Complexity-constrained trellis quantizers

• Published in: IEEE transactions on information theory Vol. 43; no. 4; pp. 1134 - 1144
• Main Authors: Larsen, M.F., Frost, R.L.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-07-1997; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Arithmetic; Computational complexity; Computational modeling; Data compression; Design methodology; Distortion measurement; Laboratories; Markov analysis; Mathematical models; Mutual information; Rate-distortion; Source coding
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/18.605574

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.