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Polina Bayvel

Publications and source records attributed to Polina Bayvel.

At least 55 records · Page 3Linked to original sources
arXiv2019

Deep Learning for Communication over Dispersive Nonlinear Channels: Performance and Comparison with Classical Digital Signal Processing

In this paper, we apply deep learning for communication over dispersive channels with power detection, as encountered in low-cost optical intensity modulation/direct detection (IM/DD) links. We consider an autoencoder based on the recently proposed sliding window bidirectional recurrent neural network (SBRNN) design to realize the transceiver for optical IM/DD communication. We show that its performance can be improved by introducing a weighted sequence estimation scheme at the receiver. Moreover, we perform bit-to-symbol mapping optimization to reduce the bit-error rate (BER) of the system. Furthermore, we carry out a detailed comparison with classical schemes based on pulse-amplitude modulation and maximum likelihood sequence detection (MLSD). Our investigation shows that for a reference 42\,Gb/s transmission, the SBRNN autoencoder achieves a BER performance comparable to MLSD, when both systems account for the same amount of memory. In contrast to MLSD, the SBRNN performance is achieved without incurring a computational complexity exponentially growing with the processed memory.

cs.IT↗
arXiv2019

A Modulation Format Correction Formula for the Gaussian Noise Model in the Presence of Inter-Channel Stimulated Raman Scattering

A closed-form formula is derived, which corrects for the modulation format dependence of the Gaussian Noise (GN) model in the presence of inter-channel stimulated Raman scattering (ISRS). The analytical result enables a rapid estimate of the nonlinear interference (NLI) for arbitrary modulation formats and avoids the need for complex integral evaluations and split-step simulations. It is shown that the modulation format dependent NLI can be approximated by two contributions, one originating from a single span and one asymptotic contribution for a large number of spans. The asymptotic contribution is solved in closed-form for an arbitrary link function, making the result applicable for generic fiber systems using lumped, distributed or hybrid amplification schemes. The methodology is applied to the ISRS GN model and a modulation format correction formula in closed-form is derived which accounts for an arbitrary number of spans, inter-channel stimulated Raman scattering, arbitrary launch power distributions and wavelength dependent dispersion and attenuation. The proposed formula is validated by numerical simulations over the entire C+L band for multiple fiber types.

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arXiv2019

Information Rate in Ultra-Wideband Optical Fiber Communication Systems Accounting for High-Order Dispersion

The effect of Kerr-induced optical fiber nonlinearities in C-band (5 THz) EDFA and C+L-band (12.5 THz) Raman-amplified optical communication systems has been studied considering the impact of third-order fiber dispersion. The performance of digital nonlinearity compensation with single channel and 250-GHz bandwidth in both EDFA and Raman amplified systems has been investigated, respectively. The achievable information rates (AIRs) and optimum code rates in each individual transmission channel have been evaluated for the DP-64QAM, the DP-256QAM and the DP-1024QAM modulation formats, both with and without the use of the probabilistic shaping technique. It is found that, for all considered modulation formats, the signal-to-noise ratios, AIRs and code rates exhibit significantly asymmetric behavior about the central channel due to the presence of the third-order dispersion. This provides a new insight that the forward error correction schemes have to be optimized asymmetrically, on a per-channel basis, to maximize the overall throughput.

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arXiv2019

End-to-End Optimized Transmission over Dispersive Intensity-Modulated Channels Using Bidirectional Recurrent Neural Networks

We propose an autoencoding sequence-based transceiver for communication over dispersive channels with intensity modulation and direct detection (IM/DD), designed as a bidirectional deep recurrent neural network (BRNN). The receiver uses a sliding window technique to allow for efficient data stream estimation. We find that this sliding window BRNN (SBRNN), based on end-to-end deep learning of the communication system, achieves a significant bit-error-rate reduction at all examined distances in comparison to previous block-based autoencoders implemented as feed-forward neural networks (FFNNs), leading to an increase of the transmission distance. We also compare the end-to-end SBRNN with a state-of-the-art IM/DD solution based on two level pulse amplitude modulation with an FFNN receiver, simultaneously processing multiple received symbols and approximating nonlinear Volterra equalization. Our results show that the SBRNN outperforms such systems at both 42 and 84\,Gb/s, while training fewer parameters. Our novel SBRNN design aims at tailoring the end-to-end deep learning-based systems for communication over nonlinear channels with memory, such as the optical IM/DD fiber channel.

cs.IT↗
arXiv2019

Dual-polarisation Non-linear Frequency-division Multiplexed Transmission with b-Modulation

There has been much interest in the non-linear frequency-division multiplexing (NFDM) transmission scheme in the optical fibre communication system. Up to date, most of the demonstrated NFDM schemes have employed only single polarisation for data transmission. Employing both polarisations can potentially double the data rate of NFDM systems. We investigate in simulation a dual-polarisation NFDM transmission with data modulation on the $b$-coefficient. First, a transformation that facilitates the dual-polarisation $b$-modulation was built upon an existing transformation. Second, the $q_c$- and $b$-modulation for dual-polarisation were compared in terms of Q-factor, spectral efficiency (SE), and correlation of sub-carriers. The correlation is quantified via information theoretic metrics, joint and individual entropy. The polarisation-multiplexed $b$-modulation system shows 1 dB Q-factor improvement over $q_c$-modulation system due to a weaker correlation of sub-carriers and less effective noise. Finally, the $b$-modulation system was optimised for high data rate, achieving a record net data rate of 400 Gbps (SE of 7.2 bit/s/Hz) over $12\times 80$ km of standard single-mode fibre (SSMF) with erbium-doped fibre amplifiers (EDFAs). Based on the above simulation results, we further point out the drawbacks of our current system and quantify the error introduced by the transceiver algorithms and non-integrability of the channel.

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arXiv2018

Volterra-assisted Optical Phase Conjugation: a Hybrid Optical-Digital Scheme For Fiber Nonlinearity Compensation

Mitigation of optical fiber nonlinearity is an active research field in the area of optical communications, due to the resulting marked improvement in transmission performance. Following the resurgence of optical coherent detection, digital nonlinearity compensation (NLC) schemes such as digital backpropagation (DBP) and Volterra equalization have received much attention. Alternatively, optical NLC, and specifically optical phase conjugation (OPC), has been proposed to relax the digital signal processing complexity. In this work, a novel hybrid optical-digital NLC scheme combining OPC and a Volterra equalizer is proposed, termed Volterra-Assisted OPC (VAO). It has a twofold advantage: it overcomes the OPC limitation in asymmetric links and substantially enhances the performance of Volterra equalizers. The proposed scheme is shown to outperform both OPC and Volterra equalization alone by up to 4.2 dB in a 1000 km EDFA-amplified fiber link. Moreover, VAO is also demonstrated to be very robust when applied to long-transmission distances, with a 2.5 dB gain over OPC-only systems at 3000 km. VAO combines the advantages of both optical and digital NLC offering a promising trade-off between performance and complexity for future high-speed optical communication systems.

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arXiv2018

A Closed-Form Approximation of the Gaussian Noise Model in the Presence of Inter-Channel Stimulated Raman Scattering

An accurate, closed-form expression evaluating the nonlinear interference (NLI) power in coherent optical transmission systems in the presence of inter-channel stimulated Raman scattering (ISRS) is derived. The analytical result enables a rapid estimate of the signal-to-noise ratio (SNR) and avoids the need for integral evaluations and split-step simulations. The formula also provides new insight into the underlying parameter dependence of ISRS on the NLI. The proposed result is applicable for dispersion unmanaged, ultra-wideband transmission systems that use optical bandwidths of up to 15 THz. The accuracy of the closed-form expression is compared to numerical integration of the ISRS Gaussian Noise model and split-step simulations in a point-to-point transmission, as well as in a mesh optical network scenario.

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arXiv2018

End-to-end Deep Learning of Optical Fiber Communications

In this paper, we implement an optical fiber communication system as an end-to-end deep neural network, including the complete chain of transmitter, channel model, and receiver. This approach enables the optimization of the transceiver in a single end-to-end process. We illustrate the benefits of this method by applying it to intensity modulation/direct detection (IM/DD) systems and show that we can achieve bit error rates below the 6.7\% hard-decision forward error correction (HD-FEC) threshold. We model all componentry of the transmitter and receiver, as well as the fiber channel, and apply deep learning to find transmitter and receiver configurations minimizing the symbol error rate. We propose and verify in simulations a training method that yields robust and flexible transceivers that allow---without reconfiguration---reliable transmission over a large range of link dispersions. The results from end-to-end deep learning are successfully verified for the first time in an experiment. In particular, we achieve information rates of 42\,Gb/s below the HD-FEC threshold at distances beyond 40\,km. We find that our results outperform conventional IM/DD solutions based on 2 and 4 level pulse amplitude modulation (PAM2/PAM4) with feedforward equalization (FFE) at the receiver. Our study is the first step towards end-to-end deep learning-based optimization of optical fiber communication systems.

cs.IT↗
arXiv2018

On the Impact of Fixed Point Hardware for Optical Fiber Nonlinearity Compensation Algorithms

Nonlinearity mitigation using digital signal processing has been shown to increase the achievable data rates of optical fiber transmission links. One especially effective technique is digital back propagation (DBP), an algorithm capable of simultaneously compensating for linear and nonlinear channel distortions. The most significant barrier to implementing this technique, however, is its high computational complexity. In recent years, there have been several proposed alternatives to DBP with reduced computational complexity, although such techniques have not demonstrated performance benefits commensurate with the complexity of implementation. In order to fully characterize the computational requirements of DBP, there is a need to model the algorithm behavior when constrained to the logic used in a digital coherent receiver. Such a model allows for the analysis of any signal recovery algorithm in terms of true hardware complexity which, crucially, includes the bit-depth of the multiplication operation. With a limited bit depth, there is quantization noise, introduced with each arithmetic operation, and it can no longer be assumed that the conventional DBP algorithm will outperform its low complexity alternatives. In this work, DBP and a single nonlinear step DBP implementation, the \textit{Enhanced Split Step Fourier} method (ESSFM), were compared with linear equalization using a generic software model of fixed point hardware. The requirements of bit depth and fast Fourier transform (FFT) size are discussed to examine the optimal operating regimes for these two schemes of digital nonlinearity compensation. For a 1000 km transmission system, it was found that (assuming an optimized FFT size), in terms of SNR, the ESSFM algorithm outperformed the conventional DBP for all hardware resolutions up to 13 bits.

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arXiv2018

Comparison of Low Complexity Coherent Receivers for UDWDM-PONs ($λ$-to-the-user)

It is predicted that demand in optical access networks will reach multi-Gb/s per user. However, the limited performance of the direct detection receiver technology currently used in the optical network units at the customers' premises restricts data rates/user. Therefore, the concept of coherent-enabled access networks has attracted attention in recent years, as this technology offers high receiver sensitivity, inherent frequency selectivity, and linear field detection enabling the full compensation of linear channel impairments. However, the complexity of conventional (dual-polarisation digital) coherent receivers has so far prevented their introduction into access networks. Thus, to exploit the benefits of coherent technology in the ONUs, low complexity coherent receivers, suitable for implementation in ONUs, are needed. In this paper, the recently proposed low complexity coherent (i.e., polarisation-independent Alamouti-coding heterodyne) receiver is, for the first time, compared in terms of its minimum receiver sensitivity with five previously reported receiver designs, including a detailed discussion on their advantages and limitations. It is shown that the Alamouti-coding based receiver approach allows the lowest number of photons per bit (PPB) transmitted (with a lower bound of 15.5 PPB in an ideal system simulations) whilst requiring the lowest optical receiver hardware complexity. It also exhibits comparable complexity to the currently deployed direct-detection receivers, which typically require >1000 PPB. Finally, a comparison of experimentally achieved receiver sensitivities and transmission distances using these receivers is presented. The highest spectral efficiency and longest transmission distance at the highest bit rate reported using the Alamouti-coding receiver, which is also the only one, to date, to have been demonstrated in a full system bidirectional transmission.

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arXiv2018

Capacity Lower Bounds of the Noncentral Chi-Channel with Applications to Soliton Amplitude Modulation

The channel law for amplitude-modulated solitons transmitted through a nonlinear optical fibre with ideal distributed amplification and a receiver based on the nonlinear Fourier transform is a noncentral chi-distribution with $2n$ degrees of freedom, where $n=2$ and $n=3$ correspond to the single- and dual-polarisation cases, respectively. In this paper, we study capacity lower bounds of this channel under an average power constraint in bits per channel use. We develop an asymptotic semi-analytic approximation for a capacity lower bound for arbitrary $n$ and a Rayleigh input distribution. It is shown that this lower bound grows logarithmically with signal-to-noise ratio (SNR), independently of the value of $n$. Numerical results for other continuous input distributions are also provided. A half-Gaussian input distribution is shown to give larger rates than a Rayleigh input distribution for $n=1,2,3$. At an SNR of $25$ dB, the best lower bounds we developed are approximately $3.68$ bit per channel use. The practically relevant case of amplitude shift-keying (ASK) constellations is also numerically analysed. For the same SNR of $25$ dB, a $16$-ASK constellation yields a rate of approximately $3.45$ bit per channel use.

cs.IT↗
arXiv2017

The Gaussian Noise Model in the Presence of Inter-channel Stimulated Raman Scattering

A Gaussian noise (GN) model is presented that properly accounts for an arbitrary frequency dependent signal power profile along the link. This enables the evaluation of the impact of inter-channel stimulated Raman scattering (ISRS) on the optical Kerr nonlinearity. Additionally, the frequency dependent fiber attenuation can be taken into account and transmission systems that use hybrid amplification schemes can be modeled, where distributed Raman amplification is partly applied over the optical spectrum. To include the latter two cases, a set of coupled ordinary differential equations must be numerically solved in order to obtain the signal power profile yielding a semi-analytical model. However for lumped amplification and negligible variation in fiber attenuation, a less complex and fully analytical model is presented which is referred to as the ISRS GN model. The derived model is exact to first-order for Gaussian modulated signals and extensively validated by numerical split-step simulations. A maximum deviation of $0.1$~dB in nonlinear interference power between simulations and the ISRS GN model is found. The model is applied to a transmission system that occupies an optical bandwidth of $10$~THz, representing the entire C+L band. At optimum launch power, changes of up to $2$~dB in nonlinear interference power due to ISRS are reported. Furthermore, comparable models published in the literature are benchmarked against the ISRS GN model.

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arXiv2017

Digital Nonlinearity Compensation in High-Capacity Optical Fibre Communication Systems: Performance and Optimisation

Meeting the ever-growing information rate demands has become of utmost importance for optical communication systems. However, it has proven to be a challenging task due to the presence of Kerr effects, which have largely been regarded as a major bottleneck for enhancing the achievable information rates in modern optical communications. In this work, the optimisation and performance of digital nonlinearity compensation are discussed for maximising the achievable information rates in spectrally-efficient optical fibre communication systems. It is found that, for any given target information rate, there exists a trade-off between modulation format and compensated bandwidth to reduce the computational complexity requirement of digital nonlinearity compensation.

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