Utility maximization for layered broadcast over Rayleigh fading channels

In this paper we consider multicast systems that use layered source coding with successive refinement in a Rayleigh fading environment. For this kind of systems, we optimally allocate the transmission power, and hence the decoding threshold of each layer, in order to maximize the expected satisfaction defined by a utility function of the decoded rates of the users. In particular, we use the Lagrangian dual problem in order to efficiently solve the primal non-convex problem for any number of layers. Furthermore, we show that for some channel statistics, it is not optimal to transmit all the layers, rather we should allocate zero power to some of the upper layers in order to maximize the expected user satisfaction.