I. Introduction
Broadcast channel coding has been shown to allow higher data rates than the traditional time-sharing broadcasting [1]. In particular, the discrete-time Gaussian broadcast channel has been studied extensively due to its practical relevance and the superposition coding and dirty paper coding were shown to achieve the capacity region of this channel [1]–[9]. The main problem in coding for broadcast channel is how to reliably multiplex more than one message into one channel symbol, while keeping the total number of channel symbols the same as in the single user channel. Previously known broadcast coding techniques multiplex the messages at the discrete-time symbol domain and the connection with the continuous-time channel is made with the Nyquist rate transmission and sampling.