Secret Key Agreement From Vector Gaussian Sources by Rate Limited Public Communication

We investigate the secret key agreement from correlated vector Gaussian sources in which legitimate parties can use public communication with limited rate. For the class of protocols with one-way public communication, we show that the optimal trade-off between the rate of key generation and the rate of the public communication is characterized as an optimization problem of a Gaussian random variable. The characterization is derived by using the enhancement technique introduced by Weingarten for multiple-input-multiple-output (MIMO) Gaussian broadcast channel.