As the quest for higher data rates continues, future generations of wireless communications are expected to concur even higher frequency bands, particularly at terahertz (THz) frequencies. Even though the vast bandwidths at the THz band promise terabit-per-second (Tbps) data rates, current baseband technologies do not support such high rates. In particular, the complexities of Tbps channel code decoding and ultra-massive multiple-input multiple-output data detection are prohibitive. This work addresses the efficient data detection and channel-code decoding problem under THz-band channel conditions and Tbps baseband processing limitations. We propose ultra-massive multiple-input multiple-output THz channel models, then investigate the corresponding performance of several candidate data detection and coding schemes. We further investigate the complexity of different detectors and decoders, motivating parallelizability at both levels. We recommend which detector to combine best with which channel code decoder under specific THz channel characteristics.