A simple converse for broadcast channels with additive white Gaussian noise (Corresp.)

Sets of achievable rates for the additive white Gaussian noise broadcast channel have been found by Cover [1] for channels with two outputs and generalized by Bergmans [2] to channels with any number of outputs. In this correspondence, we establish a simple converse showing the optimality of these sets of achievable rates. The proof is made simple by use of special properties of the Gaussian channel.