An Alternative Proof for the Capacity Region of the Degraded Gaussian MIMO Broadcast Channel

Abstract

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 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 by using it, obtains a tight (i.e., achievable) outer bound for the capacity region of the degraded Gaussian MIMO broadcast channel, by using two main technical tools. The first one is the generalized de Bruijn identity due to Palomar 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.