We analyze whether a multidimensional parity check (MDPC) or a Reed-Solomon (RS) code in combination with an auxiliary channel can improve the throughput and extend the THz transmission distance. While channel quality is addressed by various coding approaches, and an effective THz system configuration is enabled by other approaches with additional channels, their combination is new with the potential for significant improvements in quality of the data transmission. Our specific solution is designed to correct data bits at the physical layer by using a low complexity erasure code (MDPC or RS), whereby original and parity data are transferred over two separate and parallel THz channels, including one main channel and one additional channel. The results are theoretically analyzed to see that our new solution can improve throughput, support higher modulation levels and transfer data over the longer distances with THz communications.