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For diagnosing SARS-CoV-2 infection and for monitoring its spread, the implementation of external quality assessment (EQA) schemes is mandatory to assess and ensure a standard quality according to national and international guidelines. Here, we present the results of the 2020, 2021, 2022 EQA schemes in Lombardy region for assessing the quality of the diagnostic laboratories involved in SARS-CoV-2 diagnosis. In the framework of the Quality Assurance Programs (QAPs), the routinely EQA schemes are managed by the regional reference centre for diagnostic laboratories quality (RRC-EQA) of the Lombardy region and are carried out by all the diagnostic laboratories. Three EQA programs were organized: (1) EQA of SARS-CoV-2 nucleic acid detection; (2) EQA of anti-SARS-CoV-2-antibody testing; (3) EQA of SARS-CoV-2 direct antigens detection. The percentage of concordance of 1938 molecular tests carried out within the SARS-CoV-2 nucleic acid detection EQA was 97.7%. The overall concordance of 1875 tests carried out within the anti-SARS-CoV-2 antibody EQA was 93.9% (79.6% for IgM). The overall concordance of 1495 tests carried out within the SARS-CoV-2 direct antigens detection EQA was 85% and it was negatively impacted by the results obtained by the analysis of weak positive samples. In conclusion, the EQA schemes for assessing the accuracy of SARS-CoV-2 diagnosis in the Lombardy region highlighted a suitable reproducibility and reliability of diagnostic assays, despite the heterogeneous landscape of SARS-CoV-2 tests and methods. Laboratory testing based on the detection of viral RNA in respiratory samples can be considered the gold standard for SARS-CoV-2 diagnosis.

In optical communications, four-dimensional (4D) modulation formats encode information onto the quadrature components of two arbitrary orthogonal states of polarisation of the optical field. Many analytical models available in the optical communication literature allow, within a first-order perturbation framework, the computation of the average power of the nonlinear interference (NLI) accumulated in coherent fibre-optic transmission systems. However, all such models only operate under the assumption of transmitted polarisation-multiplexed two-dimensional (PM-2D) modulation formats, which only represent a limited subset of the possible dual-polarisation 4D (DP-4D) formats. Namely, only those where data transmitted on each polarisation channel are mutually independent and identically distributed. This paper presents a step-by-step mathematical derivation of the extension of existing NLI models to the class of arbitrary DP-4D modulation formats. In particular, the methodology adopted follows the one of the popular enhanced Gaussian noise model, albeit dropping most assumptions on the geometry and statistic of the transmitted 4D modulation format. The resulting expressions show that, whilst in the PM-2D case the NLI power depends only on different statistical high-order moments of each polarisation component, for a general DP-4D constellation, several other cross-polarisation correlations also need to be taken into account.

Coded modulation (CM), a combination of forward error correction (FEC) and high order modulation formats, has become a key part of modern optical communication systems. Designing CM schemes with strict complexity requirements for optical communications (e.g., data center interconnects) is still challenging mainly because of the expected low latency, low overhead, and the stringent high data rate requirements. In this paper, we propose a CM scheme with bit-wise hard-decision FEC and geometric shaping. In particular, we propose to combine the recently introduced soft-aided bit-marking decoding algorithm for staircase codes (SCCs) with geometrically-shaped constellations. The main goal of this CM scheme is to jointly boost the coding gain and provide shaping gain, while keeping the complexity low. When compared to existing CM systems based on M -ary quadrature-amplitude modulation ( M QAM, M = 64 , 128 , 256 ) and conventional decoding of SCCs, the proposed scheme shows improvements of up to 0.83 dB at a bit-error rate of 10 - 6 in the additive white Gaussian noise channel. For a nonlinear optical fiber system, simulation results show up to 24 % reach increase. In addition, the proposed CM scheme enables rate adaptivity in single-wavelength systems, offering six different data rates between 450 Gbit/s and 666 Gbit/s.

Nyquist-spaced transmission and digital signal processing have proved effective in maximising the spectral efficiency and reach of optical communication systems. In these systems, Kerr nonlinearity determines the performance limits, and leads to spectral broadening of the signals propagating in the fibre. Although digital nonlinearity compensation was validated to be promising for mitigating Kerr nonlinearities, the impact of spectral broadening on nonlinearity compensation has never been quantified. In this paper, the performance of multi-channel digital back-propagation (MC-DBP) for compensating fibre nonlinearities in Nyquist-spaced optical communication systems is investigated, when the effect of signal spectral broadening is considered. It is found that accounting for the spectral broadening effect is crucial for achieving the best performance of DBP in both single-channel and multi-channel communication systems, independent of modulation formats used. For multi-channel systems, the degradation of DBP performance due to neglecting the spectral broadening effect in the compensation is more significant for outer channels. Our work also quantified the minimum bandwidths of optical receivers and signal processing devices to ensure the optimal compensation of deterministic nonlinear distortions.

An analytical model considering modulation-dependent nonlinear effects and second-order interactions between signal and optical amplifier noise is presented for Nyquist-spaced wavelength-division-multiplexing optical communication systems. System performance of dual-polarization modulation formats, such as DP-QPSK, DP-16QAM, and DP-64QAM, is investigated using both the analytical model and numerical simulations. A good agreement between analytical and numerical results shows that, in the case of full-field nonlinearity compensation, accounting for second-order interactions becomes essential to predict system performance of both single- and multi-channel systems at optimum launched powers and beyond. This effect is validated via numerical simulations for signal bandwidths up to ∼1  THz.

The Gaussian noise model is used to estimate the performance of three digital nonlinearity compensation (NLC) algorithms in C-band, long-haul, optical fiber transmission, when the span length and NLC bandwidth are independently varied. The algorithms are receiver-side digital backpropagation (DBP), transmitter-side DBP (digital precompensation), and Split NLC (an equal division of DBP between transmitter and receiver). For transmission over 100×100 km spans, the model predicts a 0.2 dB increase in SNR when applying Split NLC (versus DBP) to a single 32 GBd channel (from 0.4 dB to 0.6 dB), monotonically increasing with NLC bandwidth up to 1.6 dB for full-field NLC. The underlying assumptions of this model and the practical considerations for implementation of Split NLC are discussed. This work demonstrates, theoretically, that, regardless of the transmission scenario, it is always beneficial to divide NLC between transmitter and receiver, and identifies the transmission regimes where Split NLC is particularly advantageous.

The relationship between modulation format and the performance of multi-channel digital back-propagation (MC-DBP) in ideal Nyquist-spaced optical communication systems is investigated. It is found that the nonlinear distortions behave independent of modulation format in the case of full-field DBP, in contrast to the cases of electronic dispersion compensation and partial-bandwidth DBP. It is shown that the minimum number of steps per span required for MC-DBP depends on the chosen modulation format. For any given target information rate, there exists a possible trade-off between modulation format and back-propagated bandwidth, which could be used to reduce the computational complexity requirement of MC-DBP.

Digital backpropagation (DBP) is a promising digital-domain technique to mitigate Kerr-induced nonlinear interference. While it successfully removes deterministic signal-signal interactions, the performance of ideal DBP is limited by stochastic effects, such as polarization-mode dispersion (PMD). In this paper, we consider an ideal full-field DBP implementation and modify it to additionally account for PMD; reversing the PMD effects in the backward propagation by passing the reverse propagated signal also through PMD sections, which concatenated equal the inverse of the PMD in the forward propagation. These PMD sections are calculated analytically at the receiver based on the total accumulated PMD of the link estimated from channel equalizers. Numerical simulations show that, accounting for nonlinear polarization-related interactions in the modified DBP algorithm, additional signal-to-noise ratio gains of 1.1 dB are obtained for transmission over 1000 km.

This paper reviews digital signal processing techniques that compensate, mitigate, and exploit fiber nonlinearities in coherent optical fiber transmission systems.

Most of the digital data transmitted are carried by optical fibres, forming the great part of the national and international communication infrastructure. The information-carrying capacity of these networks has increased vastly over the past decades through the introduction of wavelength division multiplexing, advanced modulation formats, digital signal processing and improved optical fibre and amplifier technology. These developments sparked the communication revolution and the growth of the Internet, and have created an illusion of infinite capacity being available. But as the volume of data continues to increase, is there a limit to the capacity of an optical fibre communication channel? The optical fibre channel is nonlinear, and the intensity-dependent Kerr nonlinearity limit has been suggested as a fundamental limit to optical fibre capacity. Current research is focused on whether this is the case, and on linear and nonlinear techniques, both optical and electronic, to understand, unlock and maximize the capacity of optical communications in the nonlinear regime. This paper describes some of them and discusses future prospects for success in the quest for capacity., (© 2016 The Authors.)

Superchannel transmission spaced at the symbol rate, known as Nyquist spacing, has been demonstrated for effectively maximizing the optical communication channel capacity and spectral efficiency. However, the achievable capacity and reach of transmission systems using advanced modulation formats are affected by fibre nonlinearities and equalization enhanced phase noise (EEPN). Fibre nonlinearities can be effectively compensated using digital back-propagation (DBP). However EEPN which arises from the interaction between laser phase noise and dispersion cannot be efficiently mitigated, and can significantly degrade the performance of transmission systems. Here we report the first investigation of the origin and the impact of EEPN in Nyquist-spaced superchannel system, employing electronic dispersion compensation (EDC) and multi-channel DBP (MC-DBP). Analysis was carried out in a Nyquist-spaced 9-channel 32-Gbaud DP-64QAM transmission system. Results confirm that EEPN significantly degrades the performance of all sub-channels of the superchannel system and that the distortions are more severe for the outer sub-channels, both using EDC and MC-DBP. It is also found that the origin of EEPN depends on the relative position between the carrier phase recovery module and the EDC (or MC-DBP) module. Considering EEPN, diverse coding techniques and modulation formats have to be applied for optimizing different sub-channels in superchannel systems.

The performance of digital backpropagation (DBP) equalization when applied over multiple channels to compensate for the nonlinear impairments in optical fiber transmission systems is investigated. The impact of a suboptimal multichannel DBP operation is evaluated, where implementation complexity is reduced by varying parameters such as the number of nonlinear steps per span and sampling rate. Results have been obtained for a reference system consisting of a 5×32 Gbaud PDM-16QAM superchannel with 33 GHz subchannel spacing and Nyquist pulse shaping under long-haul transmission. The reduction in the effectiveness of the algorithm is evaluated and compared with the ideal gain expected from the cancellation of the nonlinear signal distortion. The detrimental effects of polarization mode dispersion (PMD) with varying DBP bandwidth are also studied. Key parameters which ensure the effectiveness of multichannel DBP are identified.