Switched Scalar Quantizers for Hidden Markov Sources

A new 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 distortion 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, 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 are presented which compare the new system to current systems, where we see that our system performs better. It is observed that the optimal system can in fact have a next-quantizer map with stochastic components.