# Broadcasting Information subject to State Masking over a MIMO State Dependent Gaussian Channel

## TL;DR

This paper addresses secure communication over a MIMO Gaussian broadcast channel with known states, deriving capacity bounds and showing Gaussian inputs optimize state leakage minimization.

## Contribution

It introduces a new extremal inequality and proves that Gaussian inputs achieve the capacity bounds in MIMO BC with state masking.

## Key findings

- Gaussian input maximizes the state-dependent Marton's outer bound
- Inner and outer bounds coincide, establishing capacity
- Generalizes scalar Gaussian BC with state and MIMO BC without state

## Abstract

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 Marton's 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.