Performance Bounds for Subband Coding

  • William A. Pearlman
Part of the The Springer International Series in Engineering and Computer Science book series (SECS, volume 115)


The purpose of this chapter is to present some tutorial material in information theory which is pertinent to the subject of subband coding and to develop this material further in order to gain insight into the superior performance realized in subband coding systems. Except for the well-known result that PCM coding of subbands outperforms direct PCM coding of the full-band original (see [7]), which is known to be generally inefficient, there have been hardly any theoretical analyses which have shown a mean-squared error improvement for subband coding. The superior results of subband coding systems are largely empirical in nature and they have indeed been impressive in coding of images. In this chapter these superior results are quantified in formulas, which have not yet appeared in print elsewhere.


Average Mutual Information Test Channel Entropy Rate Differential Entropy Source Vector 
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  1. [1]
    D.A. Huffman, “A method for construction of minimum redundancy codes”, Proc. IRE, vol. 40, pp. 1098–1101, Sept. 1952.CrossRefGoogle Scholar
  2. [2]
    R.E. Blahut, “Computation of channel capacity and rate-distortion function”, IEEE Trans. Inform. Theory, vol. IT-18, pp. 460–473, July 1972.MathSciNetzbMATHCrossRefGoogle Scholar
  3. [3]
    R.G. Gallager, Information Theory and Reliable Communication, New York: J. Wiley and Sons, Inc., 1968.zbMATHGoogle Scholar
  4. [4]
    W.A. Pearlman and P. Jakatdar, “A transform tree code for stationary Gaussian sources”, IEEE Trans. Inform. Theory, vol. IT-31, pp. 761–768.Google Scholar
  5. [5]
    B. Mazor and W.A. Pearlman, “A trellis code construction and coding theorem for stationary Gaussian sources”, IEEE Trans. Inform. Theory, vol. IT-29, pp. 924–930, Nov. 1983.MathSciNetzbMATHCrossRefGoogle Scholar
  6. [6]
    B. Mazor and W.A. Pearlman, “A tree coding theorem for stationary Gaussian sources and the squared-error distortion measure”, IEEE Trans. Inform. Theory, vol. IT-32, pp. 156–165, March 1986.MathSciNetzbMATHCrossRefGoogle Scholar
  7. [7]
    N.S. Jayant and P. Noll, Digital Coding of Waveforms, Englewood Cliffs, NJ: Prentice Hall, 1984.Google Scholar
  8. [8]
    R. Bellman, Introduction to Matrix Analysis, 2nd Ed., New York: McGraw-Hill, 1970.zbMATHGoogle Scholar
  9. [9]
    S. Nanda, A Tree Coding Theorem and Tree Coding of Subbands with Application to Images, Ph.D. dissertation, Rensselaer Polytechnic Institute, Troy, NY, October 1988.Google Scholar
  10. [10]
    P.H. Westerink, “An optimal bit allocation for subband coding”, Proc. 1988 IEEE Int. Conf. Acoust., Speech, Signal Process., New York, April 1988, pp. 757–760.Google Scholar
  11. [11]
    J.W. Woods and S.D. O’Neil, “Subband coding of images”, IEEE Trans. Acoustics, Speech, and Signal Processing, vol. ASSP-34, pp. 1278–1286, October 1986.CrossRefGoogle Scholar
  12. [12]
    A.D. Wyner and J. Ziv, “Bounds on the rate-distortion function for stationary sources with memory”, IEEE Trans. Inform. Theory, vol. IT- 17, pp. 508–513, September 1971.MathSciNetzbMATHCrossRefGoogle Scholar
  13. [13]
    R.P. Rao and W.A. Pearlman, “On entropy rate for source encoding on a pyramid structure”, Abstracts of 1990 IEEE International Symposium on Information Theory, January 1990, San Diego, CA, pp. 57–58; also R.P. Rao and W.A. Pearlman, “On entropy rate of pyramid structures”, submitted to IEEE Trans. Inform. Theory.Google Scholar
  14. [14]
    P. Chou, T. Lookabaugh, and R.M. Gray, “Optimal pruning with applications to treestructured source coding and modeling”, IEEE Trans. Inform. Theory, vol. IT-35, pp. 299–315, March 1989.MathSciNetCrossRefGoogle Scholar
  15. [15]
    L. Breiman, J.H. Friedman, R.A. Olshen, and C.J. Stone, Classification and Regression Trees, Monterey, CA: Wadsworth, 1984.zbMATHGoogle Scholar
  16. [16]
    B. Mahesh and W.A. Pearlman, “Multiple rate code book design for vector quantization of image pyramids”, Applications of Digital Image Processing XIII, A. Tescher, Ed., Proc. SPIE 1349, July 1990.Google Scholar
  17. [17]
    J.W. Modestino, V. Bhaskaran, and J.B. Anderson, “Tree encoding of images in the presence of channel errors”, IEEE Trans. Inform. Theory, vol. IT-27, pp. 677–697, Nov. 1981.CrossRefGoogle Scholar
  18. [18]
    J.B. Anderson and J.B. Brodie, “Tree encoding of speech”, IEEE Trans. Inform. Theory, vol. IT-21, pp. 379–387, July 1975.zbMATHCrossRefGoogle Scholar
  19. [19]
    H.G. Fehn and P. Noll, “Multipath search coding of stationary signals with applications to speech”, IEEE Trans. Commun., vol. COM-30, pp. 687–701, April 1982.CrossRefGoogle Scholar
  20. [20]
    P. Kroon and E.F. Deprettere, “A class of analysis-by-synthesis predictive coders for high quality speech coding at rates between 4.8 and 16 kbits/s”, IEEE J. Select. Area Commun., vol. 6, pp. 353–363, Feb. 1988.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1991

Authors and Affiliations

  • William A. Pearlman
    • 1
  1. 1.Electrical, Computer, and Systems Engineering DepartmentRensselaer Polytechnic InstituteTroyUSA

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