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The Gaussian wiretap channel model is studied when there are multiple antennas at the sender, the receiver and the eavesdropper and the channel matrices are fixed and known to all the terminals. The secrecy capacity is characterized using a Sato type upper bound. A computable characterization of the capacity is provided. The secrecy capacity is studied in several interesting regimes. The high SNR secrecy capacity is attained by simultaneously diagonalizing the channel matrices (using the generalized singular value decomposition) and independently coding across the resulting parallel channels.
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