Probabilistically-Shaped Coded Modulation with Hard Decision Decoding for Coherent Optical Systems

We consider probabilistic shaping to maximize the achievable information rate of coded modulation (CM) with hard decision decoding. The proposed scheme using binary staircase codes outperforms its uniform CM counterpart by more than 1.3 dB for 64-QAM and 5 bits/symbol

Performance Metrics for Systems with Soft-Decision FEC and Probabilistic Shaping

High-throughput optical communication systems utilize binary soft-decision forward error correction (SD-FEC) with bit interleaving over the bit channels. The generalized mutual information (GMI) is an achievable information rate (AIR) in such systems and is known to be a good predictor of the bit error rate after SD-FEC decoding (post-FEC BER) for uniform signaling. However, for probabilistically shaped (nonuniform) signaling, we find that the normalized AIR, defined as the AIR divided by the signal entropy, is less correlated with the post-FEC BER. We show that the information quantity based on the distribution of the single bit signal, and its asymmetric loglikelihood ratio, are better predictors of the post-FEC BER. In simulations over the Gaussian channel, we find that the prediction accuracy, quantified as the peak-to-peak deviation of the post-FEC BER within a set of different modulation formats and distributions, can be improved more than 10 times compared with the normalized AIR.Comment: 4 pages, 3 figure

Performance Monitoring for Live Systems with Soft FEC and Multilevel Modulation

Performance monitoring is an essential function for margin measurements in live systems. Historically, system budgets have been described by the Q-factor converted from the bit error rate (BER) under binary modulation and direct detection. The introduction of hard-decision forward error correction (FEC) did not change this. In recent years technologies have changed significantly to comprise coherent detection, multilevel modulation and soft FEC. In such advanced systems, different metrics such as (nomalized) generalized mutual information (GMI/NGMI) and asymmetric information (ASI) are regarded as being more reliable. On the other hand, Q budgets are still useful because pre-FEC BER monitoring is established in industry for live system monitoring. The pre-FEC BER is easily estimated from available information of the number of flipped bits in the FEC decoding, which does not require knowledge of the transmitted bits that are unknown in live systems. Therefore, the use of metrics like GMI/NGMI/ASI for performance monitoring has not been possible in live systems. However, in this work we propose a blind soft-performance estimation method. Based on a histogram of log-likelihood-values without the knowledge of the transmitted bits, we show how the ASI can be estimated. We examined the proposed method experimentally for 16 and 64-ary quadrature amplitude modulation (QAM) and probabilistically shaped 16, 64, and 256-QAM in recirculating loop experiments. We see a relative error of 3.6%, which corresponds to around 0.5 dB signal-to-noise ratio difference for binary modulation, in the regime where the ASI is larger than the assumed FEC threshold. For this proposed method, the digital signal processing circuitry requires only a minimal additional function of storing the L-value histograms before the soft-decision FEC decoder.Comment: 9 pages, 9 figure

Constellation Shaping for WDM systems using 256QAM/1024QAM with Probabilistic Optimization

In this paper, probabilistic shaping is numerically and experimentally investigated for increasing the transmission reach of wavelength division multiplexed (WDM) optical communication system employing quadrature amplitude modulation (QAM). An optimized probability mass function (PMF) of the QAM symbols is first found from a modified Blahut-Arimoto algorithm for the optical channel. A turbo coded bit interleaved coded modulation system is then applied, which relies on many-to-one labeling to achieve the desired PMF, thereby achieving shaping gain. Pilot symbols at rate at most 2% are used for synchronization and equalization, making it possible to receive input constellations as large as 1024QAM. The system is evaluated experimentally on a 10 GBaud, 5 channels WDM setup. The maximum system reach is increased w.r.t. standard 1024QAM by 20% at input data rate of 4.65 bits/symbol and up to 75% at 5.46 bits/symbol. It is shown that rate adaptation does not require changing of the modulation format. The performance of the proposed 1024QAM shaped system is validated on all 5 channels of the WDM signal for selected distances and rates. Finally, it was shown via EXIT charts and BER analysis that iterative demapping, while generally beneficial to the system, is not a requirement for achieving the shaping gain.Comment: 10 pages, 12 figures, Journal of Lightwave Technology, 201

LDPC Coded Modulation with Probabilistic Shaping for Optical Fiber Systems

An LDPC coded modulation scheme with probabilistic shaping, optimized interleavers and noniterative demapping is proposed. Full-field simulations show an increase in transmission distance by 8% compared to uniformly distributed input.Comment: 3 pages, 3 figures. Paper is accepted for presentation at OFC 2015. Following the submission to OFC, the blue box in Fig. 1 has been corrected and reference [3] has been update

On Achievable Rates for Long-Haul Fiber-Optic Communications

Lower bounds on mutual information (MI) of long-haul optical fiber systems for hard-decision and soft-decision decoding are studied. Ready-to-use expressions to calculate the MI are presented. Extensive numerical simulations are used to quantify how changes in the optical transmitter, receiver, and channel affect the achievable transmission rates of the system. Special emphasis is put to the use of different quadrature amplitude modulation formats, channel spacings, digital back-propagation schemes and probabilistic shaping. The advantages of using MI over the prevailing $Q$-factor as a figure of merit of coded optical systems are also highlighted.Comment: Hard decision mutual information analysis added, two typos correcte

Performance Prediction of Nonbinary Forward Error Correction in Optical Transmission Experiments

In this paper, we compare different metrics to predict the error rate of optical systems based on nonbinary forward error correction (FEC). It is shown that the correct metric to predict the performance of coded modulation based on nonbinary FEC is the mutual information. The accuracy of the prediction is verified in a detailed example with multiple constellation formats, FEC overheads in both simulations and optical transmission experiments over a recirculating loop. It is shown that the employed FEC codes must be universal if performance prediction based on thresholds is used. A tutorial introduction into the computation of the threshold from optical transmission measurements is also given.Comment: submitted to IEEE/OSA Journal of Lightwave Technolog