On Probabilistic Shaping of Quadrature Amplitude Modulation for the Nonlinear Fiber Channel

Abstract

Abstract-Different aspects of probabilistic shaping for a multi-span optical communication system are studied. First, a numerical analysis of the additive white Gaussian noise (AWGN) channel investigates the effect of using a small number of input probability mass functions (PMFs) for a range of signalto-noise ratios (SNRs), instead of optimizing the constellation shaping for each SNR. It is shown that if a small penalty of at most 0.1 dB SNR to the full shaping gain is acceptable, just two shaped PMFs are required per quadrature amplitude modulation (QAM) over a large SNR range. For a multi-span wavelength division multiplexing (WDM) optical fiber system with 64QAM input, it is shown that just one PMF is required to achieve large gains over uniform input for distances from 1,400 km to 3,000 km. Using recently developed theoretical models that extend the Gaussian noise (GN) model and fullfield split-step simulations, we illustrate the ramifications of probabilistic shaping on the effective SNR after fiber propagation. Our results show that, for a fixed average optical launch power, a shaping gain is obtained for the noise contributions from fiber amplifiers and modulation-independent nonlinear interference (NLI), whereas shaping simultaneously causes a penalty as it leads to an increased NLI. However, this nonlinear shaping loss is found to have a relatively minor impact, and optimizing the shaped PMF with a modulation-dependent GN model confirms that the PMF found for AWGN is also a good choice for a multispan fiber system.

Hierarchical Distribution Matching: a Versatile Tool for Probabilistic Shaping

“…Recently, probabilistic shaping (PS) techniques have been widely investigated to improve the performance and the flexibility of optical fiber networks. By assigning different probabilities to the constellation symbols-e.g., trying to approximate the capacity-achieving Gaussian distribution for the additive white Gaussian noise (AWGN) channel-PS allows both to finely adapt the information rate (IR) to the available signal to noise ratio (SNR) and to reduce the gap between the IR achievable with uniform QAM constellations and the channel capacity [1,2].…”

“…">IntroductionRecently, probabilistic shaping (PS) techniques have been widely investigated to improve the performance and the flexibility of optical fiber networks. By assigning different probabilities to the constellation symbols-e.g., trying to approximate the capacity-achieving Gaussian distribution for the additive white Gaussian noise (AWGN) channel-PS allows both to finely adapt the information rate (IR) to the available signal to noise ratio (SNR) and to reduce the gap between the IR achievable with uniform QAM constellations and the channel capacity [1,2].An effective PS approach, named probabilistic amplitude shaping (PAS) and based on a proper concatenation of a fixed-to-fixed-length distribution matcher (DM) and a systematic forward error correction (FEC) encoder, has been proposed in [3]. The key element of PAS is the DM, which maps k uniformly distributed bits on N shaped (according to a desired distribution) amplitudes from the alphabet A = {1, 3, .…”

First Experimental Demonstration of Probabilistic Enumerative Sphere Shaping in Optical Fiber Communications

“…Even higher gains for the nonlinear fiber optical channel have been reported [3]. Consequently, the development of constellation shaping algorithms integrated with coded modulation has been the subject of intense research [4][5][6][7].…”

Nonlinear effect measurement based on high‐speed optical transmission communication system

“…As a communication medium, optical fiber has remarkable nonlinear characteristics, and it has fast response time and good compatibility with existing systems . The network functions such as wavelength conversion, optical buffer, and signal amplification can be achieved by using the nonlinear effects of optical fibers . With the development of network service, requirements on high‐speed optical transmission communication system have been higher and higher.…”

“…3 The network functions such as wavelength conversion, optical buffer, and signal amplification can be achieved by using the nonlinear effects of optical fibers. 4 With the development of network service, requirements on high-speed optical transmission communication system have been higher and higher. The improvement method of fiber nonlinearity has also attracted the extensive attention of researchers.…”