Optimal quantization for the one-dimensional uniform distribution with rényi-a-entropy constraints

Kybernetika

Volumn 46, Issue 1, 2010, Pages 96-113

  Kreitmeier, Wolfgang ^a  

^a UNIVERSITY OF PASSAU   (Germany)

Author keywords

entropy; Nyi ; Optimal quantization; R ; Uniform distribution

Indexed keywords

EID: 77953574608     PISSN: 00235954     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. J. Aczél and Z. Daróczy: On Measures of Information and Their Characterizations. (Mathematics in Science and Engineering Vol. 115.) Academic Press, London 1975.
2. M. S. Bazaraa, H. D. Sherali, and C. M. Shetty: Nonlinear Programming, Theory and Algorithms. Wiley, New York 1993.
3. C. Beck and F. Schlögl: Thermodynamics of Chaotic Systems. Cambridge University Press, Cambridge 1993.
4. M. Behara: Additive and Nonadditive Measures of Entropy. Wiley, New Delhi 1990.
5. J. C. Fort and G. Pages: Asymptotics of optimal quantizers for some scalar distributions. J. Comput. Appl. Math. 146 (2002), 253-275.
6. A. Ge'rsho and R. M. Gray: Vector Quantization and Signal Compression. Kluwer, Boston 1992.
7. S. Graf and H. Luschgy: The quantization of the Cantor distribution. Math. Nachr. 183 (1997), 113-133.
8. S. Graf and H. Luschgy: Foundations of Quantization for Probability Distributions. (Lecture Notes in Computer Science 1730.) Springer, Berlin 2000.
9. R.M. Gray and D. Neuhoff: Quantization. IEEE Trans. Inform. Theory 44 (1998), 2325-2383.
10. M. Grendar: Entropy and effective support size. Entropy 8 (2006), 169-174.
11. A. György and T. Linder: Optimal entropy-constrained scalar quantization of a uniform source. IEEE Trans. Inform. Theory 46 (2000), 2704-2711.
12. A. György and T. Linder: On the structure of optimal entropy-constrained scalar quantizers. IEEE Trans. Inform. Theory 48 (2002), 416-427.
13. G. H. Hardy, J. E. Littlewood and G. Polya: Inequalities. Second edition. Cambridge University Press, Cambridge 1959.
14. P. Harremoes and F. Topsøe: Inequalities between entropy and index of coincidence derived from information diagrams. IEEE Trans. Inform. Theory 47 (2001), 2944-2960.
15. M. Kesseböhmer and S. Zhu: Stability of quantization dimension and quantization for homogeneous Cantor measure. Math. Nachr. 280 (2007), 866-881.
16. W. Kreitmeier: Optimal quantization for dyadic homogeneous Cantor distributions. Math. Nachr. 281 (2008), 1307-1327.
17. F. Liese, D. Morales, and I. Vajda: Asymptotically sufficient partitions and quantizations. IEEE Trans. Inform. Theory 52 (2006), 5599-5606.
18. K. Pötzelberger and H. Strasser: Clustering and quantization by MSP-partitions. Statist. Decisions 19 (2001), 331-371.