Codes and Formulation of Appropriate Constraints via Entropy Measures
In present communication, we have developed the
suitable constraints for the given the mean codeword length and the
measures of entropy. This development has proved that Renyi-s
entropy gives the minimum value of the log of the harmonic mean
and the log of power mean. We have also developed an important
relation between best 1:1 code and the uniquely decipherable code by
using different measures of entropy.
[1] Campbell, L. L. (1965): "A coding theorem and Renyi's entropy",
Information and Control, 8, 423-429.
[2] Cheng, J. and Huang, T. K. (2006): "New lower and upper bounds on
the expected length of optimal one-to-one codes", Proceedings of the
Data Compression Conference, 43-52.
[3] Cheng, J., Huang, T. K. and Weidmann, C. (2007): "New bounds on the
expected length of optimal one-to-one codes", IEEE Trans. Inform.
Theory, 53(5), 1884-1895.
[4] Feinstein, A. (1958): "Foundations of Information Theory", McGraw-
Hill, New York.
[5] Kapur, J.N. (1995): "Measures of Information and Their Applications",
Wiley Eastern, New York.
[6] Kraft, L. G. (1949): "A Device for Quantizing Grouping and Coding
Amplitude Modulated Pulses", M.S. Thesis, Electrical Engineering
Department, MIT.
[7] Leung-Yan-Cheong, S. K. and Cover, T. M. (1978): "Some equivalences
between Shannon entropy and Kolmogrov complexity", IEEE Trans.
Inform. Theory, 24, 331-338.
[8] Renyi, A. (1961): "On measures of entropy and information",
Proceedings 4th Berkeley Symposium on Mathematical Statistics and
Probability, 1, 547-561.
[9] Rissanen, J. (1992): "Tight lower bounds for optimal code length", IEEE
Trans. Inform. Theory, 28(2), 348-349.
[10] Savari, S. A. and Naheta, A. (2004): "Bounds on the expected cost of
one-to-one codes", Proc. IEEE Int. Symp. Information Theory, 94.
[11] Shannon, C. E. (1948): "A mathematical theory of communication", Bell
System Tech J., 27, 379-423.
[1] Campbell, L. L. (1965): "A coding theorem and Renyi's entropy",
Information and Control, 8, 423-429.
[2] Cheng, J. and Huang, T. K. (2006): "New lower and upper bounds on
the expected length of optimal one-to-one codes", Proceedings of the
Data Compression Conference, 43-52.
[3] Cheng, J., Huang, T. K. and Weidmann, C. (2007): "New bounds on the
expected length of optimal one-to-one codes", IEEE Trans. Inform.
Theory, 53(5), 1884-1895.
[4] Feinstein, A. (1958): "Foundations of Information Theory", McGraw-
Hill, New York.
[5] Kapur, J.N. (1995): "Measures of Information and Their Applications",
Wiley Eastern, New York.
[6] Kraft, L. G. (1949): "A Device for Quantizing Grouping and Coding
Amplitude Modulated Pulses", M.S. Thesis, Electrical Engineering
Department, MIT.
[7] Leung-Yan-Cheong, S. K. and Cover, T. M. (1978): "Some equivalences
between Shannon entropy and Kolmogrov complexity", IEEE Trans.
Inform. Theory, 24, 331-338.
[8] Renyi, A. (1961): "On measures of entropy and information",
Proceedings 4th Berkeley Symposium on Mathematical Statistics and
Probability, 1, 547-561.
[9] Rissanen, J. (1992): "Tight lower bounds for optimal code length", IEEE
Trans. Inform. Theory, 28(2), 348-349.
[10] Savari, S. A. and Naheta, A. (2004): "Bounds on the expected cost of
one-to-one codes", Proc. IEEE Int. Symp. Information Theory, 94.
[11] Shannon, C. E. (1948): "A mathematical theory of communication", Bell
System Tech J., 27, 379-423.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:50073", author = "R. K. Tuli", title = "Codes and Formulation of Appropriate Constraints via Entropy Measures", abstract = "In present communication, we have developed the
suitable constraints for the given the mean codeword length and the
measures of entropy. This development has proved that Renyi-s
entropy gives the minimum value of the log of the harmonic mean
and the log of power mean. We have also developed an important
relation between best 1:1 code and the uniquely decipherable code by
using different measures of entropy.", keywords = "Codeword, Instantaneous code, Prefix code,Uniquely decipherable code, Best one-one code, Mean codewordlength", volume = "5", number = "3", pages = "226-5", }