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

## TL;DR

This paper evaluates various information metrics for predicting the post-FEC bit error rate in optical systems with probabilistic shaping, finding that certain bit-level measures outperform the generalized mutual information, especially for nonuniform signaling.

## Contribution

It introduces and compares new information quantities based on bit distributions and log-likelihood ratios as better predictors of post-FEC BER in probabilistic shaping scenarios.

## Key findings

- Normalized AIR is less correlated with post-FEC BER for probabilistic shaping.
- Bit distribution-based information measures outperform normalized AIR in prediction accuracy.
- Prediction accuracy can be improved more than 10 times using the proposed metrics.

## 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.