Switched scalar quantizers for hidden Markov sources

An algorithm for designing switched scalar quantizers for hidden Markov sources is described. The design problem is cast as a nonlinear optimization problem. The optimization variables are the thresholds and reproduction levels for each quantizer and the parameters defining the next-quantizer map. The cost function is the average distribution incurred by the system in steady-state. The next-quantizer map is treated as a stochastic map so that all of the optimization variables are continuous-valued, allowing the use of a gradient-based optimization procedure. This approach solves a major problem in the design of switched scalar quantizing systems, namely, that of determining an optimal next-quantizer decision rule. Details are given for computing the cost function and its gradient for weighted-squared-error distortion. Simulation results which compare the new system to current systems show that the present system performs better. It is observed that the optimal system can in fact have a next-quantizer map with stochastic components