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.

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