# Introducing Enumerative Sphere Shaping for Optical Communication Systems with Short Blocklengths

## TL;DR

This paper introduces enumerative sphere shaping (ESS) as a more efficient alternative to CCDM for optical communication systems, especially at short blocklengths, demonstrating improved performance and reach in fiber optic channels.

## Contribution

The paper proposes and evaluates enumerative sphere shaping (ESS) for optical systems, showing it outperforms CCDM at short blocklengths and enhances transmission reach.

## Key findings

- ESS has lower rate loss than CCDM at the same shaping rate.
- Finite blocklength ESS and CCDM exhibit higher effective SNR than their infinite counterparts.
- ESS with blocklength 200 extends reach by about 200 km over CCDM and 450 km over uniform signaling.

## Abstract

Probabilistic shaping based on constant composition distribution matching (CCDM) has received considerable attention as a way to increase the capacity of fiber optical communication systems. CCDM suffers from significant rate loss at short blocklengths and requires long blocklengths to achieve high shaping gain, which makes its implementation very challenging. In this paper, we propose to use enumerative sphere shaping (ESS) and investigate its performance for the nonlinear fiber optical channel. ESS has lower rate loss than CCDM at the same shaping rate, which makes it a suitable candidate to be implemented in real-time high-speed optical systems. In this paper, we first show that finite blocklength ESS and CCDM exhibit higher effective signal-to-noise ratio than their infinite blocklength counterparts. These results show that for the nonlinear fiber optical channel, large blocklengths should be avoided. We then show that for a 400 Gb/s dual-polarization 64-QAM WDM transmission system, ESS with short blocklengths outperforms both uniform signaling and CCDM. Gains in terms of both bit-metric decoding rate and bit-error rate are presented. ESS with a blocklength of 200 is shown to provide an extension reach of about 200 km in comparison with CCDM with the same blocklength. The obtained reach increase of ESS with a blocklength of 200 over uniform signaling is approximately 450 km (approximately 19%)