# Probabilistic Amplitude Shaping with Hard Decision Decoding and Staircase Codes

## TL;DR

This paper explores probabilistic amplitude shaping combined with hard decision decoding and staircase codes to enhance spectral efficiency in fiber-optic systems, demonstrating significant gains over traditional schemes.

## Contribution

It introduces the application of probabilistic amplitude shaping with hard decision decoding in conjunction with staircase codes, achieving near-capacity performance in fiber-optic communication.

## Key findings

- Significant spectral efficiency gains over baseline schemes.
- Performance within 0.57–1.44 dB of achievable information rate.
- Effective use of staircase codes with probabilistic shaping.

## Abstract

We consider probabilistic amplitude shaping (PAS) as a means of increasing the spectral efficiency of fiber-optic communication systems. In contrast to previous works in the literature, we consider probabilistic shaping with hard decision decoding (HDD). In particular, we apply the PAS recently introduced by B\"ocherer \emph{et al.} to a coded modulation (CM) scheme with bit-wise HDD that uses a staircase code as the forward error correction code. We show that the CM scheme with PAS and staircase codes yields significant gains in spectral efficiency with respect to the baseline scheme using a staircase code and a standard constellation with uniformly distributed signal points. Using a single staircase code, the proposed scheme achieves performance within $0.57$--$1.44$ dB of the corresponding achievable information rate for a wide range of spectral efficiencies.