In this thesis, we design a robust concatenated code for the Multiple-Input Multiple-Output (MIMO) system in the presence of slow Rayleigh fading with no channel side information at the transmitter (no CSIT) and perfect channel side information at the receiver (perfect CSIR). Since we are interested in the slow fading channel, outage capacity is used as the measure of performance. Good space-time codes can be designed so as to maximize the so-called rank and the determinant criteria. However, a practical system will concatenate a space-time code with an outer code at the transmitter and perform iterative decoding at the receiver. It is necessary to design the space-time code together with the outer code in practice. We will call this kind of code a concatenated space-time code. At the transmitter, we will consider the bit-to-symbol mapping and space-time code together as a space-time modulator and thus, Bit Interleaved Coded Modulation (BICM) and Multilevel coding (ML) can be applied to design outer codes for the nonbinary constellation. However, the concatenated space-time codes designed by these two methods can only be decoded with arbitrarily small error probability for a fixed channel realization and such designs are not robust over the ensemble of fading channels. Our approach of designing concatenated space-time code is to design an outer code for a space-time modulator such that the concatenated space-time code can be decoded with arbitrarily small error probability in a set of fixed channels which have the same capacity. Through this approach, we discovered a new design criterion for spacetime codes: a good space-time code should stabilize its Extrinsic Information Transfer (EXIT) charts. In other words, the robustness of a space-time code in the slow fading channel and its performance in iterative decoding can be visualized by the EXIT charts. The rank and the determinant criterion do not evaluate the performance of a space-time code in iterative decoding, but the new criterion does. Therefore, the new criterion is applicable to design concatenated space-time codes. Applying our approach and new criterion, a rate 7.2 bits/s/Hz concatenated space-time code is designed. The performance is close to the outage capacity, and the rate lost is 0.2 bits/s/Hz.