Erik Agrell

• Professor at Chalmers University of Technology

New lattice quantizers with lower normalized second moments than previously reported are constructed in 13 and 14 dimensions and conjectured to be optimal. Our construction combines an initial numerical optimization with a subsequent analytical optimization of families of lattices, whose Voronoi regions are constructed exactly. The new lattices are...

40 years ago, Conway and Sloane proposed using the highly symmetrical Coxeter–Todd lattice K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</sub> for quantization, and estimated its second moment. Since then, all published lists identify K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xml...

The Covid-19 pandemic showed forcefully the fundamental importance broadband data communication and the internet has in our society. Optical communications forms the undisputable backbone of this critical infrastructure, and it is supported by an interdisciplinary research community striving to improve and develop it further. Since the first ‘Roadm...

Multidimensional (MD) modulation formats enable a larger minimum Euclidean distance than conventional two-dimensional formats. As a structured geometric shaping method, MD Voronoi constellations (VCs) avoid the use of look-up tables and can be implemented with low-complexity encoding and decoding algorithms, outperforming quadrature amplitude modul...

Traffic demands in future elastic optical networks are expected to be heterogeneous with time-varying bandwidth. Estimating the physical-layer impairments (PLIs) for random bandwidth demands is important for cross-layer network resource provisioning. State-of-the-art PLI estimation techniques yield conservative PLI estimates using the maximum bandw...

We implemented and evaluated probabilistically-shaped multilevel coded modulation and soft-information based performance monitoring at throughputs from 200 Gb/s to 1.2 Tb/s for multi-haul fiber-optic communications. Error-free operations were observed in 5- to 128-ary modulation formats.

We consider the problem of recovering spatially resolved polarization information from receiver Jones matrices. We introduce a physics-based learning approach, improving noise resilience compared to previous inverse scattering methods, while highlight-ing challenges related to model overparameterization.

A lattice quantizer approximates an arbitrary real-valued source vector with a vector taken from a specific discrete lattice. The quantization error is the difference between the source vector and the lattice vector. In a classic 1996 paper, Zamir and Feder show that the globally optimal lattice quantizer (which minimizes the mean square error) has...

Presents corrections to the article “Power-Efficient Voronoi Constellations for Fiber-Optic Communication Systems”.

Multidimensional geometric shaping has been shown to outperform uniform quadrature amplitude modulation (QAM) in optical communication systems but the complexity of symbol decision and bit mapping can often be significant as dimensionality increases. In this paper, a low-complexity geometric shaping method based on multidimensional lattices is inve...

We give a detailed description of the Voronoi region of the Barnes-Wall lattice $\Lambda_{16}$, including its vertices, relevant vectors, and symmetry group. The exact value of its quantizer constant is calculated, which was previously only known approximately. To verify the result, we estimate the same constant numerically and propose a new very s...

We give a detailed description of the Voronoi region of the Barnes–Wall lattice Λ16, including its vertices, relevant vectors, and symmetry group. The exact value of its quantizer constant is calculated, which was previously only known approximately. To verify the result, we estimate the same constant numerically and propose a new very simple metho...

Emerging video services are associated with stringent quality-of-service (QoS) and high data-rate requirements. Moreover, the presence of data-rate-hungry mobile users in future networks necessitate sophisticated design strategies. The deployment of unmanned aerial vehicle access point (UAP)-assisted networks (UANs) has been proposed to ensure high...

Dynamic reconfigurability in optical and mobile networks can facilitate heterogeneous service provisioning while utilizing minimal resources. This allows cost-efficient service delivery resulting in high revenues for network operators. Deployment of elastic mobile and optical networks is a key driver for enabling reconfigurability in modern network...

We consider the problem of estimating an upper bound on the capacity of a memoryless channel with unknown channel law and continuous output alphabet. A novel data-driven algorithm is proposed that exploits the dual representation of capacity where the maximization over the input distribution is replaced with a minimization over a reference distribu...

In optical fiber communication, due to the random variation of the environment, the state of polarization (SOP) fluctuates randomly with time leading to distortion and performance degradation. The memory-less SOP fluctuations can be regarded as a two-by-two random unitary matrix. In this paper, for what we believe to be the first time, the capacity...

We present an algorithm for the exact computer-aided construction of the Voronoi cells of lattices with known symmetry group. Our algorithm scales better than linearly with the total number of faces and is applicable to dimensions beyond 12, which previous methods could not achieve. The new algorithm is applied to the Coxeter-Todd lattice $K_{12}$...

In this paper, we analyze the effectiveness of polarization tracking algorithms in optical transmission systems suffering from fast state of polarization (SOP) rotations and polarization-dependent loss (PDL). While most of the gradient descent (GD)-based algorithms in the literature may require step size adjustment when the channel condition change...

End-to-end autoencoder (AE) learning has the potential of exceeding the performance of human-engineered transceivers and encoding schemes, without a priori knowledge of communication-theoretic principles. In this work, we aim to understand to what extent and for which scenarios this claim holds true when comparing with fair benchmarks. Our particul...

We consider the problem of estimating an upper bound on the capacity of a memoryless channel with unknown channel law and continuous output alphabet. A novel data-driven algorithm is proposed that exploits the dual representation of capacity where the maximization over the input distribution is replaced with a minimization over a reference distribu...

In this paper, we analyze the effectiveness of polarization tracking algorithms in optical transmission systems suffering from fast state of polarization (SOP) rotations and polarization-dependent loss (PDL). While most of the gradient descent (GD)-based algorithms in the literature may require step size adjustment when the channel condition change...

End-to-end autoencoder (AE) learning has the potential of exceeding the performance of human-engineered transceivers and encoding schemes, without a priori knowledge of communication-theoretic principles. In this work, we aim to understand to what extent and for which scenarios this claim holds true when comparing with fair benchmarks. Our particul...

To enable optical interconnect fluidity in next-generation data centers, we propose adaptive transmission based on machine learning in a wavelength-routing network. We consider programmable transmitters that can apply N possible code rates to connections based on predicted bit error rate (BER) values. To classify the BER, we employ a preprocessing...

Voronoi constellations (VCs) are considered as an effective geometric shaping method due to their high power efficiencies and low complexity. In this paper, the performance of 16- and 32-dimensional VCs with a variety of spectral efficiencies transmitted in the nonlinear fiber channel are investigated. Both single-channel and wavelength-division mu...

In optical fiber communication, due to the random variation of the environment, the state of polarization (SOP) fluctuates randomly with time leading to distortion and performance degradation. The memory-less SOP fluctuations can be regarded as a two-by-two random unitary matrix. In this paper, for what we believe to be the first time, the capacity...

Voronoi constellations (VCs) are finite sets of vectors of a coding lattice enclosed by the translated Voronoi region of a shaping lattice, which is a sublattice of the coding lattice. In conventional VCs, the shaping lattice is a scaled-up version of the coding lattice. In this paper, we design low-complexity VCs with a cubic coding lattice of up...

Signal propagation in an optical fiber can be described by the nonlinear Schrdinger equation (NLSE). The NLSE has no known closed-form solution when both dispersion and nonlinearities are considered simultaneously. In this paper, we present a novel integral-form approximate model for the nonlinear optical channel, with applications to passive optic...

Although forward error-correction (FEC) coding is an essential part of modern fiber-optic communication systems, it is impractical to implement and evaluate FEC in transmission experiments and simulations. Therefore, it is desirable to accurately predict the end-to-end link performance including FEC from transmission data recorded without FEC. In t...

Probabilistic shaping (PS) has been widely studied and applied to optical fiber communications. The encoder of PS expends the number of bit slots and controls the probability distribution of channel input symbols. Not only studies focused on PS but also most works on optical fiber communications have assumed source uniformity (i.e. equal probabilit...

Signal propagation in an optical fiber can be described by the nonlinear Schr\"odinger equation (NLSE). The NLSE has no known closed-form solution, mostly due to the interaction of dispersion and nonlinearities. In this paper, we present a novel closed-form approximate model for the nonlinear optical channel, with applications to passive optical ne...

The emerging video services are associated with stringent quality-of-service (QoS) requirements and place high bandwidth demands on the core networks. Edge caching can facilitate the stringent QoS demands while easing the bandwidth requirement from core networks. However, such schemes require on-field caching equipment, in which energy consumption...

Although forward error-correction (FEC) coding is an essential part of modern fiber-optic communication systems, it is impractical to implement and evaluate FEC in transmission experiments and simulations. Therefore, it is desirable to accurately predict the end-to-end link performance including FEC from transmission data recorded without FEC. In t...

Probabilistic shaping (PS) has been widely studied and applied to optical fiber communications. The encoder of PS expends the number of bit slots and controls the probability distribution of channel input symbols. Not only studies focused on PS but also most works on optical fiber communications have assumed source uniformity (i.e. equal probabilit...

Coherent optical transmission systems naturally lead to a four dimensional (4D) signal space, i.e., two polarizations each with two quadratures. In this paper we derive an anlaytical model to quantify the impact of Kerr nonlinearity on such 4D spaces, taking the interpolarization dependency into account. This is in contrast to previous models such...

Flexible grid networks need rigorous resource planning to avoid network over-dimensioning and resource over-provisioning. The network must provision the hardware and spectrum resources statically, even for dynamic random bandwidth demands, due to the infrastructure of flexible grid networks, hardware limitations, and reconfiguration speed of the co...

A novel hierarchical subcarrier rate and distribution matching has been implemented in an FPGA at 1.032 Tb/s. The implemented subsystem achieves seamless data flow among subcarriers at a resolution < 0.01 bit per channel use.

Approaching Shannon's capacity via geometric shaping has usually been regarded as challenging due to modulation and demodulation complexity, requiring look-up tables to store the constellation points and constellation bit labeling. To overcome these challenges, in this paper, we study lattice-based geometrically shaped modulation formats in multidi...

Coherent optical transmission systems naturally lead to a four dimensional (4D) signal space, i.e., two polarizations each with two quadratures. In this paper we derive an analytical model to quantify the impact of Kerr nonlinearity on such 4Dspaces, taking the interpolarization dependency into account. This is in contrast to previous models such a...

Approaching Shannon's capacity via geometric shaping has usually been regarded as challenging due to modulation and demodulation complexity, requiring look-up tables to store the constellation points and constellation bit labeling. To overcome these challenges, in this paper, we study lattice-based geometrically shaped modulation formats in multidi...

Increasing volume, dynamism, and diversity of access traffic have complicated the challenging problem of dynamic resource allocation in passive optical networks. We introduce a general scheduling procedure for passive optical networks, which optimizes a desired performance metric for an arbitrary set of operational constraints. The proposed schedul...

Joint-channel carrier-phase estimation can improve the performance of multichannel optical communication systems. In the case of pilot-aided estimation, the pilots are distributed over a two-dimensional channel-time symbol block that is transmitted through multiple channels. However, suboptimal pilot distributions reduce the effectiveness of the ca...

Accurate performance benchmarking after forward error correction (FEC) decoding is essential for system design in optical fiber communications. Generalized mutual information (GMI) has been shown to be successful at benchmarking the bit-error rate (BER) after FEC decoding (post-FEC BER) for systems with soft-decision (SD) FEC without probabilistic...

Performance monitoring is an essential function for margin measurements in live systems. Historically, system budgets have been described by the Q-factor converted from the bit error rate (BER) under binary modulation and direct detection. The introduction of hard forward error correction (FEC) did not change this. In recent years, technologies hav...

The effects of transmitter-side multidimensional signal rotations on the performance of multichannel optical transmission are studied in the presence of laser phase noise. In particular, the laser phase noise is assumed to be uncorrelated between channels. To carry out this study, a simple multichannel laser-phase-noise model that has been experime...

The effects of transmitter-side multidimensional signal rotations on the performance of multichannel optical transmission are studied in the presence of laser phase noise. In particular, the laser phase noise is assumed to be uncorrelated between channels. To carry out this study, a simple multichannel laser-phase-noise model that has been experime...

Joint-channel carrier-phase estimation can improve the performance of multichannel optical communication systems. In the case of pilot-aided estimation, the pilots are distributed over a two-dimensional channel--time symbol block that is transmitted through multiple channels. However, suboptimal pilot distributions reduce the effectiveness of the c...

Communication using the optical fibre channel can be challenging due to nonlinear effects that arise in the optical propagation. These effects represent physical processes that originate from light propagation in optical fibres. To obtain fundamental understandings of these processes, mathematical models are typically used. These models are based o...

We investigated a suitable auxiliary channel setting and the gap between Q-factors with hard and soft demapping. The system margin definition should be reconsidered for systems employing complex coded modulation with soft forward error correction.

The standard solution for short-haul fiber-optic communications is to deploy noncoherent systems, i.e., to modulate and detect only the light intensity. In such systems, the signal is corrupted with optical noise from amplifiers and with thermal (electrical) noise. The capacity of noncoherent optical links has been studied extensively in the presen...

We investigated a suitable auxiliary channel setting and the gap between Q-factors with hard and soft demapping. The system margin definition should be reconsidered for systems employing complex coded modulation with soft forward error correction.

A novel multilevel coded modulation scheme with probabilistic shaping is presented. It can reduce the power consumption up to 9 times compared with uniform signaling in the regime of typical hard-decision FEC thresholds.

We investigate a modified split-step Fourier method (SSFM) by including low-pass filters in the linear steps. This method can simultaneously achieve a higher simulation accuracy and a slightly reduced complexity.

GMI-based end-to-end learning is shown to be highly nonconvex. We apply gradient descent initialized with Gray-labeled APSK constellations directly to the constellation coordinates. State-of-the-art constellations in 2D and 4D are found providing reach increases up to 26% w.r.t. to QAM.

GMI-based end-to-end learning is shown to be highly nonconvex. We apply gradient descent initialized with Gray-labeled APSK constellations directly to the constellation coordinates. State-of-the-art constellations in 2D and 4D are found providing reach increases up to 26\% w.r.t. to QAM.

Performance monitoring is an essential function for margin measurements in live systems. Historically, system budgets have been described by the Q-factor converted from the bit error rate (BER) under binary modulation and direct detection. The introduction of hard-decision forward error correction (FEC) did not change this. In recent years technolo...

Accurate performance prediction after forward error correction (FEC) decoding is essential for system design in optical fiber communications. While generalized mutual information (GMI) has been shown to be successful for soft-decision decoded systems, for systems using probabilistic shaping (PS), GMI is less well correlated with the bit-error rate...

Considering the time-averaged behavior of a metro elastic optical network, we develop a joint procedure for resource allocation and traffic shaping to exploit the inherent service diversity among the requests for power-efficient network operation. To support the quality of service diversity, we consider minimum transmission rate, average transmissi...

Ultra-wideband fiber optical transmission suffers from nonlinear interference (NLI) noise caused by both Kerr nonlinerity and stimulated Raman scattering (SRS). Mathematical models that address the interplay between Kerr nonliniearity and SRS exist. The main drawback of such Gaussian noise (GN) models is that they overestimate NLI due to a Gaussian...

Elastic optical networks have been proposed to support high data rates in metro and core networks. However, frequency allocation of the channels (i.e., channel ordering) in such networks is a challenging problem. This requires arranging the optical channels within the frequency grid with the objective of ensuring a minimum signal-to-noise ratio (SN...

Modular optical switch architectures combining wavelength routing based on arrayed waveguide grating (AWG) devices and multicasting based on star couplers hold promise for flexibly addressing the exponentially growing traffic demands in a cost- and power-efficient fashion. In a default switching scenario, an input port of the AWG is connected to an...

A number of simplified models, based on perturbation theory, have been proposed for the fiber-optical channel and have been extensively used in the literature. Although these models are mainly developed for the low-power regime, they are used at moderate or high powers as well. It remains unclear to what extent the capacity of these models is affec...

The sharing of lasers in space-division multiplexed multicore-fiber transmission yields correlated phase noise across the spatial channels. As a result, system performance can be improved through the use of joint-core carrier-phase estimation (CPE). However, the presence of intercore skew can reduce the potential of such schemes. This paper studies...

Presents corrections to the paper, “High capacity transmission with few-mode fibers,” (Rademacher, G.), Lightw. Technol., vol. 37, no. 2, pp. 425–432, Jan. 2019.

Distribution matching and dematching (DM/invDM) are key functions in probabilistic shaping (PS). Recently techniques for low complexity implementation of DM/invDM have been well studied. Our previously proposed hierarchical DM (HiDM) is one of the good candidates, with capacity-approaching performance with reasonable hardware resources. Though we e...

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 Br...

After reviewing models and mitigation strategies for interchannel nonlinear interference (NLI), we study its characteristics and coherence properties. 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 optimizati...

We describe optical data transmission systems using homogeneous, single-mode, multi-core fibers (MCFs). We first briefly discuss space-division multiplexing (SDM) fibers, observing that no individual SDM fiber offers overwhelming advantages over bundles of single-mode fiber (SMF) across all transmission regimes. We note that for early adoption of S...

Elastic optical networks (EONs) rely on efficient resource planning to meet future communication needs and avoid resource overprovisioning. Estimation of physical-layer impairments (PLIs) in EONs plays an important role in the network planning stage. Traditionally, the transmission reach (TR) and Gaussian noise (GN) models have been broadly employe...

The implementation difficulties of combining distribution matching (DM) and dematching (invDM) for probabilistic shaping (PS) with soft-decision forward error correction (FEC) coding can be relaxed by reverse concatenation, for which the FEC coding and decoding lies inside the shaping algorithms. PS can seemingly achieve performance close to the Sh...

The variability of source entropy due to data idling is inconsistent with most studies’ assumptions in probabilistic shaping. We propose a distribution matcher sensitive to the source entropy, and discuss its impacts on fiber-optic communications.

The performance of pilot-aided joint-channel carrier-phase estimation (CPE) in space-division multiplexed multicore fiber (MCF) transmission with correlated phase noise is studied. To that end, a system model describing uncoded MCF transmission where the phase noise comprises a common laser phase noise, in addition to core- and polarization-specifi...

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 Br...

The performance of pilot-aided joint-channel carrier-phase estimation (CPE) in space-division multiplexed multicore fiber (MCF) transmission with correlated phase noise is studied. To that end, a system model describing uncoded MCF transmission where the phase noise comprises a common laser phase noise, in addition to core- and polarization-specifi...

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) an...

Modular optical switch architectures combining wavelength routing based on arrayed waveguide grating (AWG) devices and multicasting based on star couplers hold promise for flexibly addressing the exponentially growing traffic demands in a cost- and power-efficient fashion. In a default switching scenario, an input port of the AWG is connected to an...

Reverse concatenation of forward error correction and distribution matching significantly improves the implementation capability of probabilistic constellation shaping. However, to take full advantage of the benefits, one should carefully understand the practical aspects and trade-offs.

We experimentally investigate high-capacity fewmode fiber transmission for short and medium-haul optical links. In separate experiments, we demonstrate C + L band transmission of 283 Tbit/s over a single 30 km span and recirculating loop transmission of 159 Tbit/s over 1045 km graded-index three mode fiber. The first experiment reached a data-rate...

In fiber-optic communications, evaluation of mutual information (MI) is still an open issue due to the unavailability of an exact and mathematically tractable channel model. Traditionally, lower bounds on MI are computed by approximating the (original) channel with an auxiliary forward channel. In this paper, lower bounds are computed using an auxi...

The implementation difficulties of combining distribution matching (DM) and dematching (invDM) for probabilistic shaping (PS) with soft-decision forward error correction (FEC) coding can be relaxed by reverse concatenation, for which the FEC coding and decoding lies inside the shaping algorithms. PS can seemingly achieve performance close to the Sh...

Modular design based on spatial division multiplexing switches is a promising way to improve the capacity and reduce the cabling complexity of data center networks. However, due to the coexistence of mice and elephant flows, in modular data center networks a trade-off between the blocking probability and total throughput arises. In fact, blocking e...

The problem of phase-noise compensation for correlated phase noise in coded multichannel optical transmission is investigated. To that end, a multichannel phase-noise model is introduced and the maximum a posteriori detector for this model is approximated using two frameworks, namely factor graphs (FGs) and the sum--product algorithm (SPA), as well...

The problem of phase-noise compensation for correlated phase noise in coded multichannel optical transmission is investigated. To that end, a simple multichannel phase-noise model is considered and the maximum a posteriori detector for this model is approximated using two frameworks, namely factor graphs (FGs) combined with the sum-product algorith...

The all-optical switching of multicast flows using star couplers and tunable transceivers is a promising solution for emerging cloud data center applications. However, the limited tuning range of optical components on one hand and the buffer management challenges for multicast traffic delivery on the other pose a significant impact on the performan...

Run-length code based distribution matching (DM) for probabilistic shaping is combined with a uniformalizer to realize low-complexity fixed-length DM. The proposed method is 0.4 dB better than previous low-complexity DM methods.

We propose a tool for reusing experimental or simulation data of probabilistically shaped signals with different FEC codes. A single recorded histogram of log-likelihood ratios is sufficient to examine arbitrary coding at low BERs.

We examine the feasibility of ultrahigh-scale datacenter multicasting by simultaneously taking into account the choice of architecture, modulation, and coding. Our Monte Carlo simulations indicate the dominant impact of in-band crosstalk on the throughput performance.