Analysis of a dual-rate transmission scheme for Gaussian broadcast channels

In a broadcast channel, a single transmitter communicates to receivers with different channel capacities, a typical example of which is the over-the-air 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 environment and focus on the theoretically optimal superposition scheme, where the information in tended for the better channel is superimposed on the portion of information common to both receivers. As a result, a basic grade of service is maintained throughout the entire coverage area in addition to a higher quality service offered to the receivers with better reception conditions. Using end-to-end distortion and coverage channel signal-to-noise ratio threshold measures, three specific embedded signaling modes are introduced. We demonstrate that a generalized embedding scheme provides a practical trade-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 receivers are distributed according to a circularly symmetric exponential pdf. The numerical results indicate that this model offers a higher per capita data rate comparing to the conventional single rate transmission systems. Application of this multirate broadcast holds promise for multiresolution transmission of digital audio and high definition television.