On Hierarchical Signal Constellations for the Gaussian Broadcast Channel

With the introduction of digital broadcasting techniques to radio and television, it becomes desirable to have an efficient possibility to reach receivers operating under varying degrees of received signal strength. Cover [2] showed that it is not efficient to do time sharing, that is transmitting a robust but low quality signal time multiplexed with a signal more susceptible to perturbations on the channel but having higher quality of service. Therefore various techniques exist to implement data streams of differing importance into one coded modulation scheme. This is done by adapting signal constellation, mapping and code design. In this paper we examine the performances that can be obtained and the tradeoffs that have to be made for some of the most often used constellations namely amplitude shift keying (ASK).