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Register a new userAdaptive Turbo Equalization for Nonlinearity Compensation in WDM Systems
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In this paper, the performance of adaptive turbo equalization for nonlinearity compensation (NLC) is investigated. A turbo equalization scheme is proposed where a recursive least-squares (RLS) algorithm is used as an adaptive channel estimator to track the time-varying intersymbol interference (ISI) coefficients associated with inter-channel nonlinear interference (NLI) model. The estimated channel coefficients are used by a MIMO 2x2 soft-input soft-output (SISO) linear minimum mean square error (LMMSE) equalizer to compensate for the time-varying ISI. The SISO LMMSE equalizer and the SISO forward error correction (FEC) decoder exchange extrinsic information in every turbo iteration, allowing the receiver to improve the performance of the channel estimation and the equalization, achieving lower bit-error-rate (BER) values. The proposed scheme is investigated for polarization multiplexed 64QAM and 256QAM, although it applies to any proper modulation format. Extensive numerical results are presented. It is shown that the scheme allows up to 0.7 dB extra gain in effectively received signal-to-noise ratio (SNR) and up to 0.2 bits/symbol/pol in generalized mutual information (GMI), on top of the gain provided by single-channel digital backpropagation.
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A perturbation-based nonlinear compensation scheme assisted by a feedback from the forward error correction (FEC) decoder is numerically and experimentally investigated. It is shown by numerical simulations and transmission experiments that a feedback from the FEC decoder enables improved compensation performance, allowing the receiver to operate very close to the full data-aided performance bounds. The experimental analysis considers the dispersion uncompensated transmission of a 5 x 32 GBd WDM system with DP-16QAM and DP-64QAM after 4200 km and 1120 km, respectively. The experimental results show that the proposed scheme outperforms single-channel digital backpropagation. A perturbation-based nonlinear compensation scheme assisted by a feedback from the forward error correction (FEC) decoder is numerically and experimentally investigated. It is shown by numerical simulations and transmission experiments that a feedback from the FEC decoder enables improved compensation performance, allowing the receiver to operate very close to the full data-aided performance bounds. The experimental analysis considers the dispersion uncompensated transmission of a 5 x 32 GBd WDM system with DP-16QAM and DP-64QAM after 4200 km and 1120 km, respectively. The experimental results show that the proposed scheme outperforms single-channel digital backpropagation.
The performance of enumerative sphere shaping (ESS), constant composition distribution matching (CCDM), and uniform signalling are compared at the same forward error correction rate. ESS is shown to offer a reach increase of approximately 10% and 22% compared to CCDM and uniform signalling, respectively.
Present-day communication systems routinely use codes that approach the channel capacity when coupled with a computationally efficient decoder. However, the decoder is typically designed for the Gaussian noise channel and is known to be sub-optimal for non-Gaussian noise distribution. Deep learning methods offer a new approach for designing decoders that can be trained and tailored for arbitrary channel statistics. We focus on Turbo codes and propose DeepTurbo, a novel deep learning based architecture for Turbo decoding. The standard Turbo decoder (Turbo) iteratively applies the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm with an interleaver in the middle. A neural architecture for Turbo decoding termed (NeuralBCJR), was proposed recently. There, the key idea is to create a module that imitates the BCJR algorithm using supervised learning, and to use the interleaver architecture along with this module, which is then fine-tuned using end-to-end training. However, knowledge of the BCJR algorithm is required to design such an architecture, which also constrains the resulting learned decoder. Here we remedy this requirement and propose a fully end-to-end trained neural decoder - Deep Turbo Decoder (DeepTurbo). With novel learnable decoder structure and training methodology, DeepTurbo reveals superior performance under both AWGN and non-AWGN settings as compared to the other two decoders - Turbo and NeuralBCJR. Furthermore, among all the three, DeepTurbo exhibits the lowest error floor.
Turbo codes and CRC codes are usually decoded separately according to the serially concatenated inner codes and outer codes respectively. In this letter, we propose a hybrid decoding algorithm of turbo-CRC codes, where the outer codes, CRC codes, are not used for error detection but as an assistance to improve the error correction performance. Two independent iterative decoding and reliability based decoding are carried out in a hybrid schedule, which can efficiently decode the two different codes as an entire codeword. By introducing an efficient error detecting method based on normalized Euclidean distance without CRC check, significant gain can be obtained by using the hybrid decoding method without loss of the error detection ability.
In optical communication systems, short blocklength probabilistic enumerative sphere shaping (ESS) provides both linear shaping gain and nonlinear tolerance. In this work, we investigate the performance and complexity of ESS in comparison with fiber nonlinearity compensation via digital back propagation (DBP) with different steps per span. We evaluate the impact of the shaping blocklength in terms of nonlinear tolerance and also consider the case of ESS with a Volterra-based nonlinear equalizer (VNLE), which provides lower complexity than DBP. In single-channel transmission, ESS with VNLE achieves similar performance in terms of finite length bit-metric decoding rate to uniform signaling with one step per span DBP. In the context of a dense wavelength-division multiplexing (WDM) transmission system, we show that ESS outperforms uniform signaling with DBP for different step sizes.
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