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In this paper, we study iterative demodulation and decoding methods for lattice based space-time coded systems concatenated with convolutional codes. We propose two methods based on the idea of soft interference cancellation and in one method scalar Gaussian approximation is used and in the other method vector Gaussian approximation is used. We also present the EXIT chart analyses for the performance analyses for these iterative methods. Both theoretical and simulation results show that the performance of the vector Gaussian approximation method is the same as that of the linear MMSE method. The complexity of the scalar Gaussian approximation method is the lowest among the different methods and grows linearly with the transmission rate while it still has an acceptable performance. Full diversity and full rate lattice based space-time coding is compared with the V-BLAST scheme and simulations show that the former one has a better performance than the later one even with the proposed suboptimal iterative demodulation and decoding methods.