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We present a simple but efficientalgorithm that iteratively refines the channel estimate in a turbo equalizer exploiting soft feedback (a-posteriori likelihoods) from the decoder. This algorithm, denoted as 'Soft Interference Cancelation and Correlation' (SICC), repeatedly performs an interference cancelation step followed by correlation with symbol estimates derived from the output of the decoder. The novelty lies in two facts: first, the moments of the likelihood ratio density at the decoder output are used to remove the bias of the estimate. Second, an iterative version (I-SICC) is proposed where a data block is evaluated repeatedly without activation of the channel decoder. It is shown that this variant significantly outperforms its non iterative version.