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

Tsuyoshi Yoshida, Magnus Karlsson, Erik Agrell

TL;DR

The paper addresses predicting post-FEC BER in optical systems with probabilistic shaping and binary SD-FEC. It demonstrates that the normalized AIR $I_{\text{n}}$ under nonuniform signaling poorly predicts $BER_{\text{post}}$, whereas single-bit MI $I_{\text{s}}$ and especially ASI $I_{\text{a}}$ show stronger correlation. By introducing ASI, based on the asymmetric LLR distribution, the authors achieve substantially lower prediction errors in simulations over Gaussian channels, with improvements exceeding an order of magnitude over $I_{\text{n}}$ and $I_{\text{s}}$. The findings suggest ASI as a robust, shaping-aware predictor of practical achievable rate, potentially enabling ASI-based performance estimation without FEC decoding.

Abstract

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.

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

TL;DR

The paper addresses predicting post-FEC BER in optical systems with probabilistic shaping and binary SD-FEC. It demonstrates that the normalized AIR under nonuniform signaling poorly predicts , whereas single-bit MI and especially ASI show stronger correlation. By introducing ASI, based on the asymmetric LLR distribution, the authors achieve substantially lower prediction errors in simulations over Gaussian channels, with improvements exceeding an order of magnitude over and . The findings suggest ASI as a robust, shaping-aware predictor of practical achievable rate, potentially enabling ASI-based performance estimation without FEC decoding.

Abstract

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.

Paper Structure

This paper contains 7 sections, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. System model and performance metrics
  3. System model with nonuniform signaling
  4. Performance metrics for uniform signaling
  5. Performance metrics for nonuniform signaling
  6. Simulations
  7. Conclusions

Figures (3)

  • Figure 1: System model for nonuniform PAM signaling with bit-interleaved binary SD-FEC.
  • Figure 2: Simulated post-FEC BER as a function of (a) pre-FEC BER $\text{BER}_{\text{pre}}$, (b) normalized AIR $I_{\text{n}}$, (c) SMI $I_{\text{s}}$, and (d) ASI $I_{\text{a}}$.
  • Figure 3: Comparison of prediction accuracy for (a) the metrics at $\text{BER}_{\text{post}}=10^{-4}$, and (b) $\Delta \text{BER}_{\text{post}}$ around $\text{BER}_{\text{post}}=10^{-4}$ among the studied cases.