In this paper, we extend the iterative demapping technique, also known as turbo demodulation, to OFDM. We first introduce an inner code which serves to remove the error floor, which is present in current iterative demapping schemes. This technique is then applied to OFDM with cyclic prefix or zeropadding. Using the EXIT chart, we illustrate the performance differences of various mappings and design a low-complexity inner coding scheme based on differential encoding with code doping. It is shown that this scheme removes the error floor without altering the code rate and while adding very little complexity.