The problem of channel coding over the Gaussian multiple-input multiple-output (MIMO) broadcast channel (BC) with additive independent Gaussian states is considered. The states are known in a noncausal manner to the encoder, and it wishes to minimize the amount of information that the receivers can learn from the channel outputs about the state sequence. The state leakage rate is measured as a normalized blockwise mutual information between the state sequence and the channel outputs sequences. We employ a new version of a state-dependent extremal inequality and show that Gaussian input maximizes the state-dependent version of Martons outer bound. Further we show that our inner bound coincides with the outer bound. Our result generalizes previously studied scalar Gaussian BC with state and MIMO BC without state.
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