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 Shannon limit, although there are practical implementation challenges that need to be carefully addressed. We propose a hierarchical DM (HiDM) scheme, having fully parallelized input-output interfaces and a pipelined architecture that can efficiently perform the DM/invDM without the complex operations of previously proposed methods such as constant composition DM. Furthermore, HiDM can operate at a significantly larger post-FEC bit error rate (BER) for the same post-invDM BER performance, which facilitates simulations. These benefits come at the cost of a slightly larger rate loss and required signal-to-noise ratio at a given post-FEC BER.
By exploiting the electromagnetic wave's four-dimensional signal space, we find that for the additive white Gaussian noise channel, the modulation format with best sensitivity to be an 8-level format ...with 1.76 dB asymptotic gain over BPSK, for uncoded optical transmission with coherent detection. Low-complexity modulators are presented for the format, as well as an interpretation in terms of quantum-limited sensitivity.
This paper studies the routing, modulation format, and spectrum allocation problem in elastic fiber-optical networks for static traffic. Elastic networks, based on Nyquist wavelength-division ...multiplexing or optical orthogonal frequency-division multiplexing, can efficiently utilize the optical fiber's bandwidth in an elastic manner by partitioning the bandwidth into hundreds or even thousands of subcarriers. Beside the amplified spontaneous emission noise, the nonlinear impairments of each connection is explicitly considered by utilizing an analytical model to calculate the nonlinear interference from other connections propagating in the same fibers. The objective of our work is to minimize the bandwidth, i.e., the number of used subcarriers across the network, while satisfying the demands on throughput and quality for all connections. A novel integer linear program formulation and low-complexity heuristics are proposed. Simulation results are presented to demonstrate the effectiveness of the proposed approaches. Compared with transmission reach-based benchmark methods, our methods can achieve up to 31% bandwidth reduction.
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 on approximations of the nonlinear Schrödinger equation, the differential equation that governs the propagation in an optical fibre. All available models in the literature are restricted to certain regimes of operation. Here, we present an approximate model for the nonlinear optical fibre channel in the weak-dispersion regime, in a noiseless scenario. The approximation is obtained by applying regular perturbation theory on the group-velocity dispersion parameter of the nonlinear Schrödinger equation. The proposed model is compared with three other models using the normalized square deviation metric and shown to be significantly more accurate for links with high nonlinearities and weak dispersion.
Optimal binary labelings, input distributions, and input alphabets are analyzed for the so-called bit-interleaved coded modulation (BICM) capacity, paying special attention to the low signal-to-noise ...ratio (SNR) regime. For 8-ary pulse amplitude modulation (PAM) and for 0.75 bit/symbol, the folded binary code results in a higher capacity than the binary reflected Gray code (BRGC) and the natural binary code (NBC). The 1 dB gap between the additive white Gaussian noise (AWGN) capacity and the BICM capacity with the BRGC can be almost completely removed if the input symbol distribution is properly selected. First-order asymptotics of the BICM capacity for arbitrary input alphabets and distributions, dimensions, mean, variance, and binary labeling are developed. These asymptotics are used to define first-order optimal (FOO) constellations for BICM, i.e., constellations that make BICM achieve the Shannon limit -1.59 dB. It is shown that the E b / N 0 required for reliable transmission at asymptotically low rates in BICM can be as high as infinity, that for uniform input distributions and 8-PAM there are only 72 classes of binary labelings with a different first-order asymptotic behavior, and that this number is reduced to only 26 for 8-ary phase shift keying (PSK). A general answer to the question of FOO constellations for BICM is also given: using the Hadamard transform, it is found that for uniform input distributions, a constellation for BICM is FOO if and only if it is a linear projection of a hypercube. A constellation based on PAM or quadrature amplitude modulation input alphabets is FOO if and only if they are labeled by the NBC; if the constellation is based on PSK input alphabets instead, it can never be FOO if the input alphabet has more than four points, regardless of the labeling.
This paper investigates the impact of transceiver noise on the performance of digital back-propagation (DBP). A generalized expression to estimate the signal-to-noise ratio (SNR) obtained using DBP ...in the presence of transceiver noise is described. This new expression correctly accounts for the nonlinear beating between the transceiver noise and the signal in the optical fiber transmission link. The transceiver noise-signal nonlinear beating has been identified as the main reason for the discrepancy between predicted and practical performance of DBP; which has not been previously suggested. This nonlinear beating has been included in the GN model, allowing DBP gains in practical systems to be predicted analytically. Experiments and split-step simulations with and without polarization-mode dispersion (PMD) in the transmission link have been performed. The results show that the impact of transceiver noise greatly outweighs that of PMD, and the analytical expressions are confirmed by the numerical simulations.
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 affected by the simplifying assumptions under which they are derived. In this paper, we consider single-channel data transmission based on three continuous-time optical models: (i) a regular perturbative channel, (ii) a logarithmic perturbative channel, and (iii) the stochastic nonlinear Schrödinger (NLS) channel. To obtain analytically tractable discrete-time models, we consider zero-dispersion fibers and a sampling receiver. We investigate the per-sample capacity of these models. Specifically, (i) we establish tight bounds on the capacity of the regular perturbative channel; (ii) we obtain the capacity of the logarithmic perturbative channel; and (iii) we present a novel upper bound on the capacity of the zero-dispersion NLS channel. Our results illustrate that the capacity of these models departs from each other at high powers because these models yield different capacity pre-logs. Since all three models are based on the same physical channel, our results highlight that care must be exercised in using simplified channel models in the high-power regime.
A low-complexity model for signal quality prediction in a nonlinear fiber-optic network is developed. The model, which builds on the Gaussian noise model, takes into account the signal degradation ...caused by a combination of chromatic dispersion, nonlinear signal distortion, and amplifier noise. The center frequencies, bandwidths, and transmit powers can be chosen independently for each channel, which makes the model suitable for analysis and optimization of resource allocation and routing in large-scale optical networks applying flexible-grid wavelength-division multiplexing.
On the Best Lattice Quantizers Agrell, Erik; Allen, Bruce
IEEE transactions on information theory,
12/2023, Letnik:
69, Številka:
12
Journal Article
Recenzirano
Odprti dostop
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.
Coded modulation (CM) is the combination of forward error correction (FEC) and multilevel constellations. Coherent optical communication systems result in a four-dimensional (4D) signal space, which ...naturally leads to 4D-CM transceivers. A practically attractive design paradigm is to use a bit-wise decoder, where the detection process is (suboptimally) separated into two steps: soft-decision demapping followed by binary decoding. In this paper, bit-wise decoders are studied from an information-theoretic viewpoint. 4D constellations with up to 4096 constellation points are considered. Metrics to predict the post-FEC bit-error rate (BER) of bit-wise decoders are analyzed. The mutual information is shown to fail at predicting the post-FEC BER of bit-wise decoders and the so-called generalized mutual information is shown to be a much more robust metric. For the suboptimal scheme under consideration, it is also shown that constellations that transmit and receive information in each polarization and quadrature independently (e.g., PM-QPSK, PM-16QAM, and PM-64QAM) outperform the best 4D constellations designed for uncoded transmission. Theoretical gains are as high as 4 dB, which are then validated via numerical simulations of low-density parity check codes.
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