This tutorial paper provides a foundation for integrating probabilistic shaping (PS) and forward error correction (FEC). A layered PS-FEC architecture consisting of a PS encoder and an FEC encoder is introduced, of which probabilistic amplitude shaping is a practical instance. Achievable PS encoding rates and achievable FEC decoding rates are derived using information-theoretic arguments. The developed tools are applied to the design and performance assessment of optical transponders based on measurements from optical transmission experiments.

Probabilistic Shaping and Forward Error Correction for Fiber-Optic Communication Systems

Multiplexing multiple orbital angular momentum (OAM) channels enables high-capacity optical communication. However, optical scattering from ambient microparticles in the atmosphere or mode coupling in optical fibers significantly decreases the orthogonality between OAM channels for demultiplexing and eventually increases crosstalk in communication. Here, we propose a novel scattering-matrix-assisted retrieval technique (SMART) to demultiplex OAM channels from highly scattered optical fields and achieve an experimental crosstalk of –13.8 dB in the parallel sorting of 24 OAM channels after passing through a scattering medium. The SMART is implemented in a self-built data transmission system that employs a digital micromirror device to encode OAM channels and realize reference-free calibration simultaneously, thereby enabling a high tolerance to misalignment. We successfully demonstrate high-fidelity transmission of both gray and color images under scattering conditions at an error rate of <0.08%. This technique might open the door to high-performance optical communication in turbulent environments.

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Optical orbital-angular-momentum-multiplexed data transmission under high scattering

Time, polarization, and wavelength multiplexing schemes have been used to satisfy the growing need of transmission capacity. Using space as a new dimension for communication systems has been recently suggested as a versatile technique to address future bandwidth issues. We review the potentials of harnessing the space as an additional degree of freedom for communication applications including free space optics, optical fiber installation, underwater wireless optical links, on-chip interconnects, data center indoor connections, radio frequency, and acoustic communications. We focus on the orbital angular momentum (OAM) modes and equally identify the challenges related to each of the applications of spatial modes and the particular OAM modes in communication. We further discuss the perspectives of this emerging technology. Finally, we provide the open research directions and discuss the practical deployment of OAM communication links for different applications.

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Communicating Using Spatial Mode Multiplexing: Potentials, Challenges, and Perspectives

With the ever-increasing demand for data and the radio frequency spectrum becoming congested, free space optics (FSO) may find a niche for situations where fiber is too expensive or too difficult to install. FSO is a cross-disciplinary field that draws from radio and fiber communication, astronomy, and even quantum optics, and it has seen major advances over the last three decades. In this tutorial-style review, we provide a broad overview of many of the important topics required to design, develop, and research the next generation of FSO technology.

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Roadmap to free space optics

Continuous-variable quantum key distribution (CVQKD) with a real local oscillator (LO) has been extensively studied recently due to its security and simplicity. In this paper, we propose a novel implementation of a high-key-rate CVQKD with a real LO. Particularly, with the help of the simultaneously generated reference pulse, the phase drift of the signal is tracked in real time and then compensated. By utilizing the time and polarization multiplexing techniques to isolate the reference pulse and controlling the intensity of it, not only the contamination from it is suppressed, but also a high accuracy of the phase compensation can be guaranteed. Besides, we employ homodyne detection on the signal to ensure the high quantum efficiency and heterodyne detection on the reference pulse to acquire the complete phase information of it. In order to suppress the excess noise, a theoretical noise model for our scheme is established. According to this model, the impact of the modulation variance and the intensity of the reference pulse are both analysed theoretically and then optimized according to the experimental data. By measuring the excess noise in the 25km optical fiber transmission system, a 3.14Mbps key rate in the asymptotic regime proves to be achievable. This work verifies the feasibility of the high-key-rate CVQKD with a real LO within the metropolitan area.

High key rate continuous-variable quantum key distribution with a real local oscillator

We experimentally demonstrate a high-spectral-efficiency, large-capacity, featured free-space-optical (FSO) transmission system by using low-density, parity-check (LDPC) coded quadrature phase shift keying (QPSK) combined with orbital angular momentum (OAM) multiplexing. The strong atmospheric turbulence channel is emulated by two spatial light modulators on which four randomly generated azimuthal phase patterns yielding the Andrews spectrum are recorded. The validity of such an approach is verified by reproducing the intensity distribution and irradiance correlation function (ICF) from the full-scale simulator. Excellent agreement of experimental, numerical, and analytical results is found. To reduce the phase distortion induced by the turbulence emulator, the inexpensive wavefront sensorless adaptive optics (AO) is used. To deal with remaining channel impairments, a large-girth LDPC code is used. To further improve the aggregate data rate, the OAM multiplexing is combined with WDM, and 500 Gb/s optical transmission over the strong atmospheric turbulence channels is demonstrated.

500 Gb/s free-space optical transmission over strong atmospheric turbulence channels.

We theoretically investigate and experimentally demonstrate a RF-assisted four-state continuous-variable quantum key distribution (CV-QKD) system. Classical coherent detection is implemented with a simple digital phase noise cancelation scheme. In the proposed system, there is no need for frequency and phase locking between the quantum signals and the local oscillator laser. Moreover, in principle, there is no residual phase noise, and a mean excess noise of 0.0115 (in shot-noise units) can be acquired experimentally. In addition, the minimum transmittance of 0.45 is reached experimentally for secure transmission with commercial photodetectors, and the maximum secret key rate (SKR) of >12  Mbit/s can be obtained. The proposed RF-assisted CV-QKD system opens the door of incorporating microwave photonics into a CV-QKD system and improving the SKR significantly.

RF-subcarrier-assisted four-state continuous-variable QKD based on coherent detection.

We compare the proposed geometrically-shaped(GS) 16QAM with the probabilistically-shaped(PS) 16QAM formats in both numerical simulation and experimental setup. The results show that GS-16QAM outperforms PS-16QAM.

Geometrically Shaped 16QAM Outperforming Probabilistically Shaped 16QaM

We introduce and compare typical shaping schemes suitable for optical communications. The geometrically shaped-quadrature amplitude modulation (GS-QAM) formats are characterized by the non-equidistant spacing of constellation points, transmitted uniformly, and applied to improve system capacity. On the other hand, the well-known constant composition distribution matcher (CCDM) is applied for the generation of probabilistically shaped QAM (PS-QAM) formats. Mutual information (MI) is used as a metric to analyze the performances of regular/GS/PS-MQAM formats. In a linear amplified spontaneous emission noise limited region, it can be proved by the numerical simulation that MI performances of the GS-8/16QAM are always better than regular 8/16QAM and PS-8/16QAM; the largest shaping gains can be separately reached by PS-32QAM and GS-32QAM. We continue with the experimental demonstration on the 16QAM-based transmission system, and find that GS-16QAM generally has the best MI performance. We also find that the modulation-dependent nonlinear noises of the GS-8/16/32QAM are comparable to that of the regular 8/16/32QAM and generally lower than PS-8/16/32QAM. By using the enhanced Gaussian noise model, we observe that the GS-8/16QAM formats have better performances than regular 8/16QAM and PS-8/16QAM over multi-span transmission. Meanwhile, PS-32QAM formats provide superior performance over a relatively long transmission distance.

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On the Probabilistic Shaping and Geometric Shaping in Optical Communication Systems

A high-speed four-state continuous-variable quantum key distribution (CV-QKD) system, enabled by wavelength-division multiplexing, polarization multiplexing, and orbital angular momentum (OAM) multiplexing, is studied in the presence of atmospheric turbulence. The atmospheric turbulence channel is emulated by two spatial light modulators (SLMs) on which two randomly generated azimuthal phase patterns yielding Andrews’ spectrum are recorded. The phase noise is mitigated by the phase noise cancellation (PNC) stage, and channel transmittance can be monitored directly by the D.C. level in our PNC stage. After the system calibration, a total SKR of >1.68 Gbit/s can be reached in the ideal system, featured with lossless channel and free of excess noise. In our experiment, based on commercial photodetectors, the minimum transmittances of 0.21 and 0.29 are required for OAM states of 2 (or −2) and 6 (or −6), respectively, to guarantee the secure transmission, while a total SKR of 120 Mbit/s can be obtained in case of mean transmittances.

Zhen Qu

Papers

500 Gb/s free-space optical transmission over strong atmospheric turbulence channels.

RF-subcarrier-assisted four-state continuous-variable QKD based on coherent detection.

Geometrically Shaped 16QAM Outperforming Probabilistically Shaped 16QaM

On the Probabilistic Shaping and Geometric Shaping in Optical Communication Systems

High-speed free-space optical continuous-variable quantum key distribution enabled by three-dimensional multiplexing.