Coherent terahertz (THz) wireless communication using silicon photonics technology provides critical solutions for achieving high-capacity wireless transmission beyond 5G and 6G networks and seamless connectivity with fiber-based backbone networks. However, high-quality THz signal generation and noise-robust signal detection remain challenging owing to the presence of inter-channel crosstalk and additive noise in THz wireless environments. Here, we report coherent THz wireless communication using a silicon photonic integrated circuit that includes a dual-parallel Mach-Zehnder modulator (MZM) and advanced digital signal processing (DSP). The structure and fabrication of the dual-parallel MZM-based silicon photonic integrated circuit are systematically optimized using the figure of merit (FOM) method to improve the modulation efficiency while reducing the overall optical loss. The advanced DSP compensates for in-phase and quadrature (IQ) imbalance as well as phase noise by orthogonally decoupling the IQ components in the frequency domain after adaptive signal equalization and carrier phase estimation. The experimental results show a reduction in phase noise that induces degradation of transmission performance, successfully demonstrating error-free 1-m THz wireless transmission with bit-error rates of 10-6 or less at a data rate of 50 Gbps.