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Orthogonal signal-division multiplexing (OSDM) is one of the generalized modulation schemes that bring the gap between orthogonal frequency division multiplexing (OFDM) and single carrier frequency domain equalization (SC-FDE). By performing encoding upon subvectors of each interleaved block, it enjoys a flexible resource management with low peakto- average power ratio (PAPR). Meanwhile, the OSDM induces the intervector interference (IVI) inherently, which requires a more powerful equalizer. By deriving the input and output system model, this paper proposes a time domain soft decision feedback equalizer (SDFE) on per vector equalization with successful soft interference cancellation (SSIC). In addition, this paper takes the whole OSDM block to perform the channel encoding rather than on each vector of the OSDM. Simulation and experimental results demonstrate that the proposed SDFE with SSIC structure outperforms the conventional minimum mean square error (MMSE) equalizer and the block encoding (BE) scheme outperforms the vector encoding (VE) scheme, because theoretically the longer the encoded bit stream is, the more stable and more confident the maximum a posteriori probability (MAP) decoder will be.