We have analyzed the possibility of long-haul superchannel transmission with an aggregate serial bit rate exceeding 1 Tb/s by using the mode-multiplexed multidimensional signaling. We considered nonbinary quasi-cyclic LDPC-coded OFDM signals transmitted over few-mode fibers (FMFs). The optimum vector-form nonlinear Schrödinger equation is developed to evaluate the performance of the proposed system. Both the impacts of nonlinear effects and nonlinear interaction between spatial modes have been included through the modified nonlinear Schrödinger equation we applied for the FMF case. Both two-dimensional and optimized four-dimensional (4D) signal constellations have been considered. To overcome the constraints imposed by the linear and nonlinear impairments in FMF, we proposed the use of block-coded modulation with advanced channel estimation and compensation techniques. We verified by means of simulation that the transmission of an aggregate serial bit rate of 1.2 Tb/s over 3000 km is achievable with a proposed LDPC-coded QPSK-OFDM format, whereas superchannel transmission with an aggregate serial rate of 2.4 Tb/s over 1800 km is achievable with the 16-QAM format. When a 4D 16-ary optimized constellation is used, we can extend the transmission distance of mode-multiplexed QPSK-OFDM by an additional 300 km.