# On Product Codes with Probabilistic Amplitude Shaping for High-Throughput Fiber-Optic Systems

## TL;DR

This paper explores the integration of probabilistic amplitude shaping with product codes and hard decision decoding in fiber-optic systems, achieving significant spectral efficiency gains and improved performance through iterative decoding techniques.

## Contribution

It demonstrates the application of PAS to PCs with HDD, identifying conditions for component code selection, and introduces iterative bounded distance decoding to enhance system performance.

## Key findings

- Achieves up to 2.7 dB gain with PAS and PCs.
- Improves spectral efficiency by approximately 1 bit/channel use.
- Employs iterative decoding to further enhance performance.

## Abstract

Probabilistic amplitude shaping (PAS) can flexibly vary the spectral efficiency (SE) of fiber-optic systems. In this paper, we demonstrate the application of PAS to bit-wise hard decision decoding (HDD) of product codes (PCs) by finding the necessary conditions to select the PC component codes. We show that PAS with PCs and HDD yields gains up to $2.7$ dB and SE improvement up to approximately $1$ bit/channel use compared to using PCs with uniform signaling and HDD. Furthermore, we employ the recently introduced iterative bounded distance decoding with combined reliability of PCs to improve performance of PAS with PCs and HDD.