ECE 729 Theory of Information Processing and Transmission

References on the Lloyd-Max Algorithm

  1. J. Max, ``Quantizing for minimum distortion,'' IRE Trans. Inform. Theory, vol. IT-6, pp. 7-12, Mar. 1960.
  2. S. P. Lloyd, ``Least squares quantization in PCM,'' unpublished Bell Laboratories Memorandum, July 31, 1957; also IEEE Trans. Inform. Theory, vol. IT-28, no. 2, pp. 129-137, Mar. 1982.
  3. A. V. Trushkin, ``Sufficient conditions for uniqueness of a locally optimal quantizer for a class of convex error weighting functions,'' IEEE Trans. Inform. Theory, vol. IT-28, no. 2, pp. 187-198, Mar. 1982.
  4. J. C. Kieffer, ``Exponential rate of convergence for Lloyd's method I,'' IEEE Trans. Inform. Theory, vol. IT-28, no. 2, pp. 205-210, Mar. 1982.
  5. J. C. Kieffer, ``Uniqueness of locally optimal quantizer for log-concave density and convex error weighting function,'' IEEE Trans. Inform. Theory, vol. IT-29, no. 1, pp. 42-47, Jan. 1983.
  6. A. V. Trushkin, ``Monotony of Lloyd's method II for log-concave density and convex error weighting function,'' IEEE Trans. Inform. Theory, vol. IT-30, no. 2, pp. 380-383, Mar. 1984.
  7. J. A. Gubner, ``Distributed estimation and quantization,'' IEEE Trans. Inform. Theory, vol. 39, no. 4, pp. 1456-1459, July 1993.

    Abstract: An algorithm is developed for the design of a nonlinear, n-sensor, distributed estimation system subject to communication and computation constraints. The algorithm uses only bivariate probability distributions and yields locally optimal estimators that satisfy the required system constraints. It is shown that the algorithm is a generalization of the classical Lloyd-Max results.