Sequence-Selection-Based Constellation Shaping for Nonlinear Channels

Probabilistic shaping is, nowadays, a pragmatic and popular approach to improve the performance of coherent optical fiber communication systems. In the linear regime, the potential of probabilistic shaping in terms of shaping gain and rate granularity is well known, and its practical implementation has been mostly mastered. In the nonlinear regime, the advantages offered by probabilistic shaping remain not only valid, but might also increase thanks to the appealing opportunity to use the same technique to mitigate nonlinear effects and obtain an additional nonlinear shaping gain. Unfortunately, despite the recent research efforts, the optimization of conventional shaping techniques, such as probabilistic amplitude shaping (PAS), yields a relevant nonlinear shaping gain only in particular scenarios of limited practical interest, e.g., in the absence of carrier phase recovery. Recently, a more theoretical approach, referred to as sequence selection, has been proposed to understand the performance and limitation of nonlinear constellation shaping. Sequence selection shapes the distribution of the transmitted symbols by selecting or discarding the sequences generated by a certain source according to a metric that measures their quality. In this manuscript, after a brief review of conventional probabilistic shaping, we use sequence selection to investigate through simulations the potential, opportunities, and challenges offered by probabilistic shaping for nonlinear channels. First, we show that ideal sequence selection is able to provide up to 0.13 b/s/Hz additional gain with respect to PAS with an optimized blocklength. However, this additional gain is obtained only if the selection metric accounts for the signs of the symbols, ruling out the possibility of using one of the simple recently proposed sign-independent metrics. We also show that, while the signs must be known to compute the selection metric, there is no need to shape them, since nearly the same gain can be obtained by properly selecting the amplitudes (with a sign-dependent metric) and leaving the signs uniform i.i.d. Furthermore, we show that the selection depends in a non-critical way on the symbol rate and link length: the sequences selected for a certain scenario still provide a relevant gain if the link length or baud rate are modified (within a reasonable range). Then, we analyze and compare several practical implementations of sequence selection by taking into account interaction with forward error correction (FEC), information loss due to selection, and complexity. Overall, we conclude that the single block and the multi block FEC-independent bit scrambling are the best options for the practical implementation of sequence selection, with a gain up to 0.08 b/s/Hz. The main challenge and limitation to their practical implementation remains the evaluation of the metric, whose complexity is currently too high. Finally, we show that the nonlinear shaping gain provided by sequence selection persists when carrier phase recovery is included, in contrast to the nonlinear shaping gain offered by optimizing the blocklength of conventional PAS techniques

\u3cem\u3eSecuring Employer-based Pensions: An International Perspective.\u3c/em\u3e Zvi Bodie, Olivia S. Mitchell and John A. Turner.

Zvi Bodie, Olivia S. Mitchell and John A. Turner. Securing Employer- based Pensions: An International Perspective. Philadelphia, University of Pennsylvania Press, 1996. $44.95 hardcover

On the Nonlinear Shaping Gain with Probabilistic Shaping and Carrier Phase Recovery

The performance of different probabilistic amplitude shaping (PAS)techniques in the nonlinear regime is investigated, highlighting its dependence on the PAS block length and the interaction with carrier phase recovery (CPR). Different PAS implementations are considered, based on different distribution matching (DM) techniques—namely, sphere shaping, shell mapping with different number of shells, and constant composition DM—and amplitude-to-symbol maps. When CPR is not included, PAS with optimal block length provides a nonlinear shaping gain with respect to a linearly optimized PAS (with infinite block length); among the considered DM techniques, the largest gain is obtained with sphere shaping. On the other hand, the nonlinear shaping gain becomes smaller, or completely vanishes, when CPR is included, meaning that in this case all the considered implementations achieve a similar performance for a sufficiently long block length. Similar results are obtained in different link configurations ($1\times 180$ km, $15\times 80$ km, and $27\times 80$ km single-mode-fiber links), and also including laser phase noise, except when in-line dispersion compensation is used. Furthermore, we define a new metric, the nonlinear phase noise (NPN) metric, which is based on the frequency resolved logarithmic perturbation models and explains the interaction of CPR and PAS. We show that the NPN metric is highly correlated with the performance of the system. Our results suggest that, in general, the optimization of PAS in the nonlinear regime should always account for the presence of a CPR algorithm. In this case, the reduction of the rate loss (obtained by using sphere shaping and increasing the DM block length) turns out to be more important than the mitigation of the nonlinear phase noise (obtained by using constant-energy DMs and reducing the block length), the latter being already granted by the CPR algorithm

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

Exploring The Potential of Probabilistic Shaping Technique in Quantum Key Distribution Systems

We investigated the role of probabilistic shaping in the optimization of the secure key rate of a continuous variable quantum key distribution system with discrete modulation in both homodyne and heterodyne scheme

Probabilistic Amplitude Shaping for Continuous-Variable Quantum Key Distribution with Discrete Modulation over a Wiretap Channel

To achieve the maximum information transfer and face a possible eavesdropper, the samples transmitted in continuous-variable quantum key distribution (CV-QKD) protocols are to be drawn from a continuous Gaussian distribution. As a matter of fact, in practical implementations the transmitter has a finite (power) dynamics and the Gaussian sampling can be only approximated. This requires the quantum protocols to operate at small powers. In this paper, we show that a suitable probabilistic amplitude shaping of a finite set of symbols allows to approximate at will the optimal channel capacity also for increasing average powers. We investigate the feasibility of this approach in the framework of CV-QKD, propose a protocol employing discrete quadrature amplitude modulation assisted with probabilistic amplitude shaping, and we perform the key generation rate analysis assuming a wiretap channel and lossless homodyne detection

Phase noise mitigation in photonics-based radio frequency multiplication

Two photonics-based radio frequency multiplication schemes for the generation of high-frequency carriers with low phase noise are proposed and experimentally demonstrated. With respect to conventional frequency multiplication schemes, the first scheme induces a selective cancelation of phase noise at periodic frequency-offset values, whereas the second scheme provides a uniform 3-dB mitigation of phase noise. The two schemes are experimentally demonstrated for the generation of a 110-GHz carrier by sixfold multiplication of an 18.3-GHz carrier. In both cases, the experimental results confirm the phase noise reduction predicted by theory

Sub-Nyquist Field Trial Using Time Frequency Packed DP-QPSK Super-Channel Within Fixed ITU-T Grid

Sub-Nyquist time frequency packing technique was demonstrated for the first time in a super channel field trial transmission over long-haul distances. The technique allows a limited spectral occupancy even with low order modulation formats. The transmission was successfully performed on a deployed Australian link between Sydney and Melbourne which included 995 km of uncompensated SMF with coexistent traffic. 40 and 100 Gb/s co-propagating channels were transmitted together with the super-channel in a 50 GHz ITU-T grid without additional penalty. The super-channel consisted of eight sub-channels with low-level modulation format, i.e. DP-QPSK, guaranteeing better OSNR robustness and reduced complexity with respect to higher order formats. At the receiver side, coherent detection was used together with iterative maximum-a-posteriori (MAP) detection and decoding. A 975 Gb/s DP-QPSK super-channel was successfully transmitted between Sydney and Melbourne within four 50GHz WSS channels (200 GHz). A maximum potential SE of 5.58 bit/s/Hz was achieved with an OSNR=15.8 dB, comparable to the OSNR of the installed 100 Gb/s channels. The system reliability was proven through long term measurements. In addition, by closing the link in a loop back configuration, a potential SE*d product of 9254 bit/s/Hz*km was achieved

Candidate paths for impairment-aware PCE in 10-100 Gb/s optical networks

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Roadmap of optical communications

© 2016 IOP Publishing Ltd. Lightwave communications is a necessity for the information age. Optical links provide enormous bandwidth, and the optical fiber is the only medium that can meet the modern society's needs for transporting massive amounts of data over long distances. Applications range from global high-capacity networks, which constitute the backbone of the internet, to the massively parallel interconnects that provide data connectivity inside datacenters and supercomputers. Optical communications is a diverse and rapidly changing field, where experts in photonics, communications, electronics, and signal processing work side by side to meet the ever-increasing demands for higher capacity, lower cost, and lower energy consumption, while adapting the system design to novel services and technologies. Due to the interdisciplinary nature of this rich research field, Journal of Optics has invited 16 researchers, each a world-leading expert in their respective subfields, to contribute a section to this invited review article, summarizing their views on state-of-the-art and future developments in optical communications