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In this paper, we introduce a simple bit-interleaved binary space-time code (B-STC) for a coded multi-input multi-output (MIMO) system to obtain an increase in information rate, where two transmit and two receive antennas are used. We derive a probability density function (pdf) of log-likelihood ratio (LLR) for the B-STC decoder output and approximate it with the pdf of MIMO detector output having the degraded SNR. The average bit error probability at the i-th iteration is represented in terms of moment generating function with differently distributed SNRs. Although the iterative decoder in the B-STC structure increases the computational complexity, the number of iterations i is not large (i≤3). Because the proposed B-STC scheme is a binary code for MIMO systems, different types of channel codes and various space-time codes can be concatenated. To achieve near-capacity performance on MIMO channels, an iterative receiver structure with a soft interference cancellation scheme can be also adopted as an outer iteration. And the proposed scheme can be extended to arbitrary number of transmit and receive antennas.