In a broadcast channel, a single transmitter communicates to receivers with
different channel capacities, a typical example of which is the over-the-a
ir television broadcasting. A natural question that arises is evaluation of
the optimal information transfer rate in such an environment. For the two-
receiver case, we examine various transmission scenarios in this environmen
t and focus on the theoretically optimal superposition scheme, where the in
formation in tended for the better channel is superimposed on the portion o
f information common to both receivers. As a result, a basic grade of servi
ce is maintained throughout the entire coverage area in addition to a highe
r quality service offered to the receivers with better reception conditions
. Using end-to-end distortion and coverage channel signal-to-noise ratio th
reshold measures, three specific embedded signaling modes are introduced. W
e demonstrate that a generalized embedding scheme provides a practical trad
e-off between distortion and coverage radius. The scheme is also formulated
in terms of an optimization problem, seeking the best embedding factor for
a given application. To verify the theoretical results, we idealize a dual
rate transmission system over a Gaussian broadcast channel, in which recei
vers are distributed according to a circularly symmetric exponential pdf. T
he numerical results indicate that this model offers a higher per capita da
ta rate comparing to the conventional single rate transmission systems. App
lication of this multirate broadcast holds promise for multiresolution tran
smission of digital audio and high definition television.