Metodi Plamenov Yankov

Constellation Shaping for Fiber-Optic Channels With QAM and High Spectral Efficiency

In this letter, the fiber-optic communication channel with a quadrature amplitude modulation (QAM) input constellation is treated. Using probabilistic shaping, we show that high-order QAM constellations can achieve and slightly exceed the lower bound on the channel capacity, set by ring constellations. We then propose a mapping function for turbo-coded bit-interleaved coded modulation based on optimization of the mutual information between the channel input and output. Using this mapping, spectral efficiency as high as 6.5 bits/s/Hz/polarization is achieved on a simulated single channel long-haul fiber-optical link excluding the pilot overhead, used for synchronization, and taking into account frequency and phase mismatch impairments, as well as laser phase noise and analog-to-digital conversion quantization impairments. The simulations suggest that major improvements can be expected in the achievable rates of optical networks with high-order QAM.

Low-Complexity Tracking of Laser and Nonlinear Phase Noise in WDM Optical Fiber Systems

In this paper, the wavelength division multiplexed (WDM) fiber optic channel is considered. It is shown that for ideal distributed Raman amplification (IDRA), the Wiener process model is suitable for the non-linear phase noise due to cross phase modulation from neighboring channels. Based on this model, a phase noise tracking algorithm is presented. We approximate the distribution of the phase noise at each time instant by a mixture of Tikhonov distributions, and derive a closed form expression for the posterior probabilities of the input symbols. This reduces the complexity dramatically compared to previous trellis-based approaches, which require numerical integration. Further, the proposed method performs very well in low-to-moderate signal-to-noise ratio (SNR), where standard decision directed (DD) methods, especially for high-order modulation, fail. The proposed algorithm does not rely on averaging, and therefore does not experience high error floors at high SNR in severe phase noise scenarios. The laser linewidth (LLW) tolerance is thereby increased for the entire SNR region compared to previous DD methods. In IDRA WDM links, the algorithm is shown to effectively combat the combined effect of both laser phase noise and non-linear phase noise, which cannot be neglected in such scenarios. In a more practical lumped amplification scheme, we show near-optimal performance for 16 QAM, 64 QAM, and 256 QAM with LLW up to 100 kHz, and reasonable performance for LLW of 1 MHz for 16 QAM and 64 QAM, at the moderate received SNR region. The performance in these cases is close to the information rate achieved by the above mentioned trellis processing.

Digital signal processing for fiber nonlinearities [Invited]

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

Compensation of XPM interference by blind tracking of the nonlinear phase in WDM systems with QAM input

Exploiting temporal correlations in the phase, achievable rates are studied and a blind trellis-based receiver is presented. Gains of 0.5 bit per symbol are found in point-to-point links irrespective of the symbol rate. These gains disappear in network configurations.

Improved energy efficiency for optical transport networks by elastic forward error correction

In this paper we propose a scheme for reducing the energy consumption of optical links by means of adaptive forward error correction (FEC). The scheme worksby performing on the fly adjustments to the code rate of the FEC, adding extra parity bits to the data stream whenever extra capacity is available. We show that this additional parity information decreases the number of necessary decoding iterations and thus reduces the power consumption in iterative decoders during periods of low load. The code rate adjustments can be done on a frame-by-frame basis and thus make it possible to manipulate the balance between effective data rate and FEC coding gain without any disruption to the live traffic. As a consequence, these automatic adjustments can be performed very often based on the current traffic demand and bit error rate performance of the links through the network. The FEC scheme itself is designed to work as a transparent add-on to transceivers running the optical transport network (OTN) protocol, adding an extra layer of elastic soft-decision FEC to the built-in hard-decision FEC implemented in OTN, while retaining interoperability with existing OTN equipment. In order to facilitate dynamic code rate adaptation, we propose a programmable encoder and decoder design approach, which can implement various codes depending on the desired code rate using the same basic circuitry. This design ensures optimal coding gain performance with a modest overhead for supporting multiple codes with minimal impact on the area and power requirements of the decoder.

Experimental analysis of pilot-based equalization for probabilistically shaped WDM systems with 256QAM/1024QAM

Pilot based equalization is studied in a 5×10 GBaud WDM transmission experiment. The equalization is independent of the modulation format and is demonstrated for 256/1024QAM with uniform and probabilistically optimized distribution using an optimized pilot insertion rate of 2–5%.

Temporal Probabilistic Shaping for Mitigation of Nonlinearities in Optical Fiber Systems

In this paper, finite state machine sources (FSMSs) are used to shape quadrature amplitude modulation (QAM) for nonlinear transmission in optical fiber communication systems. The previous optimization algorithm for FSMSs is extended to cover an average power constraint, thus enabling temporal optimization with multiamplitude constellations output, such as QAM. The optimized source results in increased received SNR and, thereby, increased achievable information rates (AIR)s under memoryless assumption. The AIR is increased even further when taking the channel and transmitter memory into account via trellis processing at the receiver. Significant gains are reported in the highly nonlinear region of transmission for an FSMS of up to second order and 16QAM and particularly for unrepeated transmission. At the optimal launch power of WDM transmission, the FSMS order needs to be increased further in order to notably outperform previous probabilistic shaping schemes.

Experimental Comparison of Probabilistic Shaping Methods for Unrepeated Fiber Transmission

This paper studies the impact of probabilistic shaping on effective signal-to-noise ratios (SNRs) and achievable information rates (AIRs) in a back-to-back configuration and in unrepeated nonlinear fiber transmissions. For the back-to-back setup, various shaped quadrature amplitude modulation (QAM) distributions are found to have the same implementation penalty as uniform input. By demonstrating in transmission experiments that shaped QAM input leads to lower effective SNR than uniform input at a fixed average launch power, we experimentally confirm that shaping enhances the fiber nonlinearities. However, shaping is ultimately found to increase the AIR, which is the most relevant figure of merit, as it is directly related to spectral efficiency. In a detailed study of these shaping gains for the nonlinear fiber channel, four strategies for optimizing QAM input distributions are evaluated and experimentally compared in wavelength division multiplexing (WDM) systems. The first shaping scheme generates a Maxwell–Boltzmann (MB) distribution based on a linear additive white Gaussian noise channel. The second strategy uses the Blahut–Arimoto algorithm to optimize an unconstrained QAM distribution for a split-step Fourier method based channel model. In the third and fourth approach, MB-shaped QAM and unconstrained QAM are optimized via the enhanced Gaussian noise (EGN) model. Although the absolute shaping gains are found to be relatively small, the relative improvements by EGN-optimized unconstrained distributions over linear AWGN optimized MB distributions are up to 59%. This general behavior is observed in 9-channel and fully loaded WDM experiments.

Approximating the constellation constrained capacity of the MIMO channel with discrete input

In this paper the capacity of a Multiple Input Multiple Output (MIMO) channel is considered, subject to average power constraint, for multi-dimensional discrete input, in the case when no channel state information is available at the transmitter. We prove that when the constellation size grows, the QAM constrained capacity converges to Gaussian capacity, directly extending the AWGN result from [1]. Simulations show that for a given constellation size, a rate close to the Gaussian capacity can be achieved up to a certain SNR point, which can be found efficiently by optimizing the constellation for the equivalent orthogonal channel, obtained by the singular value decomposition. Furthermore, lower bounds on the constrained capacity are derived for the cases of square and tall MIMO matrix, by optimizing the constellation for the equivalent channel, obtained by QR decomposition.

Experimental Verification of Rate Flexibility and Probabilistic Shaping by 4D Signaling

The rate flexibility and probabilistic shaping gain of 4-dimensional signaling is experimentally tested for short-reach, unrepeated transmission. A rate granularity of 0.5 bits/QAM symbol is achieved with a distribution matcher based on a simple look-up table.