In this study, the authors propose a joint iterative detection and decoding (JIDD) method for a turbo coded multiple-input multiple-output (MIMO) system, with a linear order of complexity. Accurate estimation of soft information should be conditioned for excellent performance of the JIDD, but it usually requires an exponential order of complexity. They propose a method which improves the performance of soft interference cancellation minimum mean-squared error (SIC-MMSE) method by increasing the reliability of the soft information utilised for interference cancellation. The proposed method utilises a posteriori probabilities from the MIMO detector as well as a priori probabilities from the turbo decoder, and perform soft minimum mean-squared error filtering for symbol level detection. With this approach, soft information is fully fed into the symbol detection process, and thus the reliability of soft symbol is increased. In addition, they can separate out the bit-level soft estimation process by using a simple linear method. Simulation results show that the proposed method provides substantial complexity reduction, with a bit error rate performance comparable to the conventional SIC-MMSE methods.