Elie Awwad

Polarization-time coding for PDL mitigation in long-haul PolMux OFDM systems

In this paper, we present a numerical, theoretical and experimental study on the mitigation of Polarization Dependent Loss (PDL) with Polarization-Time (PT) codes in long-haul coherent optical fiber transmissions using Orthogonal Frequency Division Multiplexing (OFDM). First, we review the scheme of a polarization-multiplexed (PolMux) optical transmission and the 2 × 2 MIMO model of the optical channel with PDL. Second, we introduce the Space-Time (ST) codes originally designed for wireless Rayleigh fading channels, and evaluate their performance, as PT codes, in mitigating PDL through numerical simulations. The obtained behaviors and coding gains are different from those observed on the wireless channel. In particular, the Silver code performs better than the Golden code and the coding gains offered by PT codes and forward-error-correction (FEC) codes aggregate. We investigate the numerical results through a theoretical analysis based on the computation of an upper bound of the error probability of the optical channel with PDL. The derived upper bound yields a design criterion for optimal PDL-mitigating codes. Furthermore, a transmission experiment of PDL-mitigation in a 1,000 km optical fiber link with inline PDL validates the numerical and theoretical findings. The results are shown in terms of Q-factor distributions. The mean Q-factor is improved with PT coding and the variance is also narrowed.

Space-Time Coding Schemes for MDL-Impaired Mode-Multiplexed Fiber Transmission Systems

Spatial division multiplexing (SDM) holds out the prospects of increasing the capacities of optical fiber transmission links, especially with the recent achievements in the design of few-mode fibers and few-mode optical amplifiers. However, these systems are impaired by the capacity-limiting mode dependent loss (MDL) arising from imperfections in the optical fiber and inline components. Optical solutions were suggested to reduce, yet not completely remove, the accumulated MDL in the link through the use of strong coupling fibers and mode scramblers. Inspired by our previous study on mitigating polarization dependent loss (PDL), we present space-time (ST) coding schemes to mitigate MDL in mode-multiplexed optical transmission systems. We show, for the first time, that the combination of redundancy-free ST coding solutions with inline mode scrambling and optimal maximum-likelihood (ML) detection can completely absorb the SNR penalties induced by the MDL. The performance was assessed through simulations of three- and six-mode multiplexed systems where MDL levels up to 10 dB were observed. However, given the increased computational complexity of the suggested ML-decoded ST schemes, we present two reduced-complexity ST solutions offering a near-optimal performance. The first one consists in using a sub-optimal decoder and the second is a multiblock ST coding approach that can be scaled up for larger SDM systems.

Space-Time Codes for Mode-Multiplexed Optical Fiber Transmission Systems

We propose space-time codes to mitigate mode dependent loss in spatial division multiplexed optical transmission systems using multi-mode fibers. The codes can replace or complement mode scrambling used to reduce loss disparities between the modes.

Mitigation of PDL in coherent optical communications: How close to the fundamental limit?

Considering coherent optical transmissions with PDL disturbance, we evaluate how far from the fundamental limit (based on the outage probability) are conventional coding schemes using Polarization-Time codes and/or LDPC codes.

Design criterion of polarization-time codes for optical fiber channels

Coherent detection with Polarization Multiplexing (PolMux) is the most promising technique for future optical fiber transmission systems. However, the optical channel suffers from non-unitary impairments known as Polarization Dependent Loss (PDL). Space-Time coding, originally designed for wireless Rayleigh fading channels, was proven to be capable of mitigating PDL. Coding gains of ST codes were evaluated through simulations and experiments that showed differences in their performance on the optical channel and on the wireless channel. In this paper, we derive an upper bound of the pairwise error probability of an optical channel considering the PDL effect. This upper bound explains the performance of ST codes used to mitigate PDL and yields the design criterion that a code should satisfy in order to completely mitigate PDL.

Space-time codes for fiber communications: Coding gain and experimental validation

Dual polarization coherent systems are considered to be an attractive solution for optical fiber transmissions beyond 100Gb/s. Polarization multiplexing (PolMux) doubles the channel capacity and the spectral efficiency by transmitting two signals on the orthogonal polarization states. However optical polarization-dependent impairments, such as polarization mode dispersion (PMD) or polarization dependent loss (PDL) in optical fibers, may induce severe performances degradation. As PolMux systems can be seen as 2×2 MIMO channels, Space-Time codes can be used to enhance the transmission performance. The performances of the Golden code and the Silver code, which are the two best Space-Time codes in wireless communications, are evaluated in the case of optical PolMux OFDM systems by numerical simulations and validated by experiments. We show that Space-Time coding are inefficient against dispersion effects such as PMD but can dramatically mitigate PDL effects. Moreover, the obtained results show that, unlike in wireless communications, the Silver code outperforms the Golden code.

Space-time coding and optimal scrambling for mode multiplexed optical fiber systems

Approaching the capacity limits of single-mode fiber based optical transmission systems, new fibers supporting the propagation of up to six orthogonal spatial modes, called few-mode fibers, stand as promising candidates for future high-capacity systems. Extensive research is being carried out to further increase the number of modes to multiplex more data. This technique is known as spatial division multiplexing (SDM). However, the co-existence of modes in the same space leads to inevitable modal crosstalk that may induce a loss of their orthogonality as well as power disparities. This phenomenon is called mode dependent loss (MDL) and mainly arises from optical components such as few-mode amplifiers. Although optical solutions were suggested to reduce MDL by inserting mode scramblers or using fibers with strong modal coupling, MDL was unfortunately not completely removed. In this work, we propose a DSP solution based on Space-Time (ST) coding along with OFDM, originally designed for multi-antenna channels, to mitigate MDL in SDM systems. We show that a combination of ST coding at the transmitter and an optimal distribution of mode scramblers in the optical link can completely absorb the penalties induced by important levels of MDL in 6-mode SDM systems. Later on, we address the complexity and scalability of the ST-coding solution and propose a sub-optimal decoding scheme that keeps the MDL-induced penalty low while considerably reducing the decoding complexity.