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In this paper, we analyze the semiblind mutual information (MI) between the input and output of a MIMO channel. To that end we consider the popular block fading model. We assume that some training/pilot symbols get inserted at the beginning of each burst. We show that the average MI over a transmission burst can be decomposed into symbol position dependent contributions. The MI component at a certain symbol position optimally combines semiblind information up to that symbol position (with perfect input recovery up to that position) with blind information from the rest of the burst. We also analyze the asymptotic regime for which we can formulate optimal channel estimates and evaluate the capacity loss with respect to the known channel case. Asymptotically, the decrease in MI involves Fisher information matrices for certain channel estimation problems. We also suggest to exploit correlations in the channel model to improve estimation performance and minimize capacity loss.