Generalized Mutual Information Research Articles

214.7 Tbit/s S, C, and L-band transmission over 50 km SSMF based on silicon photonic integrated transceivers

We experimentally demonstrate a 214.7 Tbit/s generalized mutual information (GMI) estimated throughput by ultra-wideband wavelength division multiplexing (WDM) transmission in standard single-mode fiber (SSMF). With 50-GHz grid, 396 transmission channels are used to deliver 49 GBaud probabilistically constellation-shaped (PCS) 256 quadrature amplitude modulation (QAM) and PCS-64QAM signals. Silicon photonic integrated transceiver is employed to complete electro-optic and optic-electro conversion of the modulated signals. S, C, and L-band rare-earth-doped amplifiers enable the 19.8 THz bandwidth WDM transmission without the assistance of distributed Raman amplification. The measured data rate shows great potential for Silicon photonic devices deployed in ultra-wideband WDM transmission.

Bayesian generative adversarial network emulator based end-to-end learning strategy of the probabilistic shaping for OAM mode division multiplexing IM/DD transmission.

Orbital angular momentum (OAM) mode division multiplexing (MDM) has emerged as a new multiplexing technology that can significantly increase transmission capacity. In addition, probabilistic shaping (PS) is a well-established technique that can increase the transmission capacity of an optical fiber to close to the Shannon limit. However, both the mode coupling and the nonlinear impairment lead to a considerable gap between the OAM-MDM channel and the conventional additive white Gaussian noise (AWGN) channel, meaning that existing PS technology is not suitable for an OAM-MDM intensity-modulation direct-detection (IM-DD) system. In this paper, we propose a Bayesian generative adversarial network (BGAN) emulator based on an end-to-end (E2E) learning strategy with probabilistic shaping (PS) for an OAM-MDM IM/DD transmission with two modes. The weights and biases of the BGAN emulator are treated as a probability distribution, which can be accurately matched to the stochastic nonlinear model of OAM-MDM. Furthermore, a BGAN emulator based on an E2E learning strategy is proposed to find the optimal probability distribution of PS for an OAM-MDM IM/DD system. An experiment was conducted on a 200 Gbit/s two OAM modes carrierless amplitude phase-32(CAP-32) signal over a 5 km ring-core fiber transmission, and the results showed that the proposed BGAN emulator outperformed a conventional CGAN emulator, with improvements in modelling accuracy of 29.3% and 26.3% for the two OAM modes, respectively. Moreover, the generalized mutual information (GMI) of the proposed E2E learning strategy outperformed the conventional MB distribution and the CGAN emulator by 0.31 and 0.33 bits/symbol and 0.16 and 0.2 bits/symbol for the two OAM modes, respectively. Our experimental results demonstrate that the proposed E2E learning strategy with the BGAN emulator is a promising candidate for OAM-MDM IM/DD optic fiber communication.

End-to-End Deep Learning of Joint Geometric Probabilistic Shaping Using a Channel-Sensitive Autoencoder

In this paper, we propose an innovative channel-sensitive autoencoder (CSAE)-aided end-to-end deep learning (E2EDL) technique for joint geometric probabilistic shaping. The pretrained conditional generative adversarial network (CGAN) is introduced in the CSAE which performs differentiable substitution of the optical fiber channel model under variable input optical power (IOP) levels. This enables the CSAE-aided E2EDL to design optimal joint geometric probabilistic shaping schemes for optical fiber communication systems at varying IOPs. The results of the proposed CSAE-aided E2EDL technique show that for a dual-polarization 64-Gbaud signal with a transmission distance of 5 × 80 km, when the modulation format is a 64-quadrature amplitude modulation (QAM) or a 128-QAM, the maximum generalized mutual information (GMI) level learned via CSAE-aided E2EDL is 5.9826 or 6.8384 bits/symbol under varying IOPs, respectively. In addition, the pretrained CGAN, as a substitution for optical fiber transmission model, accurately characterizes the distortion of signals with different IOPs, with an average bit error ratio (BER) difference of only 1.83%, an average mean square error (MSE) of 0.0041 and an average K-L divergence of 0.0046. In summary, this paper delivers new insights into the application of E2EDL and demonstrates the feasibility of joint geometric probabilistic shaping-based E2EDL for fiber optic communication systems with varying IOPs.

Optimizing the probability mass function of complex modulated signals through adaptive channel characterization.

We propose a probability mass function (PMF) optimization scheme for quadrature amplitude modulation (QAM) signals by considering the parametric characteristic of the training sequence. The training sequence for optimization is mapped in standard Maxwell-Boltzmann (M-B) distribution, and the considered characterizing parameters incorporate either the noise variance or the error matrix of the received symbols. The proposed PMF optimization is based on independent reallocation within each constellation ring, generating new distribution with almost the same entropy and transmitted power as the original distribution. This reallocation mechanism is model-free and iterative-free with very low computational complexity. By characterizing the channel in terms of constellation performance asymmetry, PMF reallocation can be effectively implemented to supplement the existing equalization algorithm. The effectiveness of this approach is experimentally verified in a 40-km transmission system with 24 Gbaud 64-QAM signals under three different scenarios. Through PMF reallocation, we achieve generalized mutual information (GMI) improvement of ∼0.06 and throughput improvement of ∼1.5 Gbit/s before forward error correction in comparison with the standard M-B distribution. The proposed mechanism provides a solution to obtain the optimal PMF in practical communication channels, which suffer from various types of noises and distortions.

Learning additional latent representations using variational autoencoders

A noticeable trend of machine learning is to deal with data of various modalities. Besides multimodal motivation, learning more from general information without forgetting the prior, or incremental learning, could also benefit unimodal machine learning. Human understanding often starts from a simplistic, generic view of the whole problem and then fills in the details and nuances. Incremental learning could enable imitation of such a learning process to learn more and potentially faster. This paper examines the possibility of learning additional latent variables from known latent variables for variational autoencoders. A method is proposed to facilitate learning additional information based on a modified β-TCVAE loss function that incorporates known general mutual information. A qualitative comparison is conducted on the dSprites dataset to evaluate the effect of this modification and the change of network structures on the learned latent, which hints at the structural tendency for β-TCVAE to learn new information from explicit known latent.

PER Prediction in MIMO-OFDM Systems With Approximate Demodulation: A GMI-Based Method

In multiple-input-multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems, the symbols in a packet may undergo different signal-to-interference-plus-noise ratio (SINR) levels, making packet error rate (PER) prediction a challenging task. Effective SINR mapping (ESM) simplifies this problem by mapping the SINRs on different symbols to a single packet-level effective SINR. A novel ESM method, referred to as mean generalized mutual information mapping (MGMIM), is put forward in this paper. The proposed method transforms the SINR of each symbol to the generalized mutual information (GMI) and then derives an effective SINR from the mean GMI measure over different symbols. The derived effective SINR summarizes the effect of all the SINRs on the packet, which would produce the same PER performance under an additive white Gaussian noise (AWGN) channel. Compared to existing techniques, MGMIM does not require MCS-dependent tuning parameters but delivers competitive or even better PER prediction accuracy. More importantly, MGMIM allows reliable PER prediction when the receiver employs approximate demodulation, which boosts its applicability in practice. These features are demonstrated by comparative numerical simulations.

Artificial Neural Network Assisted Probabilistic and Geometric Shaping for Flexible Rate High-Speed PONs

In this paper, we employ artificial neural networks (ANNs) to optimize joint probabilistic shaping (PS) and geometric shaping (GS) for a realistic 50G IM/DD passive optical network (PON) link. Apart from being able to find a generalized mutual information (GMI)-maximizing modulation for channel conditions unseen at the training phase, the compatibility of the ANN training with Monte Carlo simulation also enables us to use a more complicated channel model that more closely resembles a real PON system where fiber dispersion, bandwidth limitation and digital signal processing (DSP) are present. The forward error correction (FEC) requirement that must be satisfied in an actual implementation is imposed on the learned modulation by including a normalized GMI (NGMI) penalty term in the loss function. The proposed scheme is demonstrated with simulations. Results show that the ANN can achieve similar performance compared to a case-by-case optimization while also being capable of generalizing to a wide range of received optical power (ROP) from −30 dBm to −18 dBm and/or a broad range of fiber distance from 0 km to 20 km. About 0.1-bits/symbol GMI improvement is attained compared to uniform modulation.

3.61 Pbit/s S, C, and L-Band Transmission With 19-Core Single-Mode Fiber

We experimentally demonstrate a 3.61 Pbit/s generalized mutual information (GMI) estimated throughput by space division multiplexing (SDM) and wavelength division multiplexing (WDM) combined transmission over 19-core single-mode fiber. Covering 17 THz bandwidth with a 25-GHz grid in S, C, and L band, 680 wavelength channels are used to deliver 24.5 GBaud probabilistically constellation-shaped (PCS) 256 quadrature amplitude modulation (QAM) and PCS-64QAM signals. The measured data rate shows a great potential for S/C/L-band transmission to dramatically enhance the achievable data rate in multi-core fibers.

GS-16QAM OFDM with ANN scheme combined with LFM signal for joint communication and radar sensing system.

In this Letter, an integrated waveform geometrically shaped (GS) 16 quadrature amplitude modulation (QAM) based orthogonal frequency division multiplexing (OFDM) communication signal combined with a linear frequency modulation (LFM) radar signal is proposed and experimentally demonstrated in a W-band communication and radar detection system. The proposed method can generate communication and radar signals simultaneously. The inherent error propagation and the interference of the radar signal limit the transmission performance of the joint communication and radar sensing system. Thus, an artificial neural network (ANN) scheme is proposed for the GS-16QAM OFDM signal. After 0.8-m wireless transmission, the experimental results show that the receiver sensitivity and normalized general mutual information (NGMI) of the GS-16QAM OFDM are improved compared with that of the OFDM with uniform 16QAM at the forward error correction (FEC) threshold of 3.8 × 10-3. In addition, multi-target radar detection in centimeter level radar ranging is realized.

Performance analysis of hybrid geometric-probabilistic shaped 8/12 quadrature amplitude modulation for coherent optical communication system

A hybrid shaping (HS) scheme based on geometric shaping (GS) and probabilistic shaping (PS) in a coherent optical communication system is proposed. A particle swarm optimization algorithm and Maxwell-Boltzmann distribution are employed to sequentially implement GS and PS. The results demonstrate that hybrid shaped 8/12-ary quadrature amplitude modulation (HS-8/12QAM) is superior to regular-8/12QAM (R-8/12QAM) in terms of reducing the bit error rate (BER) and increasing the generalized mutual information (GMI). HS-8QAM achieves a 2 dB optical signal-to-noise ratio (OSNR) gain and 0.45 bits / symbol GMI gain compared with R-8QAM. Meanwhile, HS-12QAM achieves 1.9 dB OSNR gain and 0.68 bits/symbol GMI gain compared with R-12QAM. In addition, HS-8/12QAM is better than R-8/12QAM in terms of transmission distance and data rate.

Demonstration and Characterization of High-Throughput 200.5 Tbit/s S+C+L Transmission over 2x100 PSCF Spans

Recent advances in multi-band amplification support ultra-wideband (UWB) systems as a suitable solution to cope with the increasing fiber communications traffic demand. The combination of UWB with spectral-efficient modulation formats can significantly increase in the total throughput of wavelength division multiplexed (WDM) transmission systems. <p xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">In this work, we demonstrate a 240×70 Gbaud PCS-256QAM WDM transmission using an optical bandwidth of 150 nm across the S, C and L bands. We combine doped-fiber amplifiers, semiconductor optical amplifiers (SOA) and backward distributed Raman amplification to achieve 200.5 Tbit/s of total generalized mutual information (GMI) throughput over two 100 km pure-silica-core fibers (PSCFs). We also present the digital twin of this experiment, providing the impact of wavelength-dependent impairments on the system performance. Our results demonstrate the feasibility of high-throughput multi-span UWB transmission.

Initialized autoencoders to find constellations robust to residual laser phase noise

Autoencoder (AE) has been used to find quadrature amplitude modulation (QAM) constellations robust to optical impairments, such as residual laser phase noise or fiber nonlinearities. We examine AE for constellations for fiber links with residual phase noise following phase recovery. We study 1) improved constellations via AE neural network (NN) initialization, 2) bit-to-symbol mappings for AE constellations, and 3) performance enhancement from the AE decoder as a detection algorithm. We compare our performance to several other phase-noise-optimized constellations, using an identical phase recovery method for fair comparison. We confirm the improved performance of our constellations experimentally as well as via simulation. Our AE initialization technique (using previous constellations found experimentally, empirically, numerically, etc.) is shown to improve constellations for 16QAM and 64QAM. A bit-to-symbol mapping is essential to benefit fully from AE constellations, but is intractable to optimize. We use an ad hoc approach that derives mappings from our initialization constellations. Our AE initialization technique leads to performance improvements over the previous QAM constellations under all metrics: generalized mutual information (GMI), bit error rate (BER) and symbol error rate (SER). We examine the gap between BER and SER due to non-optimal bit-to-symbol mappings. The AE approach to constellation design has as a byproduct an optimized detector: the AE decoder. We quantify the improvement of this detector over the classic maximum likelihood detection that neglects phase noise.

Low-complexity amplitude-division irregular QAM formats for short-reach unamplified coherent optical systems.

A low-complexity scheme is proposed to realize irregular uniform quadrature amplitude modulation (QAM) formats with Gray mapping, which are named amplitude-division irregular QAM (AD-Ir-QAM) formats. Compared to conventional probabilistic shaping (PS) with the Maxwell-Boltzmann (MB) distribution (PS-MB), irregular QAM formats show a smaller peak-to-average power (PAPR) and achieve a better performance in systems with the peak-power constraint. Compared with irregular QAM formats realized by PS (PS-Ir-QAM), AD-Ir-QAM formats realize a more flexible rate adaptation and have a lower implementation complexity. Experimental results obtained in an unamplified coherent optical system show that, at a generalized mutual information (GMI) of 4.5 bits/2D-symbol, AD-Ir-100QAM achieves gains of 2.1 and 0.5 dB in the power budget over PS-MB-100QAM and PS-Ir-100QAM, respectively.

Orthant-symmetric four-dimensional geometric shaping for fiber-optic channels via a nonlinear interference model.

Maximizing the data throughput for optical fiber communication via signal shaping has usually been regarded as challenging due to the nonlinear interference and implementation/optimization complexity. To overcome these challenges, in this paper, we propose an efficient four-dimensional (4D) geometric shaping (GS) approach to design 4D 512-ary and 1024-ary modulation formats by maximizing the generalized mutual information (GMI) using a 4D nonlinear interference (NLI) model, which makes these modulation formats more nonlinear-tolerant. In addition, we propose and evaluate a fast and low-complexity orthant-symmetry based modulation optimization algorithm via neural networks, which allows to improve the optimization speed and GMI performance for both linear and nonlinear fiber transmission systems. The optimized modulation formats with spectral efficiencies of 9 and 10 bit/4D-sym demonstrate a GMI improvement of up to 1.35 dB compared with their quadrature amplitude modulation (QAM) counterparts in additive white Gaussian noise (AWGN) channel. Numerical simulations of optical transmission over two types of fibers show that the 4D NLI model-learned modulation formats could extend the transmission reach by up to 34% and 12% with respect to the QAM formats and the AWGN-learned 4D modulation formats, respectively. Results of effective signal-to-noise ratio are also presented, which confirm that the extra gains in optical fiber channel come from the enhanced SNR by reducing the modulation-dependent NLI.

Performance Analysis and Power Tilt Mitigation of Ultra-Wideband WDM Transmission Systems

Ultra-wideband (UWB) wavelength division multiplexing (WDM) transmission, which utilizes low-loss spectral windows of single-mode fiber for data transmission, is a highly promising method for increasing the capacity of optical communication. In this paper, we investigate the performance of a UWB WDM transmission system that covers the widely used C+L band as well as the additional O-, E-, and S-bands. We establish the transmission system for UWB and discuss the effects of the channel, including Kerr nonlinearity and inter-channel interference from inter-channel stimulated Raman scattering (ISRS) between O-, E-, S-, C-, and L-bands. Moreover, we demonstrate an optimization scheme for compensating the spectral power tilt caused by SRS in the S+C+L band system, which utilizes the Raman amplifier and the partition particle swarm optimization (PPSO) algorithm. The results show that the power tilt value of the algorithm is reduced from 18 to 2.93 dB, and the iteration speed is improved by 10% compared with the normal particle swarm algorithm. The scheme provides an efficient way to improve the generalized mutual information (GMI) performance of UWB WDM systems.

Performance enhanced geometrically shaped 32-ary quadrature amplitude modulation enabled by swarm intelligence algorithm

The geometrically shaped 32-ary quadrature amplitude modulation (GS-32QAM) signal enabled by swarm intelligence algorithm is proposed in high-speed and long-haul coherent optical communication system. The geometric shaping (GS) is obtained by constructing a generic constellation optimization scheme applying particle swarm algorithm (PSO), wolf pack algorithm (WPA), and marine predator algorithm (MPA), respectively. The complexity of three algorithms applied to GS-32QAM is systematically analyzed, where MPA can obtain better search results with slightly higher complexity than PSO. The results show that the optimized constellation is significantly better than the uniform signal in terms of reducing bit error rate and increasing generalized mutual information (GMI). The maximum GMI gain of GS signal with PSO and WPA are both 0.25 bit / sym, and the maximum GMI gain of GS signal with MPA is up to 0.3 bit / sym. At the hard-decision forward error correlation limitation of 3.8 × 10 − 3, compared with uniform signal, the GS signal with PSO, WPA, and MPA can provide the optical signal-to-noise ratio gain of 1, 1.1, and 1.6 dB tolerance, respectively. In terms of data rate, compared with uniform signal, three GS signals can increase by 33, 36, and 43 Gbit / s, respectively.

A new scheme for adding a pilot at direct current component location in photonics-assisted OFDM MMW system

This paper proposes a new scheme, that is, a constant is added to the real part or imaginary part of the signal at the transmitting end, and the constant becomes a pilot at the location of DC component, thereby replacing the scheme of traditional manual bias IQ modulator to generate a pilot. By adopting this scheme, the purpose of frequency offset estimation can be achieved, and the performance can be improved by quantitatively optimizing the magnitude of the constant at the same time. Using this technology and combined probability shaping technology, a 3.4Gbaud 256QAM OFDM signal can be transmitted 700 m wireless distance, achieving the normalized general mutual information (NGMI) threshold of 0.83 with 25% soft-decision forward-error correction (SD-FEC) overhead.

Information Rates for Channels with Fading, Side Information and Adaptive Codewords.

Generalized mutual information (GMI) is used to compute achievable rates for fading channels with various types of channel state information at the transmitter (CSIT) and receiver (CSIR). The GMI is based on variations of auxiliary channel models with additive white Gaussian noise (AWGN) and circularly-symmetric complex Gaussian inputs. One variation uses reverse channel models with minimum mean square error (MMSE) estimates that give the largest rates but are challenging to optimize. A second variation uses forward channel models with linear MMSE estimates that are easier to optimize. Both model classes are applied to channels where the receiver is unaware of the CSIT and for which adaptive codewords achieve capacity. The forward model inputs are chosen as linear functions of the adaptive codeword's entries to simplify the analysis. For scalar channels, the maximum GMI is then achieved by a conventional codebook, where the amplitude and phase of each channel symbol are modified based on the CSIT. The GMI increases by partitioning the channel output alphabet and using a different auxiliary model for each partition subset. The partitioning also helps to determine the capacity scaling at high and low signal-to-noise ratios. A class of power control policies is described for partial CSIR, including a MMSE policy for full CSIT. Several examples of fading channels with AWGN illustrate the theory, focusing on on-off fading and Rayleigh fading. The capacity results generalize to block fading channels with in-block feedback, including capacity expressions in terms of mutual and directed information.

Power-Efficient Voronoi Constellations for Fiber-Optic Communication Systems

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 multiplexing systems are considered for the transmission of the VCs, as well as different signal processing schemes, including chromatic dispersion compensation and digital backpropagation. Multiple performance metrics including the uncoded bit error rate, mutual information (MI), and generalized mutual information (GMI) of VCs are evaluated. Compared with quadrature amplitude modulation (QAM) formats, the VCs provide 1.0–2.4 dB launch power gains, up to 0.50 bits/symbol/dimension-pair MI gains, up to around 30% potential reach increase at the same MI, and up to 0.30 bits/symbol/dimension-pair GMI gains in a limited launch power range. The observed performance gains over QAM are found higher than in the back-to-back case. Moreover, a general GMI estimation method for very large constellations using importance sampling is proposed for the first time.

1.57 Tb/s PDM-layered 80QAM-OFDM in super-channel transmission based on self-homodyne comb

In this paper, polarization division multiplexing-layered 80-ary quadrature amplitude modulation-orthogonal frequency division multiplexing (PDM-layered 80QAM-OFDM) is proposed and demonstrated in super-channel system based on self-homodyne comb. The composition of the super-channel is derived from the optical comb generated by a single laser-driven dual polarized Mach-Zehnder modulator (DP-MZM) modulated by odd sideband suppression. Since the optical comb generated by the transmitter is used as a local oscillator (LO) signal for self-homodyne coherent detection. This scheme effectively reduces the system cost and alleviates the performance constraints caused by phase noise. Moreover, the bit error rate (BER) and generalized mutual information (GMI) of layered 24QAM/48QAM/80QAM-OFDM are evaluated to obtain the highest transmission rate and the laser linewidth tolerance of the system. The results show that in Additive White Gaussian Noise (AWGN) channel, layered QAM signal realized by low-complexity constellation layering technique can significantly improve the BER performance at a small entropy cost compared with ordinary QAM signals. Meanwhile, the layered 80QAM can achieve a signal-to-noise ratio (SNR) gain of 2.7 dB. In addition, after 40 km standard single mode fiber (SSMF) transmission, the total data rate of the system can reach 1.57 Tbit/s and the corresponding spectral efficiency (SE) is 12 bit/s/Hz when the BER of the super-channel system meets soft decision-forward error correction (SD-FEC) threshold.