A Quantization Theoretic Perspective on Simulcast and Layered Multicast Optimization

We consider rate optimization in multicast systems that use several multicast trees on a communication network. The network is shared between different applications. For that reason, we model the available bandwidth for multicast as stochastic. For specific network topologies, we show that the multicast rate optimization problem is equivalent to the optimization of scalar quantization. We use results from rate-distortion theory to provide a bound on the achievable performance for the multicast rate optimization problem. A large number of receivers makes the possibility of adaptation to changing network conditions desirable in a practical system. To this end, we derive an analytical solution to the problem that is asymptotically optimal in the number of multicast trees. We derive local optimality conditions, which we use to describe a general class of iterative algorithms that give locally optimal solutions to the problem. Simulation results are provided for the multicast of an i.i.d. Gaussian process, an i.i.d. Laplacian process, and a video source.