arXiv subjects
Publications and source records attributed to Erik Agrell.
The Manakov equation governs the propagation of signals in dual-polarization systems. Its solution is usually approximated by regular perturbation on the nonlinear Kerr parameter. In this paper, we propose a novel regular perturbation on the group-velocity dispersion parameter for the Manakov equation.
Time-varying distortions in communication systems can significantly degrade the performance of soft-decision forward error correction. This paper presents a burst-aware (BA) low-density parity-check (LDPC) decoding scheme for channels affected by bursty phase noise. By applying differential coding to a Wiener process with time-varying innovation variance, bursty differential phase noise is obtained. Simulation results demonstrate that, compared to conventional decoding, the BA scheme achieves gains in the signal-to-noise ratio of up to $0.7$~dB at a bit error rate (BER) of $4\cdot10^{-3}$ and more than $1$~dB at a packet error rate (PER) of $1\cdot10^{-2}$. Furthermore, by iterating between channel estimation and \ac{ldpc} decoding, forming the proposed iterative burst-aware (IBA) decoding scheme, the gains increase to $1.4$~dB and more than $3$~dB, respectively. More importantly, the IBA scheme significantly improves robustness to bursty phase noise. Compared with the conventional scheme, the IBA scheme can reduce both \ac{ber} and \ac{per} by up to two orders of magnitude under severe bursty phase noise.
We propose physics-informed digital twin (PIDT): a fiber parameter estimation approach that combines a parameterized split-step method with a physics-informed loss. PIDT improves accuracy and convergence speed with lower complexity compared to previous neural operators.
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 constructed from glued products of previously known lattices, by scaling the component lattices and then optimizing the scale factors. A two-parameter family of lattices in 13 dimensions reveals an intricate landscape of phase changes as the parameters are varied.
The capacity of a discrete-time channel with correlated phase noises is investigated. In particular, the electro-optic frequency comb system is considered, where the phase noise of each subchannel is a combination of two independent Wiener phase-noise sources. Capacity upper and lower bounds are derived for this channel and are compared with lower bounds obtained by numerically evaluating the achievable information rates using quadrature amplitude modulation constellations. Capacity upper and lower bounds are provided for the high signal-to-noise ratio (SNR) regime. The multiplexing gain (pre-log) is shown to be $M-1$, where $M$ represents the number of subchannels. A constant gap between the asymptotic upper and lower bounds is observed, which depends on the number of subchannels $M$. For the specific case of $M=2$, capacity is characterized up to a term that vanishes as the SNR grows large.
We explore the optimal pilot positioning for phase tracking in electro-optic frequency comb setups. We show that, in contrast to previous results for regular multichannel systems, allocating the first and the last channels for pilots is optimal given a fixed pilot overhead
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 highlighting challenges related to model overparameterization.
Lattices with minimal normalized second moments are designed using a new numerical optimization algorithm. Starting from a random lower-triangular generator matrix and applying stochastic gradient descent, all elements are updated towards the negative gradient, which makes it the most efficient algorithm proposed so far for this purpose. A graphical illustration of the theta series, called theta image, is introduced and shown to be a powerful tool for converting numerical lattice representations into their underlying exact forms. As a proof of concept, optimized lattices are designed in dimensions up to 16. In all dimensions, the algorithm converges to either the previously best known lattice or a better one. The dual of the 15-dimensional laminated lattice is conjectured to be optimal in its dimension and its exact normalized second moment is computed.
40 years ago, Conway and Sloane proposed using the highly symmetrical Coxeter-Todd lattice $K_{12}$ for quantization, and estimated its second moment. Since then, all published lists identify $K_{12}$ as the best 12-dimensional lattice quantizer. Surprisingly, $K_{12}$ is not optimal: we construct two new 12-dimensional lattices with lower normalized second moments. The new lattices are obtained by gluing together 6-dimensional lattices.
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 simple method to quantify the variance of such estimates, which is far more accurate than the commonly used jackknife estimator.
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 $K_{12}$ as well as to a family of lattices obtained from laminating $K_{12}$. By optimizing this family, we obtain a new 13-dimensional lattice, whose quantizer constant is smaller than any published at the time of submission. (For subsequent improvements, see Note added in proof after the Conclusions.)
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 changes, we propose tracking algorithms that can perform similarly or better without parameter tuning. Numerical simulation results show higher robustness of the proposed algorithms to SOP and PDL drift compared to GD-based algorithms, making them promising candidates to be used in aerial fiber links where the SOP can potentially drift rapidly, and therefore becomes challenging to track.
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 distribution on the channel output. To efficiently compute the required divergence maximization between the conditional channel and the reference distribution, we use a modified mutual information neural estimator that takes the channel input as an additional parameter. We numerically evaluate our approach on different memoryless channels and show empirically that the estimated upper bounds closely converge either to the channel capacity or to best-known lower bounds.
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 particular focus is on memoryless multiple-input multiple-output (MIMO) and multi-user (MU) systems. Four case studies are considered: two point-to-point (closed-loop and open-loop MIMO) and two MU scenarios (MIMO broadcast and interference channels). For the point-to-point scenarios, we explain some of the performance gains observed in prior work through the selection of improved baseline schemes that include geometric shaping as well as bit and power allocation. For the MIMO broadcast channel, we demonstrate the feasibility of a novel AE method with centralized learning and decentralized execution. Interestingly, the learned scheme performs close to nonlinear vector-perturbation precoding and significantly outperforms conventional zero-forcing. Lastly, we highlight potential pitfalls when interpreting learned communication schemes. In particular, we show that the AE for the considered interference channel learns to avoid interference, albeit in a rotated reference frame. After de-rotating the learned signal constellation of each user, the resulting scheme corresponds to conventional time sharing with geometric shaping.
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 white quantization error: for a uniformly distributed source, the covariance of the error is the identity matrix, multiplied by a positive real factor. We generalize the theorem, showing that the same property holds (i) for any lattice whose mean square error cannot be decreased by a small perturbation of the generator matrix, and (ii) for an optimal product of lattices that are themselves locally optimal in the sense of (i). We derive an upper bound on the normalized second moment (NSM) of the optimal lattice in any dimension, by proving that any lower- or upper-triangular modification to the generator matrix of a product lattice reduces the NSM. Using these tools and employing the best currently known lattice quantizers to build product lattices, we construct improved lattice quantizers in dimensions 13 to 15, 17 to 23, and 25 to 48. In some dimensions, these are the first reported lattices with normalized second moments below the best known upper bound.
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 of the polarization drift channel under an average power constraint with imperfect channel knowledge is characterized. An achievable information rate (AIR) is derived when imperfect channel knowledge is available and is shown to be highly dependent on the channel estimation technique. It is also shown that a tighter lower bound can be achieved when a unitary estimation of the channel is available. However, the conventional estimation algorithms do not guarantee a unitary channel estimation. Therefore, by considering the unitary constraint of the channel, a data-aided channel estimator based on the Kabsch algorithm is proposed, and its performance is numerically evaluated in terms of AIR. Monte Carlo simulations show that Kabsch outperforms the least-square error algorithm. In particular, with complex, Gaussian inputs and eight pilot symbols per block, Kabsch improves the AIR by 0:2 to 0:35 bits/symbol throughout the range of studied signal-to-noise ratios.
The optimal lattice quantizer is the lattice which minimizes the (dimensionless) second moment $G$. In dimensions $1$ to $8$, it has been proven that the optimal lattice quantizer is one of the classical lattices, or there is good evidence for this. In contrast, more than two decades ago, convincing numerical studies showed that in dimension $9$, a non-classical lattice is optimal. The structure and properties of this lattice depend upon a real parameter $a>0$, whose value was only known approximately. Here, we give a full description of this one-parameter family of lattices and their Voronoi cells, and calculate their (scalar and tensor) second moments analytically as a function of $a$. The value of $a$ which minimizes $G$ is an algebraic number, defined by the root of a $9$th order polynomial, with $a \approx 0.573223794$. For this value of $a$, the covariance matrix (second moment tensor) is proportional to the identity, consistent with a theorem of Zamir and Feder for optimal quantizers. The structure of the Voronoi cell depends upon $a$, and undergoes phase transitions at $a^2 = 1/2$, $1$ and $2$, where its geometry changes abruptly. At each transition, the analytic formula for the second moment changes in a very simple way. Our methods can be used for arbitrary one-parameter families of layered lattices, and may thus provide a useful tool to identify optimal quantizers in other dimensions as well.
This document lists some errors found in the second edition of Error Control Coding by Shu Lin and Daniel J. Costello, Jr.