High-Cardinality Hybrid Shaping for 4D Modulation Formats in Optical Communications Optimized via End-to-End Learning

In this paper we carry out a joint optimization of probabilistic (PS) and geometric shaping (GS) for four-dimensional (4D) modulation formats in long-haul coherent wavelength division multiplexed (WDM) optical fiber communications using an auto-encoder framework. We propose a 4D 10 bits/symbol constellation which we obtained via end-to-end deep learning over the split-step Fourier model of the fiber channel. The constellation achieved 13.6% reach increase at a data rate of approximately 400 Gbits/second in comparison to the ubiquitously employed polarization multiplexed 32-QAM format at a forward error correction overhead of 20%.Comment: 5 pages, 3 figure

End-to-end Optimization of Constellation Shaping for Wiener Phase Noise Channels with a Differentiable Blind Phase Search

As the demand for higher data throughput in coherent optical communication systems increases, we need to find ways to increase capacity in existing and future optical communication links. To address the demand for higher spectral efficiencies, we apply end-to-end optimization for joint geometric and probabilistic constellation shaping in the presence of Wiener phase noise and carrier phase estimation. Our approach follows state-of-the-art bitwise auto-encoders, which require a differentiable implementation of all operations between transmitter and receiver, including the DSP algorithms. In this work, we show how to modify the ubiquitous blind phase search (BPS) algorithm, a popular carrier phase estimation algorithm, to make it differentiable and include it in the end-to-end constellation shaping. By leveraging joint geometric and probabilistic constellation shaping, we are able to obtain a robust and pilot-free modulation scheme improving the performance of 64-ary communication systems by at least 0.1 bit/symbol compared to square QAM constellations with neural demappers and by 0.05 bit/symbol compared to previously presented approaches applying only geometric constellation shaping

Adaptive Geometric Constellation Shaping in a Transmission System with a Real-time Optimisation Loop

We demonstrate the real-time performance of an adaptive intelligent transceiver, tailoring the constellation shape to the transmission system by iteratively maximising the information throughput, quantified by the GMI

Geometric Constellation Shaping for Fiber-Optic Channels via End-to-End Learning

End-to-end learning has become a popular method to optimize a constellation shape of a communication system. When the channel model is differentiable, end-to-end learning can be applied with conventional backpropagation algorithm for optimization of the shape. A variety of optimization algorithms have also been developed for end-to-end learning over a non-differentiable channel model. In this paper, we compare gradient-free optimization method based on the cubature Kalman filter, model-free optimization and backpropagation for end-to-end learning on a fiber-optic channel modeled by the split-step Fourier method. The results indicate that the gradient-free optimization algorithms provide a decent replacement to backpropagation in terms of performance at the expense of computational complexity. Furthermore, the quantization problem of finite bit resolution of the digital-to-analog and analog-to-digital converters is addressed and its impact on geometrically shaped constellations is analysed. Here, the results show that when optimizing a constellation with respect to mutual information, a minimum number of quantization levels is required to achieve shaping gain. For generalized mutual information, the gain is maintained throughout all of the considered quantization levels. Also, the results implied that the autoencoder can adapt the constellation size to the given channel conditions

Probabilistic Shaping for Multidimensional Signals with Autoencoder-based End-to-end Learning

This work proposes a system that optimises multidimensional signal transmission, utilising signals with probabilistic shaping designed with the aid of end-to-end learning of an autoencoder-based architecture. For the first time, this work reports bit mapping optimisation for multidimensional signals and applied the newly derived optimised signals to the probabilistic shaping system. The autoencoder employs two neural networks for the transceiver, separated by the embedded channel. The optimisation of the autoencoder configuration is implemented for probabilistic shaping for n-dimensional signals. Specifically, We investigate a 4-dimensional (4D) signal employing 2 successive time slots that has better noise immunity relative to regular 2-dimensional quadrature amplitude modulation (QAM) signals. We propose a new application of autoencoders in communication systems based on 4D signals and apply machine learning to optimise the 4D probabilistic shaping on the basis of receiver signal-to-noise-ratio (SNR). The performance of the optimised probabilistically shaped 4D signals is evaluated in terms of the bit error rate (BER) and mutual information. Simulation results show that the proposed probabilistically shaped 4D signal achieves better BER performance relative to the unshaped 4D and regular 2D QAM. We demonstrate the mutual information of the proposed signal with varying SNR, showing its improved capacity in comparison with other constellations

Constellation Shaping in Optical Communication Systems

Exploiting the full-dimensional capacity of coherent optical communication systems is needed to overcome the increasing bandwidth demands of the future Internet. To achieve capacity, both coding and shaping gains are required, and they are, in principle, independent. Therefore it makes sense to study shaping and how it can be achieved in various dimensions and how various shaping schemes affect the whole performance in real systems. This thesis investigates the performance of constellation shaping methods including geometric shaping (GS) and probabilistic shaping (PS) in coherent fiber-optic systems. To study GS, instead of considering machine learning approaches or optimization of irregular constellations in two dimensions, we have explored multidimensional lattice-based constellations. These constellations provide a regular structure with a fast and low-complexity encoding and decoding. In simulations, we show the possibility of transmitting and detecting constellation with a size of more than 10^{28} points which can be done without a look-up table to store the constellation points. Moreover, improved performance in terms of bit error rate, symbol error rate, and transmission reach are demonstrated over the linear additive white Gaussian noise as well as the nonlinear fiber channel compared to QAM formats.Furthermore, we investigate the performance of PS in two separate scenarios, i.e., transmitter impairments and transmission over hybrid systems with on-off keying channels. In both cases, we find that while PS-QAM outperforms the uniform QAM in the linear regime, uniform QAM can achieve better performance at the optimum power in the presence of transmitter or channel nonlinearities

Machine Learning in Digital Signal Processing for Optical Transmission Systems

The future demand for digital information will exceed the capabilities of current optical communication systems, which are approaching their limits due to component and fiber intrinsic non-linear effects. Machine learning methods are promising to find new ways of leverage the available resources and to explore new solutions. Although, some of the machine learning methods such as adaptive non-linear filtering and probabilistic modeling are not novel in the field of telecommunication, enhanced powerful architecture designs together with increasing computing power make it possible to tackle more complex problems today. The methods presented in this work apply machine learning on optical communication systems with two main contributions. First, an unsupervised learning algorithm with embedded additive white Gaussian noise (AWGN) channel and appropriate power constraint is trained end-to-end, learning a geometric constellation shape for lowest bit-error rates over amplified and unamplified links. Second, supervised machine learning methods, especially deep neural networks with and without internal cyclical connections, are investigated to combat linear and non-linear inter-symbol interference (ISI) as well as colored noise effects introduced by the components and the fiber. On high-bandwidth coherent optical transmission setups their performances and complexities are experimentally evaluated and benchmarked against conventional digital signal processing (DSP) approaches. This thesis shows how machine learning can be applied to optical communication systems. In particular, it is demonstrated that machine learning is a viable designing and DSP tool to increase the capabilities of optical communication systems