This study proposes a novel coding scheme that enables the simultaneous transmission of extra bits alongside low-density parity-check (LDPC) encoded data over an additive white Gaussian noise channel. Significantly, this is achieved without increasing the bandwidth or transmission power requirements. At the transmitter, the LDPC encoded bits first undergo a pseudorandom bit-flipping process. The flipping pattern is determined by the additional bits intended for transmission. The modified bit sequence is then mapped to in-phase and quadrature Cartesian coordinates, forming a two-dimensional signal constellation. This sequence of signal points is divided into multiple groups. Each group is subjected to a distinct angle of rotation in the complex plane, with the rotation values once again dictated by the additional bits. The resulting rotated in-phase/quadrature signal groups comprise the transmitted signal sequence. In the receiver, a customized decoding algorithm is employed. The algorithm first uses a serial list decoder incorporating an early stopping rule to reliably detect the embedded additional bits from the received signal observations. With knowledge of the additional bits, the effect they imposed during transmission via bit-flipping and constellation rotation can be eliminated. The conventional LDPC message passing decoder can then be applied to recover the encoded data bits.