Modulation Augmentation and Constellation Shaping for LDPC-Coded QPSK

2026-09-30

AI Summary

This study addresses the limited applicability and insufficient spectral efficiency of probabilistic constellation shaping (PCS) for QPSK by proposing a joint optimization scheme based on short sparse codes. Specifically, short shaping codes are introduced into an LDPC-coded QPSK system, where sparse codewords govern non-uniform mapping to achieve Gaussian-like distribution shaping. The codebook and mapping relationship are jointly optimized, and a log-likelihood ratio (LLR) refinement algorithm is designed at the receiver to enhance channel protection. Experimental results demonstrate that, compared with the 5G NR standard, the proposed method achieves performance gains of 0.6 dB and 0.53 dB under QPSK and 16QAM, respectively, effectively overcoming the shaping bottleneck inherent in low-order modulation schemes.

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.

Problem

• Constellation Shaping
• QPSK
• LDPC
• Spectral Efficiency
• Probabilistic Shaping

Innovation

• Probabilistic Shaping
• LDPC Codes
• QPSK
• Constellation Shaping
• Joint Optimization