission lines improves over the uncoded even in presence of chromatic dispersion.

Performance comparison of optical 8-ary differential phase-shift keying systems with different electrical decision schemes: Comment.

We summarize three electrical decision schemes that have been proposed for 8-level differential phase-shift keying, briefly discuss their performance and complexity, and comment that two of these schemes have been confused in an earlier comparison in Optics Express.