Huffman-Coded Sphere Shaping for Extended-Reach Single-Span Links

TL;DR

This paper experimentally evaluates Huffman-coded sphere shaping (HCSS) for energy-efficient data transmission over extended single-span fiber links, demonstrating near-optimal performance with low complexity and specific sequence length benefits.

Contribution

It introduces an experimental analysis of HCSS in nonlinear fiber links, highlighting its practical advantages and optimal sequence length for energy efficiency.

Findings

HCSS achieves a 0.37 bits/4D-symbol gain with sequence length 32.

Naive Maxwell-Boltzmann distribution matching yields 0.18 bits/4D-symbol gain.

Coded system with 425 Gb/s net data rate performs effectively with HCSS.

Abstract

Huffman-coded sphere shaping (HCSS) is an algorithm for finite-length probabilistic constellation shaping, which provides nearly optimal energy efficiency at low implementation complexity. In this paper, we experimentally study the nonlinear performance of HCSS employing dual-polarization 64-ary quadrature amplitude modulation (DP-64QAM) in an extended reach single-span link comprising 200 km of standard single mode fiber (SSMF). We investigate the effects of shaping sequence length, dimensionality of symbol mapping, and shaping rate. We determine that the na\"ive approach of Maxwell-Boltzmann distribution matching - which is optimal in the additive white Gaussian noise channel - provides a maximum achievable information rate gain of 0.18 bits/4D-symbol in the infinite length regime. Conversely, HCSS can achieve a gain of 0.37 bits/4Dsymbol using amplitude sequence lengths of 32, which may be implemented without multiplications, using integer comparison and addition operations only. Coded system performance, with a net data rate of approximately 425 Gb/s for both shaped and uniform inputs, is also analyzed.