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In this paper we consider a soft-input soft-output equalizer, for MIMO intersymbol interference channels, used in a turbo equalization scheme. We derive the equalizer on the basis of a cyclic factor graph representation and the sum-product algorithm, with two different message schedules (serial and parallel). In the sum-product algorithm we use Gaussian messages, which results in a low-complexity LMMSE equalizer implementation. Computer simulations show that, for the turbo equalization application, the proposed equalizer has a good bit error rate performance compared with the optimal MAP equalizer, while achieving a remarkable reduction in complexity.