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 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

Replacing the Soft FEC Limit Paradigm in the Design of Optical Communication Systems

The FEC limit paradigm is the prevalent practice for designing optical communication systems to attain a certain bit-error rate (BER) without forward error correction (FEC). This practice assumes that there is an FEC code that will reduce the BER after decoding to the desired level. In this paper, we challenge this practice and show that the concept of a channel-independent FEC limit is invalid for soft-decision bit-wise decoding. It is shown that for low code rates and high order modulation formats, the use of the soft FEC limit paradigm can underestimate the spectral efficiencies by up to 20%. A better predictor for the BER after decoding is the generalized mutual information, which is shown to give consistent post-FEC BER predictions across different channel conditions and modulation formats. Extensive optical full-field simulations and experiments are carried out in both the linear and nonlinear transmission regimes to confirm the theoretical analysis

Performance Prediction Recipes for Optical Links

Although forward error-correction (FEC) coding is an essential part of modern fiber-optic communication systems, it is impractical to implement and evaluate FEC in transmission experiments and simulations. Therefore, it is desirable to accurately predict the end-to-end link performance including FEC from transmission data recorded without FEC. In this tutorial, we provide ready-to-implement "recipes" for such prediction techniques, which apply to arbitrary channels and require no knowledge of information or coding theory. The appropriate choice of recipe depends on properties of the FEC encoder and decoder. The covered metrics include bit error rate, symbol error rate, achievable information rate, and asymptotic information, in all cases computed using a mismatched receiver. Supplementary software implementations are available

Information Rates and post-FEC BER Prediction in Optical Fiber Communications

Information-theoretic metrics to analyze optical fiber communications systems with binary and nonbinary soft-decision FEC are reviewed. The numerical evaluation of these metrics in both simulations and experiments is also discussed. Ready-to-use closed-form approximations are presented.Comment: Invited paper, OFC 201

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

Post-FEC BER Benchmarking for Bit-Interleaved Coded Modulation with Probabilistic Shaping

Accurate performance benchmarking after forward error correction (FEC) decoding is essential for system design in optical fiber communications. Generalized mutual information (GMI) has been shown to be successful at benchmarking the bit-error rate (BER) after FEC decoding (post-FEC BER) for systems with soft-decision (SD) FEC without probabilistic shaping (PS). However, GMI is not relevant to benchmark post-FEC BER for systems with SD-FEC and PS. For such systems, normalized GMI (NGMI), asymmetric information (ASI), and achievable FEC rate have been proposed instead. They are good at benchmarking post-FEC BER or to give an FEC limit in bit-interleaved coded modulation (BICM) with PS, but their relation has not been clearly explained so far. In this paper, we define generalized L-values under mismatched decoding, which are connected to the GMI and ASI. We then show that NGMI, ASI, and achievable FEC rate are theoretically equal under matched decoding but not under mismatched decoding. We also examine BER before FEC decoding (pre-FEC BER) and ASI over Gaussian and nonlinear fiber-optic channels with approximately matched decoding. ASI always shows better correlation with post-FEC BER than pre-FEC BER for BICM with PS. On the other hand, post-FEC BER can differ at a given ASI when we change the bit mapping, which describes how each bit in a codeword is assigned to a bit tributary.Comment: 14 pages, 8 figure

Polarization-ring-switching for nonlinearity-tolerant geometrically-shaped four-dimensional formats maximizing generalized mutual information

In this paper, a new four-dimensional 64-ary polarization ring switching (4D-64PRS) modulation format with a spectral efficiency of 6 bit/4D-sym is introduced. The format is designed by maximizing the generalized mutual information (GMI) and by imposing a constant-modulus on the 4D structure. The proposed format yields an improved performance with respect to state-of-the-art geometrically shaped modulation formats for bit-interleaved coded modulation systems at the same spectral efficiency. Unlike previously published results, the coordinates of the constellation points and the binary labeling of the constellation are jointly optimized. When compared with polarization-multiplexed 8-ary quadrature-amplitude modulation (PM-8QAM), gains of up to 0.7 dB in signal-to-noise ratio are observed in the additive white Gaussian noise (AWGN) channel. For a long-haul nonlinear optical fiber system of 8,000 km, gains of up to 0.27 bit/4D-sym (5.5% data capacity increase) are observed. These gains translate into a reach increase of approximately 16% (1,100 km). The proposed modulation format is also shown to be more tolerant to nonlinearities than PM-8QAM. Results with LDPC codes are also presented, which confirm the gains predicted by the GMI.Comment: 12 pages, 12 figure

Compressed Shaping: Concept and FPGA Demonstration

Probabilistic shaping (PS) has been widely studied and applied to optical fiber communications. The encoder of PS expends the number of bit slots and controls the probability distribution of channel input symbols. Not only studies focused on PS but also most works on optical fiber communications have assumed source uniformity (i.e. equal probability of marks and spaces) so far. On the other hand, the source information is in general nonuniform, unless bit-scrambling or other source coding techniques to balance the bit probability is performed. Interestingly, one can exploit the source nonuniformity to reduce the entropy of the channel input symbols with the PS encoder, which leads to smaller required signal-to-noise ratio at a given input logic rate. This benefit is equivalent to a combination of data compression and PS, and thus we call this technique compressed shaping. In this work, we explain its theoretical background in detail, and verify the concept by both numerical simulation and a field programmable gate array (FPGA) implementation of such a system. In particular, we find that compressed shaping can reduce power consumption in forward error correction decoding by up to 90% in nonuniform source cases. The additional hardware resources required for compressed shaping are not significant compared with forward error correction coding, and an error insertion test is successfully demonstrated with the FPGA.Comment: 10 pages, 12 figure