An alternative proof for the capacity region of the degraded Gaussian MIMO broadcast channel

We provide an alternative proof for the capacity region of the degraded Gaussian multiple-input multiple-output (MIMO) broadcast channel. Our proof does not use the channel enhancement technique as opposed to the original proof of Weingertan et. al. and the alternative proof of Liu et. al. Our proof starts with the single-letter description of the capacity region of the degraded broadcast channel, and directly evaluates it for the degraded Gaussian MIMO broadcast channel by using two main technical tools. The first one is the generalized de Bruin identity which provides a connection between the differential entropy and the Fisher information matrix. The second tool we use is an inequality due to Dembo which lower bounds the differential entropy in terms of the Fisher information matrix.