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This letter presents a new soft feedback interference cancellation (SFIC) based equalizer suitable for iterative receivers applying turbo equalization. SFIC offers a very low computational complexity depending only linearly on the channel memory length. Despite its low complexity, SFIC shows a very good BER performance. Simulation results for the severely intersymbol interference distorted Proakis C channel show, that our approach performs within 0.5 dB to the powerful turbo equalization scheme based on MMSE linear filtering with time-varying coefficients and fails the mathematical optimum maximum a-posteriori (MAP) equalizer only by 1.2 dB.