We investigate a space-time coding scheme with four or more transmit antennas based on a matrix-Alamouti scheme in a quasi-static fading environment. The receiver consists of an Alamouti combiner followed by an iterative joint detection and decoding process. A priori probabilities fed back from the decoder are used to both get more reliable estimates of the transmitted symbols and efficiently remove inter-block interference. Interblock interference is removed using techniques known in multiuser communication. The theoretical bounds of this scheme are established through the study of its outage probability.