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Vahid Aref

Publications and source records attributed to Vahid Aref.

At least 37 records · Page 2Linked to original sources
arXiv2019

Spatially Coupled LDPC Codes with Non-uniform Coupling for Improved Decoding Speed

We consider spatially coupled low-density parity-check codes with finite smoothing parameters. A finite smoothing parameter is important for designing practical codes that are decoded using low-complexity windowed decoders. By optimizing the amount of coupling between spatial positions, we show that we can construct codes with improved decoding speed compared with conventional, uniform smoothing constructions. This leads to a significantly better performance under decoder complexity constraints while keeping the degree distribution regular. We optimize smoothing configurations using differential evolution and illustrate the performance gains by means of a simulation.

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arXiv2019

Statistics of the Nonlinear Discrete Spectrum of a Noisy Pulse

In the presence of additive Gaussian noise, the statistics of the nonlinear Fourier transform (NFT) of a pulse are not yet completely known in closed form. In this paper, we propose a novel approach to study this problem. Our contributions are twofold: first, we extend the existing Fourier Collocation (FC) method to compute the whole discrete spectrum (eigenvalues and spectral amplitudes). We show numerically that the accuracy of FC is comparable to the state-of-the-art NFT algorithms. Second, we apply perturbation theory of linear operators to derive analytic expressions for the joint statistics of the eigenvalues and the spectral amplitudes when a pulse is contaminated by additive Gaussian noise. Our analytic expressions closely match the empirical statistics obtained through simulations.

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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

Efficient Precoding Scheme for Dual-Polarization Multi-Soliton Spectral Amplitude Modulation

Spectral amplitude modulation for dual-polarization multi-soliton transmission is considered. We show, that spectral amplitudes become highly correlated during propagation along a noisy fiber link. Thus, joint equalization is generally needed at the receiver. We propose a simple precoding scheme to almost remove these correlations. It significantly improves the detection performance even without any complex equalization. The spectral amplitudes are transformed into pairs of common and differential information part. We show, that the differential part is almost preserved along the link, even in the presence of noise. Thus, it can be detected directly from the received spectral amplitudes with high reliability. Using the precoding, disjoint detection of the common and the differential part causes only a small performance loss. We analyze our precoding and verify its performance gain in Split-Step-Fourier simulations by comparing it to the conventional independent modulation of spectral amplitudes for first and second order solitons.

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arXiv2018

Time-Bandwidth Product Perspective for Multi-Soliton Phase Modulation

Multi-soliton pulses are potential candidates for fiber optical transmission where the information is modulated and recovered in the so-called nonlinear Fourier domain. While this is an elegant technique to account for the channel nonlinearity, the obtained spectral efficiency, so far, is not competitive with classic Nyquist-based schemes. This is especially due to the observation that soliton pulses generally exhibit a large time-bandwidth product. We consider the phase modulation of spectral amplitudes of higher order solitons, taking into account their varying spectral and temporal behavior when propagating along the fiber. For second and third order solitons, we numerically optimize the pulse shapes to minimize the time-bandwidth product. We study the behavior of multi-soliton pulse duration and bandwidth and generally observe two corner cases where we approximate them analytically. We use these results to give an estimate on the minimal achievable time-bandwidth product per eigenvalue.

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arXiv2018

Nonlinear Fourier Transform of Truncated Multi-Soliton Pulses

Multi-soliton pulses, as special solutions of the Nonlinear Schroedinger Equation (NLSE), are potential candidates for optical fiber transmission where the information is modulated and recovered in the so-called nonlinear Fourier domain. For data communication, the exponentially decaying tails of a multi-soliton must be truncated. Such a windowing changes the nonlinear Fourier spectrum of the pulse. The results of this paper are twofold: (i) we derive the simple closed-form expressions for the nonlinear spectrum, discrete and continuous spectrum, of a symmetrically truncated multi-soliton pulse from tight approximation of the truncated tails. We numerically show the accuracy of the closed-form expressions. (ii) We show how to find, in general, the eigenvalues of the discrete spectrum from the continuous spectrum. We present this method for the application in hand.

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arXiv2018

A Compressed Sensing Approach for Distribution Matching

In this work, we formulate the fixed-length distribution matching as a Bayesian inference problem. Our proposed solution is inspired from the compressed sensing paradigm and the sparse superposition (SS) codes. First, we introduce sparsity in the binary source via position modulation (PM). We then present a simple and exact matcher based on Gaussian signal quantization. At the receiver, the dematcher exploits the sparsity in the source and performs low-complexity dematching based on generalized approximate message-passing (GAMP). We show that GAMP dematcher and spatial coupling lead to asymptotically optimal performance, in the sense that the rate tends to the entropy of the target distribution with vanishing reconstruction error in a proper limit. Furthermore, we assess the performance of the dematcher on practical Hadamard-based operators. A remarkable feature of our proposed solution is the possibility to: i) perform matching at the symbol level (nonbinary); ii) perform joint channel coding and matching.

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arXiv2018

Precoding for Dual Polarization Soliton Transmission

We consider dual-polarized optical multi-soliton pulse transmission. Modulating the nonlinear spectrum, it becomes highly correlated in noisy fiber links. We propose a simple precoding to significantly reduce the correlation, allowing disjoint detection of spectral amplitudes.

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arXiv2018

Statistics of the Eigenvalues of a Noisy Multi-Soliton Pulse

For Nonlinear-Frequency Division-Multiplexed (NFDM) systems, the statistics of the received nonlinear spectrum in the presence of additive white Gaussian noise (AWGN) is an open problem. We present a novel method, based on the Fourier collocation algorithm, to compute these statistics.

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arXiv2018

Probabilistic Eigenvalue Shaping for Nonlinear Fourier Transform Transmission

We consider a nonlinear Fourier transform (NFT)-based transmission scheme, where data is embedded into the imaginary part of the nonlinear discrete spectrum. Inspired by probabilistic amplitude shaping, we propose a probabilistic eigenvalue shaping (PES) scheme as a means to increase the data rate of the system. We exploit the fact that for an NFT-based transmission scheme the pulses in the time domain are of unequal duration by transmitting them with a dynamic symbol interval and find a capacity-achieving distribution. The PES scheme shapes the information symbols according to the capacity-achieving distribution and transmits them together with the parity symbols at the output of a low-density parity-check encoder, suitably modulated, via time-sharing. We furthermore derive an achievable rate for the proposed PES scheme. We verify our results with simulations of the discrete-time model as well as with split-step Fourier simulations.

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arXiv2018

Finite-Length Analysis of Spatially-Coupled Regular LDPC Ensembles on Burst-Erasure Channels

Regular spatially-Coupled LDPC (SC-LDPC) ensembles have gained significant interest since they were shown to universally achieve the capacity of binary memoryless channels under low-complexity belief-propagation decoding. In this work, we focus primarily on the performance of these ensembles over binary channels affected by bursts of erasures. We first develop an analysis of the finite length performance for a single burst per codeword and no errors otherwise. We first assume that the burst erases a complete spatial position, modeling for instance node failures in distributed storage. We provide new tight lower bounds for the block erasure probability ($P_{\mathrm{B}}$) at finite block length and bounds on the coupling parameter for being asymptotically able to recover the burst. We further show that expurgating the ensemble can improve the block erasure probability by several orders of magnitude. Later we extend our methodology to more general channel models. In a first extension, we consider bursts that can start at a random position in the codeword and span across multiple spatial positions. Besides the finite length analysis, we determine by means of density evolution the maximnum correctable burst length. In a second extension, we consider the case where in addition to a single burst, random bit erasures may occur. Finally, we consider a block erasure channel model which erases each spatial position independently with some probability $p$, potentially introducing multiple bursts simultaneously. All results are verified using Monte-Carlo simulations.

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arXiv2017

Does the Cross-Talk Between Nonlinear Modes Limit the Performance of NFDM Systems?

We show a non-negligible cross-talk between nonlinear modes in Nonlinear Frequency-Division Multiplexed system when data is modulated over the nonlinear Fourier spectrum, both the continuous spectrum and the discrete spectrum, and transmitted over a lumped amplified fiber link. We evaluate the performance loss if the cross-talks are neglected.

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arXiv2017

On Time-Bandwidth Product of Multi-Soliton Pulses

Multi-soliton pulses are potential candidates for fiber optical transmission where the information is modulated and recovered in the so-called nonlinear Fourier domain. While this is an elegant technique to account for the channel nonlinearity, the obtained spectral efficiency, so far, is not competitive with the classic Nyquist-based schemes. In this paper, we study the evolution of the time-bandwidth product of multi-solitons as they propagate along the optical fiber. For second and third order soliton pulses, we numerically optimize the pulse shapes to achieve the smallest time-bandwidth product when the phase of the spectral amplitudes is used for modulation. Moreover, we analytically estimate the pulse-duration and bandwidth of multi-solitons in some practically important cases. Those estimations enable us to approximate the time-bandwidth product for higher order solitons.

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arXiv2017

Wave-like Decoding of Tail-biting Spatially Coupled LDPC Codes Through Iterative Demapping

For finite coupling lengths, terminated spatially coupled low-density parity-check (SC-LDPC) codes show a non-negligible rate-loss. In this paper, we investigate if this rate loss can be mitigated by tail-biting SC-LDPC codes in conjunction with iterative demapping of higher order modulation formats. Therefore, we examine the BP threshold of different coupled and uncoupled ensembles. A comparison between the decoding thresholds approximated by EXIT charts and the density evolution results of the coupled and uncoupled ensemble is given. We investigate the effect and potential of different labelings for such a set-up using per-bit EXIT curves, and exemplify the method for a 16-QAM system, e.g., using set partitioning labelings. A hybrid mapping is proposed, where different sub-blocks use different labelings in order to further optimize the decoding thresholds of tail-biting codes, while the computational complexity overhead through iterative demapping remains small.

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arXiv2017

Design Aspects of Multi-Soliton Pulses for Optical Fiber Transmission

We explain how to optimize the nonlinear spectrum of multi-soliton pulses by considering the practical constraints of transmitter, receiver, and lumped-amplified link. The optimization is applied for the experimental transmission of 2ns soliton pulses with independent on-off keying of 10 eigenvalues over 2000 km of NZ-DSF fiber spans.

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