Several approximate non-linear fiber propagation models have been proposed over the years. Recent re-consideration and extension of earlier modeling efforts has led to the formalization of the so-called Gaussian-noise (GN) model. The evidence collected so far hints at the GN-model as being a relatively simple and, at the same time, sufficiently reliable tool for performance prediction of uncompensated coherent systems, characterized by a favorable accuracy versus complexity trade-off. This paper tries to gather the recent results regarding the GN-model definition, understanding, relations versus other models, validation, limitations, closed form solutions, approximations and, in general, its applications and implications in link analysis and optimization, also within a network environment.

The GN-Model of Fiber Non-Linear Propagation and its Applications

A transmission system with adjustable data rate for single-carrier coherent optical transmission is proposed, which enables high-speed transmission close to the Shannon limit. The proposed system is based on probabilistically shaped 64-QAM modulation formats. Adjustable shaping is combined with a fixed-QAM modulation and a fixed forward-error correction code to realize a system with adjustable net data rate that can operate over a large reach range. At the transmitter, an adjustable distribution matcher performs the shaping. At the receiver, an inverse distribution matcher is used. Probabilistic shaping is implemented into a coherent optical transmission system for 64-QAM at 32 Gbaud to realize adjustable operation modes for net data rates ranging from 200 to 300 Gb/s. It is experimentally demonstrated that the optical transmission of probabilistically shaped 64-QAM signals outperforms the transmission reach of regular 16-QAM and regular 64-QAM signals by more than 40% in the transmission reach.

Rate Adaptation and Reach Increase by Probabilistically Shaped 64-QAM: An Experimental Demonstration

Driven primarily by cloud service and data-center applications, short-reach optical communication has become a key market segment and growing research area in recent years. Short-reach systems are characterized by direct detection-based receiver configurations and other low-cost and small form factor components that induce transmission impairments unforeseen in their coherent counterparts. Innovative signaling and digital signal processing (DSP) play a pivotal role in enabling these components to realize their ultimate potentials and meet data rate requirements in cost-effective manners. This paper presents an overview of recent DSP developments for short-reach communications systems and discusses future trends.

Digital Signal Processing for Short-Reach Optical Communications: A Review of Current Technologies and Future Trends

We use a wideband optical comb source with 10THz bandwidth for 2.15 Pb/s transmission over 31km of a new, homogeneous 22-core single-mode multi-core fiber using 399 × 25GHz spaced, 6.468 Tb/s spatial-super-channels comprising 24.5GBaud PDM-64QAM modulation in each core.

2.15 Pb/s transmission using a 22 core homogeneous single-mode multi-core fiber and wideband optical comb

Artificial intelligence (AI) methods in optical networks: A comprehensive survey

We successfully realized layered decoding for LDPC convolutional codes designed for application in high speed optical transmission systems. A relatively short code with 20% redundancy was FPGA-emulated with a Q-factor of 5.7dB at BER of 10−15.

LDPC convolutional codes using layered decoding algorithm for high speed coherent optical transmission

We present FPGA-based emulation results of a single QC-LDPC code with 20% redundancy designed for applications in 100 Gb/s optical transmission systems. Error floor-free transmission can be achieved at BER of 10−15 with a Q factor of 5.9 dB.

FPGA verification of a single QC-LDPC code for 100 Gb/s optical systems without error floor down to BER of 10 −15

Unlike ultralong coherent optical systems that seriously suffer from fiber nonlinearities, short-reach noncoherent systems such as data center interconnections, which utilize small, cheap, and low-bandwidth components, are sensitive to nonlinearities that are mainly produced by devices responsible for electrical signal amplification, modulation, and demodulation. One of the most promising schemes for these applications is the four-level pulse amplitude modulation format combined with intensity modulation and direct detection; however, it can be significantly degraded by linear and nonlinear intersymbol interference. Linear and nonlinear signal degradation can efficiently be handled by different types of equalizers. In many cases, the straightforward linear equalizer cannot lower the error rate at the acceptable level. Therefore, much stronger equalizers based on nonlinear models such as the Volterra series are proposed. Volterra filter that can also be orthogonalized by the Wiener model is well described in the existing literature, and, in this paper, we investigate the most critical points related to high-speed Volterra filter design and implementation. Several experiments are carried out in order to indicate filter requirements/complexity, acquisition, and stability. We also provide a simple guidance for filter complexity reduction and useful hints for channel acquisition.

Volterra and Wiener Equalizers for Short-Reach 100G PAM-4 Applications

We demonstrate a 56 Gb/s four-level pulse-amplitude modulation (PAM-4) transmission using direct detection and a long-wavelength 18-GHz bandwidth vertical-cavity surface-emitting laser as directly modulated light source for short-reach inter- and intra-connects in datacenters and short-reach networks. Error-free transmission over 2 km at 7% hard-decision forward-error correction threshold is achieved by applying powerful equalization schemes at the receiver side. Three equalization schemes, i.e., a maximum likelihood estimation (MLSE), a feed-forward equalizer (FFE), and a combination of the FFE and the MLSE are thoroughly investigated, and the performance comparison between them is carried out.

Directly PAM-4 Modulated 1530-nm VCSEL Enabling 56 Gb/s/ $\lambda $ Data-Center Interconnects

Direct detection systems with advanced modulation schemes are of great importance in metropolitan networks, because of their low cost and low power requirements. In particular, PAM-4 has attracted considerable attention, but has significant transmission distance limitations in the C-band. To extend its reach, we used a dual drive Mach-Zehnder modulator to generate a chromatic dispersion (CD) pre-compensated signal with an extra (j-1) multiplication to align the optical carrier and the modulated optical signal; by doing so, we achieved successful 128 Gbit/s transmission over an 80 km SSMF link, the longest reported reach of single lane 100 Gbit/s PAM-4 signals over DCF-free links. Synchronized bandwidth pre-compensation was also used, to reduce the influence of bandwidth-limitations.

Nebojsa Stojanovic

Papers

LDPC convolutional codes using layered decoding algorithm for high speed coherent optical transmission

FPGA verification of a single QC-LDPC code for 100 Gb/s optical systems without error floor down to BER of 10 −15

Volterra and Wiener Equalizers for Short-Reach 100G PAM-4 Applications

Directly PAM-4 Modulated 1530-nm VCSEL Enabling 56 Gb/s/ $\lambda $ Data-Center Interconnects

Transmission of single lane 128 Gbit/s PAM-4 signals over an 80 km SSMF link, enabled by DDMZM aided dispersion pre-compensation.