A system and method for transmitting data, including one or more Low Density Parity Check (LDPC) encoders configured to encode one or more streams of input data; a signal constellation generation module configured to generate one or more signal constellations; one or more modulators configured to generate one or more signals using hybrid multidimensional coded modulation; a modified orthogonal polynomial generation module configured to generate modified orthogonal polynomials for use as electrical basis functions; and one or more mode-multiplexers and transmitters configured to mode-multiplex and transmit one or more LDPC-coded data streams over a transmission medium.