Systems and methods for encoding streams of input data using at least two nonbinary low density parity check (NB-LDPC) encoders; generating NB-LDPC coded optimum signal constellations; performing orthogonal frequency division multiplexing (OFDM) on the NB-LDPC coded four-dimensional (4-D) optimum signal constellations; generating signals using mappers, the mappers configured to assign bits of signals to the signal constellations and to associate the bits of the one or more signals with signal constellation points. Output of the 4-D mappers is modulated using a 4-D OFDM transmitter and a 4-D modulator onto a transmission medium using block coded-modulation, and the modulated output is transmitted by mode-multiplexing independent 4-D OFDM data streams onto fiber. The transmitted modulated output is received, mode-demultiplexed, and demodulated using polarization diversity receivers, one per spatial mode, channel estimation and compensation methods are performed to overcome impairments in the transmission medium; and received data is decoded using non-binary decoders.