arXiv subjects
Publications and source records attributed to Polina Bayvel.
A new probabilistic shaping distribution that outperforms Maxwell-Boltzmann is studied for the nonlinear fiber channel. Additional gains of 0.1 bit/symbol MI or 0.2 dB SNR for both DP-256QAM and DP-1024QAM are reported after 200 km nonlinear fiber transmission.
The efficiency of digital nonlinearity compensation (NLC) is analyzed in the presence of noise arising from amplified spontaneous emission noise (ASE) as well as from a non-ideal transceiver subsystem. Its impact on signal-to-noise ratio (SNR) and reach increase is studied with particular emphasis on split NLC, where the digital back-propagation algorithm is divided between transmitter and receiver. An analytical model is presented to compute the SNR's for non-ideal transmission systems with arbitrary split NLC configurations. When signal-signal nonlinearities are compensated, the performance limitation arises from residual signal-noise interactions. These interactions consist of nonlinear beating between the signal and co-propagating ASE and transceiver noise. While transceiver noise-signal beating is usually dominant for short transmission distances, ASE noise-signal beating is dominant for larger transmission distances. It is shown that both regimes behave differently with respect to the optimal NLC split ratio and their respective reach gains. Additionally, simple formulas for the prediction of the optimal NLC split ratio and the reach increase in those two regimes are reported. It is found that split NLC offers negligible gain with respect to conventional digital back-propagation (DBP) for distances less than 1000 km using standard single-mode fibers and a transceiver (back-to-back) SNR of 26 dB, when transmitter and receiver inject the same amount of noise. However, when transmitter and receiver inject an unequal amount of noise, reach gains of 56% on top of DBP are achievable by properly tailoring the split NLC algorithm. The theoretical findings are confirmed by numerical simulations.
The study on carrier phase estimation (CPE) approaches, involving a one-tap normalized least-mean-square (NLMS) algorithm, a block-wise average algorithm, and a Viterbi-Viterbi algorithm has been carried out in the long-haul high-capacity dispersion-unmanaged coherent optical systems. The close-form expressions and analytical predictions for bit-error-rate behaviors in these CPE methods have been analyzed by considering both the laser phase noise and the equalization enhanced phase noise. It is found that the Viterbi-Viterbi algorithm outperforms the one-tap NLMS and the block-wise average algorithms for a small phase noise variance (or effective phase noise variance), while the three CPE methods converge to a similar performance for a large phase noise variance (or effective phase noise variance). In addition, the differences between the three CPE approaches become smaller for higher-level modulation formats.
Achievable information rates (AIRs) of wideband optical communication systems using ~40 nm (~5 THz) EDFA and ~100 nm (~12.5 THz) distributed Raman amplification are estimated based on a first-order perturbation analysis. The AIRs of each individual channel have been evaluated for DP-64QAM, DP-256QAM, and DP-1024QAM modulation formats. The impact of full-field nonlinear compensation (FF-NLC) and probabilistically shaped constellations using a Maxwell-Boltzmann distribution were studied and compared to electronic dispersion compensation. It is found that a probabilistically shaped DP-1024QAM constellation combined with FF-NLC yields AIRs of ~75 Tbit/s for the EDFA scheme and ~223 Tbit/s for the Raman amplification scheme over 2000 km standard single mode fibre transmission.
Achievable rates of the nonlinear frequency-division multiplexing (NFDM) and wavelength-division multiplexing (WDM) subject to the same power and bandwidth constraints are computed as a function of transmit power in the standard single-mode fiber. NFDM achieves higher rates than WDM.
Using coherent optical detection and digital signal processing, laser phase noise and equalization enhanced phase noise can be effectively mitigated using the feed-forward and feed-back carrier phase recovery approaches. In this paper, theoretical analyses of feed-back and feed-forward carrier phase recovery methods have been carried out in the long-haul high-speed n-level phase shift keying (n-PSK) optical fiber communication systems, involving a one-tap normalized least-mean-square (LMS) algorithm, a block-wise average algorithm, and a Viterbi-Viterbi algorithm. The analytical expressions for evaluating the estimated carrier phase and for predicting the bit-error-rate (BER) performance (such as the BER floors) have been presented and discussed in the n-PSK coherent optical transmission systems by considering both the laser phase noise and the equalization enhanced phase noise. The results indicate that the Viterbi-Viterbi carrier phase recovery algorithm outperforms the one-tap normalized LMS and the block-wise average algorithms for small phase noise variance (or effective phase noise variance), while the one-tap normalized LMS algorithm shows a better performance than the other two algorithms for large phase noise variance (or effective phase noise variance). In addition, the one-tap normalized LMS algorithm is more sensitive to the level of modulation formats.
An analytical model is presented for assessing the performance of the bit-error-rate (BER) in the differential m-level phase shift keying (m-PSK) transmission systems, where the influence of equalization enhanced phase noise (EEPN) has been considered. Theoretical analysis has been carried out in differential quadrature phase shift keying (DQPSK), differential 8-PSK (D8PSK), and differential 16-PSK (D16PSK) coherent optical transmission systems. The influence of EEPN on the BER performance, in term of signal-to-noise ratio (SNR), are investigated for different fiber dispersion, LO laser linewidths, symbol rates, and modulation formats. Our analytical model achieves a good agreement with previously reported EEPN induced BER floors, and can give an accurate prediction for the DQPSK system, and a leading-order approximation for the D8PSK and the D16PSK systems.
A comprehensive study of the coded performance of long-haul spectrally-efficient WDM optical fiber transmission systems with different coded modulation decoding structures is presented. Achievable information rates are derived for three different square QAM formats and the optimal format is identified as a function of distance and specific decoder implementation. The four cases analyzed combine hard-decision (HD) or soft-decision (SD) decoding together with either a bit-wise or a symbol-wise demapper, the last two suitable for binary and nonbinary codes, respectively. The information rates achievable for each scheme are calculated based on the mismatched decoder principle. These quantities represent true indicators of the coded performance of the system for specific decoder implementations and when the modulation format and its input distribution are fixed. In combination with the structure of the decoder, two different receiver-side equalization strategies are also analyzed: electronic dispersion compensation and digital backpropagation. We show that, somewhat unexpectedly, schemes based on nonbinary HD codes can achieve information rates comparable to SD decoders and that, when SD is used, switching from a symbol-wise to a bit-wise decoder results in a negligible penalty. Conversely, from an information-theoretic standpoint, HD binary decoders are shown to be unsuitable for spectrally-efficient, long-haul systems.
Current research efforts are focussed on overcoming the apparent limits of communication in single mode optical fibre resulting from distortion due to fibre nonlinearity. It has been experimentally demonstrated that this Kerr nonlinearity limit is not a fundamental limit; thus it is pertinent to review where the fundamental limits of optical communications lie, and direct future research on this basis. This paper details recently presented results. The work herein briefly reviews the intrinsic limits of optical communication over standard single mode optical fibre (SMF), and shows that the empirical limits of silica fibre power handling and transceiver design both introduce a practical upper bound to the capacity of communication using SMF, on the order of 1 Pbit/s. Transmission rates exceeding 1 Pbit/s are shown to be possible, however, with currently available optical fibres, attempts to transmit beyond this rate by simply increasing optical power will lead to an asymptotically zero fractional increase in capacity.
Probabilistic shaping of quadrature amplitude modulation (QAM) is used to enhance the sensitivity of an optical communication system. Sensitivity gains of 0.43 dB and 0.8 dB are demonstrated in back-to-back experiments by shaping of 16QAM and 64QAM, respectively. Further, numerical simulations are used to prove the robustness of probabilistic shaping to a mismatch between the constellation used and the signal-to-noise ratio (SNR) of the channel. It is found that, accepting a 0.1 dB SNR penalty, only four shaping distributions are required to support these gains for 64QAM.
In this Letter we analyze the benefit of digital compensation of fiber nonlinearity, where the digital signal processing is divided between the transmitter and receiver. The application of the Gaussian noise model indicates that, where there are two or more spans, it is always beneficial to split the nonlinearity compensation. The theory is verified via numerical simulations, investigating transmission of single channel 50 GBd polarization division multiplexed 256-ary quadrature amplitude modulation over 100 km standard single mode fiber spans, using lumped amplification. For this case, the additional increase in mutual information achieved over transmitter- or receiver-side nonlinearity compensation is approximately 1 bit for distances greater than 2000 km. Further, it is shown, theoretically, that the SNR gain for long distances and high bandwidth transmission is 1.5 dB versus transmitter- or receiver-based nonlinearity compensation.
A closed-form expression for a lower bound on the per soliton capacity of the nonlinear optical fibre channel in the presence of (optical) amplifier spontaneous emission (ASE) noise is derived. This bound is based on a non-Gaussian conditional probability density function for the soliton amplitude jitter induced by the ASE noise and is proven to grow logarithmically as the signal-to-noise ratio increases.
The potential of optimum selection of modulation and forward error correction (FEC) overhead (OH) in future transparent nonlinear optical mesh networks is studied from an information theory perspective. Different network topologies are studied as well as both ideal soft-decision (SD) and hard-decision (HD) FEC based on demap-and-decode (bit-wise) receivers. When compared to the de-facto QPSK with 7% OH, our results show large gains in network throughput. When compared to SD-FEC, HD-FEC is shown to cause network throughput losses of 12%, 15%, and 20% for a country, continental, and global network topology, respectively. Furthermore, it is shown that most of the theoretically possible gains can be achieved by using one modulation format and only two OHs. This is in contrast to the infinite number of OHs required in the ideal case. The obtained optimal OHs are between 5% and 80%, which highlights the potential advantage of using FEC with high OHs.
Lower bounds on mutual information (MI) of long-haul optical fiber systems for hard-decision and soft-decision decoding are studied. Ready-to-use expressions to calculate the MI are presented. Extensive numerical simulations are used to quantify how changes in the optical transmitter, receiver, and channel affect the achievable transmission rates of the system. Special emphasis is put to the use of different quadrature amplitude modulation formats, channel spacings, digital back-propagation schemes and probabilistic shaping. The advantages of using MI over the prevailing $Q$-factor as a figure of merit of coded optical systems are also highlighted.
The FEC limit paradigm is the prevalent practice for designing optical communication systems to attain a certain bit-error rate (BER) without forward error correction (FEC). This practice assumes that there is an FEC code that will reduce the BER after decoding to the desired level. In this paper, we challenge this practice and show that the concept of a channel-independent FEC limit is invalid for soft-decision bit-wise decoding. It is shown that for low code rates and high order modulation formats, the use of the soft FEC limit paradigm can underestimate the spectral efficiencies by up to 20%. A better predictor for the BER after decoding is the generalized mutual information, which is shown to give consistent post-FEC BER predictions across different channel conditions and modulation formats. Extensive optical full-field simulations and experiments are carried out in both the linear and nonlinear transmission regimes to confirm the theoretical analysis.