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Achievable Rates for Four-Dimensional Coded Modulation with a Bit-Wise Receiver

Alex Alvarado, Erik Agrell

TL;DR

The paper addresses the problem of achievable rates for 4D constellations in coherent optical CM when using a suboptimal bit-wise receiver. It uses MI for ML decoding and GMI for bit-wise decoding, and shows GMI depends on binary labeling; the analysis is validated with LDPC simulations. Key findings are that PM-QPSK outperforms the best uncoded 4D constellation by about $1$ dB, while multidimensional constellations often incur large GMI penalties at practical rates; PM-QPSK remains best across SNRs. For higher-dimensional 4D schemes (e.g., $M=256$), trends persist, and Gray labeling can reduce complexity, guiding constellation and labeling design for spectral efficiency with bit-wise receivers.

Abstract

We study achievable rates for four-dimensional (4D) constellations for spectrally efficient optical systems based on a (suboptimal) bit-wise receiver. We show that PM-QPSK outperforms the best 4D constellation designed for uncoded transmission by approximately 1 dB. Numerical results using LDPC codes validate the analysis.

Achievable Rates for Four-Dimensional Coded Modulation with a Bit-Wise Receiver

TL;DR

The paper addresses the problem of achievable rates for 4D constellations in coherent optical CM when using a suboptimal bit-wise receiver. It uses MI for ML decoding and GMI for bit-wise decoding, and shows GMI depends on binary labeling; the analysis is validated with LDPC simulations. Key findings are that PM-QPSK outperforms the best uncoded 4D constellation by about dB, while multidimensional constellations often incur large GMI penalties at practical rates; PM-QPSK remains best across SNRs. For higher-dimensional 4D schemes (e.g., ), trends persist, and Gray labeling can reduce complexity, guiding constellation and labeling design for spectral efficiency with bit-wise receivers.

Abstract

We study achievable rates for four-dimensional (4D) constellations for spectrally efficient optical systems based on a (suboptimal) bit-wise receiver. We show that PM-QPSK outperforms the best 4D constellation designed for uncoded transmission by approximately 1 dB. Numerical results using LDPC codes validate the analysis.

Paper Structure

This paper contains 4 sections, 2 figures.

Table of Contents

  1. Introduction
  2. Model and Achievable Rates
  3. Numerical Results
  4. Conclusions

Figures (2)

  • Figure 1: Transmitter and receiver structures.
  • Figure 2: Top: MI (solid lines) and GMI (dashed lines) for three constellations. Bottom: BER for the LDPC code with different rates and PM-QPSK (green), $\mathcal{C}_{4,16}$ (red), and SO-PM-QPSK (blue).