Simultaneous real-time transmission of multiple Markov sources over a shared channel

Consider a communication system in which a transmitter observes n independent Markov sources and has to jointly quantize them in real-time for a single receiver. Although the model is a special case of real-time quantization of Markov sources, a direct application of the results of real-time quantization is infeasible due to computational complexity. We restrict attention to a encoding-decoding strategies having a specific structure, and identify a dynamic program to find the best strategies with that structure. This dynamic program has uncountable state space. For the special case when all source alphabets are equal to each other and to the quantization alphabet, we reduce the dynamic program to one with a countable state space. We then present a finite-state approximation of this dynamic programming. The feasibility of the approach is shown by means of examples.