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Superposition mapping (SM) is a newly evolved non-bijective modulation format. By superimposing a certain number of the binary symbols, SM is able to form a Gaussian-like constellation which has the potential to approach the channel capacity bound. Compared to conventional bijective mapping schemes such as PSK and QAM, SM does have some unique performance characteristics. In conjunction with BICM-OFDM, in this paper we investigate the performance of SM over multipath fading channels. Furthermore, a water-filling algorithm is proposed for BICM-OFDM with SM in order to exploit the diversity of the channel.