Lattice Codes and Generalized Minimum-Distance Decoding for OFDM Systems

Lattice coding of orthogonal frequency-division multiplexing (OFDM) systems is considered. Mapping of multilevel construction lattices to OFDM blocks is shown, and a methodology for probabilistic analysis of multistage generalized minimum distance (GMD) decoding of the received OFDM blocks is shown. As a case study, transmission of points from a 128-dimensional Barnes-Wall lattice is considered. Tight approximations to the system-error rate are obtained and verified by simulation. It appears that GMD decoding of lattice-encoded OFDM provides high coding gain at low complexity