Modulation Augmentation and Constellation Shaping for LDPC-Coded QPSK
Abstract
While constellation shaping improves spectral efficiency, its application to quadrature phase-shift keying (QPSK) remains limited. We address this limitation by incorporating a short shaping code into low-density parity-check (LDPC)-coded QPSK systems. Specifically, a subset of LDPC codeword bits is used as shaping bits and mapped by the shaping code to a sparse codeword that enables probabilistic shaping by controlling non-equiprobable selection between lower- and higherenergy QPSK constellations. Because zeros dominate the sparse codeword, lower-energy constellation points are transmitted more frequently, yielding a Gaussian-like symbol distribution. By exploiting the channel-code protection of the shaping bits, we develop receiver algorithms that refine shaping-bit log-likelihood ratios (LLRs) using LDPC decoder feedback. Joint optimization of the shaping codebook, bit-to-symbol mapping and constellations enables the proposed shaping scheme to achieve gains of up to 0.6 and 0.53 dB over 5G New Radio (NR) LDPC-coded QPSK and QAM-16, respectively.
Related
- How Does Probabilistic Constellation Shaping Control Ranging Sidelobe Levels in ISAC?
- Covert Digital Semantic Communication With Movable Antennas: Constellation Shaping, Spatial Optimization, and Semantic Mapping
- Offline Approximate Value Iteration: A Reinforcement Learning Approach for Satellite Constellation Deployment
- Fluid Antenna Secure Channel-driven Constellation (FASCC): a Physical Layer Security approach
- Venusian Radio Occultation Constellation Design and Reconfiguration Problems: A Benders Decomposition Approach
BibTeX
@misc{wan2026modulation,
title = {{Modulation Augmentation and Constellation Shaping for LDPC-Coded QPSK}},
author = {Heping Wan and Joonyoung Cho and Sandesh Rao Mattu and Jamin Shah and Nishant Mehrotra and Charlie Jianzhong Zhang and Robert Calderbank},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00427},
eprint = {2610.00427},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00427},
}
RIS
TY - UNPB
TI - Modulation Augmentation and Constellation Shaping for LDPC-Coded QPSK
AU - Heping Wan
AU - Joonyoung Cho
AU - Sandesh Rao Mattu
AU - Jamin Shah
AU - Nishant Mehrotra
AU - Charlie Jianzhong Zhang
AU - Robert Calderbank
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00427
UR - https://arxiv.org/abs/2610.00427
AB - While constellation shaping improves spectral efficiency, its application to quadrature phase-shift keying (QPSK) remains limited. We address this limitation by incorporating a short shaping code into low-density parity-check (LDPC)-coded QPSK systems. Specifically, a subset of LDPC codeword bits is used as shaping bits and mapped by the shaping code to a sparse codeword that enables probabilistic shaping by controlling non-equiprobable selection between lower- and higherenergy QPSK constellations. Because zeros dominate the sparse codeword, lower-energy constellation points are transmitted more frequently, yielding a Gaussian-like symbol distribution. By exploiting the channel-code protection of the shaping bits, we develop receiver algorithms that refine shaping-bit log-likelihood ratios (LLRs) using LDPC decoder feedback. Joint optimization of the shaping codebook, bit-to-symbol mapping and constellations enables the proposed shaping scheme to achieve gains of up to 0.6 and 0.53 dB over 5G New Radio (NR) LDPC-coded QPSK and QAM-16, respectively.
ER -