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In this paper, we present a bit allocation scheme for a closed-loop MIMO-OFDM (multiple input multiple output-orthogonal frequency division multiplexing) system using V-BLAST (vertical-Bell laboratories layered space-time) detector with soft channel decoding. A fully adaptive modulation and coding scheme may provide the optimal performance, but requires excessive feedback information. Instead, the proposed scheme controls the code rate of the channel coding and assigns the same modulation and coding to the set of selected sub-channels, which greatly reduces the feedback overhead while achieving good performance. Simulation results show that the proposed scheme with minimal feedback provides significant performance improvement over the conventional bit allocation schemes.