LDPC-Hadamard Code-Assisted OTFS in High-Mobility Scenarios

In high-speed mobile scenarios, Orthogonal Time Frequency Space (OTFS) effectively addresses the Doppler frequency shift. Channel coding enhances the performance of OTFS systems by adding redundancy and error correction capabilities. However, existing coding schemes still face limitations when dealing with complex conditions such as highly dynamic channel variations, delay spread, and Doppler effects. This paper proposes a Low-Density Parity-Check (LDPC)-Hadamard code to assist OTFS in combating complex channel conditions, thereby improving data transmission efficiency. In particular, the LDPC-Hadamard code leverages the sparsity of LDPC and the orthogonality of Hadamard codes to address the issue of rapidly varying channels in OTFS systems. Additionally, a low-complexity quasi-cyclic LDPC code construction algorithm is proposed to decrease the coding complexity. Otherwise, a Log-Likelihood Ratio Belief Propagation (LLR-BP) decoding algorithm is introduced, which reduces the computational complexity. Therefore, the proposed coding and decoding methods enable the OTFS to achieve better performance in low SNR conditions. Compared to conventional quasi-cyclic LDPC schemes, the proposed LDPC-Hadamard code-assisted OTFS system exhibits a 0.2 dB SNR gain and achieves a lower BER of $10^{-6}$ at 1.1 dB SNR, demonstrating enhanced robustness against Doppler-induced impairments in highly dynamic channels.