Low-Complexity Geometrical Shaping for 4D Modulation Formats via Amplitude Coding

TL;DR

This paper introduces a low-complexity four-dimensional amplitude coding scheme for geometrical signal shaping, enabling real-time generation of high-efficiency modulation formats with minimal spectral loss.

Contribution

It proposes a novel 4D amplitude coding architecture that simplifies geometric shaping, avoiding complex look-up tables and arithmetic coding, suitable for high-speed applications.

Findings

Achieves spectral efficiency of 6 and 7 bits/4D-sym formats.

Losses below 0.05 dB compared to baseline formats.

Real-time implementation with simple logic circuits.

Abstract

Signal shaping is vital to approach Shannon's capacity, yet it is challenging to implement at very high speeds. For example, probabilistic shaping often requires arithmetic coding to realize the target distribution. Geometric shaping requires look-up tables to store the constellation points. In this paper, we propose a four-dimensional amplitude coding (4D-AC) geometrical shaper architecture. The proposed architecture can generate in real time geometrically shaped 4D formats via simple logic circuit operations and two conventional quadrature amplitude modulation (QAM) modulators. This paper describes the 4D-AC used in generating approximated versions of two recently proposed 4D orthant symmetric modulation formats with spectral efficiencies of 6 bit/4D-sym and 7 bit/4D-sym, respectively. Numerical results show losses below 0.05 dB when compared against the baseline formats.