Complexity-constrained trellis quantizers

A reasonable measure of quantizer complexity is the expected number of quanta per input sample for which distortion is computed. Given this measure, a rate-distortion-complexity theory is obtained by extending earlier work in alphabet-constrained rate-distortion theory. Numerical results show that operation on the alphabet-constrained rate-distortion bound can be obtained with a complexity of two. Furthermore, Lloyd-Max conditions are shown to describe the minimum of a slightly constrained version of the rate-distortion-complexity problem. Complexity-constrained design methods are applied first to trellis-coded quantizers, where they are shown to reduce arithmetic operations by at least 25%. They are then used to develop model-based trellis quantizers, the trellises of which are derived from a Markov model of the source. Simulation results confirm that excellent performance can be obtained with modest complexity.