Information-Theoretic Tools for Optical Communications Engineers [Invited]

Fundamental information-theoretic concepts are explained for nonspecialists, with emphasis on their practical usAge. The notions of a \u27FEC threshold\u27 and a \u27nonlinear Shannon limit\u27 are critically reviewed, highlighting their limitations and possible alternatives

Phase Noise Compensation for Nonlinearity-Tolerant Digital Subcarrier Systems With High-Order QAM

The fundamental penalty of subcarrier modulation (SCM) with independent subcarrier phase noise processing is estimated. It is shown that the fundamental signal-to-noise ratio (SNR) penalty related to poorer phase noise tolerance of decreased baudrate subcarriers increases significantly with modulation format size and can potentially exceed the gains of the nonlinear tolerance of SCM. A low-complexity algorithm is proposed for joint subcarrier phase noise processing, which is scalable in the number of subcarriers and recovers almost entirely the fundamental SNR penalty with respect to single-carrier systems operating at the same net data-rate. The proposed algorithm enables high-order modulation formats with high count of subcarriers to be safely employed for nonlinearity mitigation in optical communication systems

Scope and Limitations of the Nonlinear Shannon Limit

The concept and significance of the so called nonlinear Shannon limit are reviewed and their relation to the channel capacity is analyzed from an information theory point of view. It is shown that this is a limit (if at all) holding only for conventional detection strategies. Indeed, it should only be considered as a limit to the information rate that can be achieved with a given modulation/detection scheme. By virtue of some simple examples and theoretical results, it is also shown that, using the same approximated models commonly adopted for deriving the nonlinear Shannon limit, the information rate can be arbitrarily increased by increasing the input power. To this aim, the validity of some popular approximations to the output distribution is also examined to show that their application outside the scope for which they were devised can lead to pitfalls. To the best of our belief, the existence of a true nonlinear Shannon limit has still not been demonstrated, and the problem of determining the channel capacity of a fiber-optic system in the presence of Kerr nonlinearities is still an open issue

Nonlinearity Mitigation in WDM Systems: Models, Strategies, and Achievable Rates

After reviewing models and mitigation strategies for interchannel nonlinear interference (NLI), we focus on the frequency-resolved logarithmic perturbation model to study the coherence properties of NLI. Based on this study, we devise an NLI mitigation strategy which exploits the synergic effect of phase and polarization noise compensation (PPN) and subcarrier multiplexing with symbol-rate optimization. This synergy persists even for high-order modulation alphabets and Gaussian symbols. A particle method for the computation of the resulting achievable information rate and spectral efficiency (SE) is presented and employed to lower-bound the channel capacity. The dependence of the SE on the link length, amplifier spacing, and presence or absence of inline dispersion compensation is studied. Single-polarization and dual-polarization scenarios with either independent or joint processing of the two polarizations are considered. Numerical results show that, in links with ideal distributed amplification, an SE gain of about 1 bit/s/Hz/polarization can be obtained (or, in alternative, the system reach can be doubled at a given SE) with respect to single-carrier systems without PPN mitigation. The gain is lower with lumped amplification, increases with the number of spans, decreases with the span length, and is further reduced by in-line dispersion compensation. For instance, considering a dispersion-unmanaged link with lumped amplification and an amplifier spacing of 60 km, the SE after 80 spans can be be increased from 4.5 to 4.8 bit/s/Hz/polarization, or the reach raised up to 100 spans (+25%) for a fixed SE.Comment: Submitted to Journal of Lightwave Technolog

How to Increase the Achievable Information Rate by Per-Channel Dispersion Compensation

Deploying periodic inline chromatic dispersion compensation enables reducing the complexity of the digital back propagation (DBP) algorithm. However, compared with nondispersion-managed (NDM) links, dispersion-managed (DM) ones suffer a stronger cross-phase modulation (XPM). Utilizing per-channel dispersion-managed (CDM) links (e.g., using fiber Bragg grating) allows for a complexity reduction of DBP, while abating XPM compared to DM links. In this paper, we show for the first time that CDM links enable also a more effective XPM compensation compared to NDM ones, allowing a higher achievable information rate (AIR). This is explained by resorting to the frequency-resolved logarithmic perturbation model and showing that per-channel dispersion compensation increases the frequency correlation of the distortions induced by XPM over the channel bandwidth, making them more similar to a conventional phase noise. We compare the performance (in terms of the AIR) of a DM, an NDM, and a CDM link, considering two types of mismatched receivers: one neglects the XPM phase distortion and the other compensates for it. With the former, the CDM link is inferior to the NDM one due to an increased in-band signal--noise interaction. However, with the latter, a higher AIR is obtained with the CDM link than with the NDM one owing to a higher XPM frequency correlation. The DM link has the lowest AIR for both receivers because of a stronger XPM

Capacity Analysis and Receiver Design in the Presence of Fiber Nonlinearity

The majority of today\u27s global Internet traffic is conveyed through optical fibers. The ever-increasing data demands have pushed the optical systems to evolve from using regenerators and direct-direction receivers to a coherent multi-wavelength network. Future services like cloud computing and virtual reality will demand more bandwidth, so much so that the so called capacity-crunch is anticipated to happen in near future. Therefore, studying the capacity of the optical system is needed to better understanding and utilizing the existing fiber network.The characterization of the capacity of the dispersive and nonlinear optical fiber described by the nonlinear Schr{\"o}dinger equation is an open problem. There are a number of lower bounds on the capacity which are mainly obtained based on the mismatched decoding principle or by analyzing simplified channels. These lower bounds either fall to zero at high powers or saturate. The question whether the fiber-optical capacity has the same behavior as the lower bounds at high power is still open. Indeed, the only known upper bound increases with the power unboundedly. In this thesis, we first study how the fiber nonlinear distortion is modeled in some simplified channels and what is the influence of the simplifying assumptions on the capacity. To do so, the capacity of three different memoryless simplified models of the fiber-optical channel are studied. The results show that in the high-power regime the capacities of these models grow with different pre-logs, which indicates the profound impact of the simplifying assumptions on the capacity of these channels. Next, we turn our attention to demodulation and detection processes in the presence of fiber nonlinearity. We study a two-user memoryless network. It is shown that by deploying a nonlinearity-tailored demodulator, the performance improves substantially compared with matched filtering and sampling. In the absence of dispersion, we show that with the new receiver, unlike with matched filtering and sampling, arbitrarily low bit error rates can be achieved. Furthermore, we show via simulations that performance improvements can be obtained also for a low-dispersion fiber.Then, we study the performance of three different dispersion compensation methods in the presence of inter-channel nonlinear interference. The best performance, in terms of achievable information rate, is obtained by a link with inline per-channel dispersion compensation combined with a receiver that compensates for inter-channel nonlinearities. Finally, the capacity analysis is performed for short-reach noncoherent channel, where the source of nonlinearity is not the fiber but a square-law receiver. Capacity bounds are established in the presence of optical and thermal noises. Using these bounds we show that optical amplification is beneficial at low signal-to-noise ratios (SNRs), and detrimental at high SNRs. We quantify the SNR regime for each case for a wide range of channel parameters

A Simple Strategy for Mitigating XPM in Nonlinear WDM Optical Systems

Resilience to cross-phase modulation (XPM) can be improved by employing multicarrier modulation formats. The impact of the number of subcarriers on the achievable information rate is discussed and a possible XPM compensation strategy is suggested

A simple strategy for mitigating XPM in nonlinear WDM optical systems

Resilience to cross-phase modulation (XPM) can be improved by employing multicarrier modulation formats. The impact of the number of subcarriers on the achievable information rate is discussed and a possible XPM compensation strategy is suggested