A proof of the strong converse theorem for Gaussian broadcast channels via the Gaussian Poincaré inequality

摘要

We prove that 2-user Gaussian broadcast channels admit the strong converse. This implies that for every sequence of block codes with an asymptotic maximal error probability smaller than one, the limit points of the corresponding sequence of rate pairs must lie within the capacity region derived by Cover and Bergmans. The main mathematical tool required for our analysis is a logarithmic Sobolev inequality known as the Gaussian Poincaré inequality.