Noiseless Coding Theorems on New Generalized Useful Information Measure of order α and β type
Keywords:Shannonâ€™s entropy, codeword length, useful information measure, Kraft inequality, Holderâ€™s inequality, Huffman codes, Shannon-Fano codes, Noiseless coding theorem
AbstractIn this paper we define new generalized useful average code-word length Â of order and type and its relationship with new generalized useful information measure of order and type has been discussed. The lower and upper bound of, in terms of are derived for a discrete noiseless channel. The measures defined in this communication are not only new but some well known measures are the particular cases of our proposed measures that already exist in the literature of useful information and coding theory. The noiseless coding theorems for discrete channel proved in this paper are verified by considering Huffman and Shannon-Fano coding schemes on taking empirical data. The important properties of Â have also been studied.
Belis M, Guiasu S. A quantitative-qualitative Measure of Information in cybernetic System. IEEE Transaction on information theory, 1968; 14:593-594
Bhaker U.S, Hooda D.S. Mean value characterization of â€˜usefulâ€™ information measure. Tamkang Journal of Mathematics, 1993; 24:283-294
Bhat A.H, Baig M.A.K. Some coding theorems on generalized Reyniâ€™s entropy of order and type International Journal of Applied Mathematics and Information Sciences Letters, 2016; 5:1-5
Campbell L.L. A coding theorem and Renyiâ€™s entropy. Information and control, 1965; 8:423-429
Guiasu S, Picard C.F. Borne inferieure de la longueur de certain codes. C.R Academic Sciences, Paris, 1971; 273:248-251
Gurdial, Pessoa F. On â€˜usefulâ€™ Information of order Journal of Combinatorics Information and System Sciences, 1977; 2:158â€“162
Hartley R.V.L. Transmission of information. Bell System Technical Journal, 1928; 7: 535-563
Hooda D.S, Bhaker U.S. A generalized â€˜usefulâ€™ information measure and coding theorems. Soochow Journal of Mathematics, 1997; 23:53â€“62
Jain P, Tuteja R.K. On coding theorem connected with â€˜usefulâ€™ entropy of order International Journal of Mathematics and Mathematical Sciences, 1989; 12:193-198
Khan A.B, Bhat B.A, Pirzada S. Some results on a generalized â€˜usefulâ€™ information measure. Journal of Inequalities in Pure and Applied Mathematics, 2005; 6:117
Kraft L.G. A device for quantizing grouping and coding amplitude modulates pulses. M.S Thesis, Department of Electrical Engineering, MIT, Cambridge, 1949
Longo G. A noiseless coding theorem for source having utilities. SIAM Journal of Applied Mathematics, 1976; 30:739-748
Mitter J, Mathur Y.D. Comparison of entropies of power distributions. ZAMM, 1972; 52:239-240
Nyquist H. Certain factors affecting telegraph speed. Bell System Technical Journal, 1924; 3:324-346
Nyquist H. Certain topics in telegraphy transmission theory. Journal of the American Institute of Electrical Engineers, 1928; 47:617
Renyi A. On measure of entropy and information. In: Proceeding Fourth Berkely Symposium on Mathematical Statistics and probability, University of California Press, 1961; 1:547-561
Shannon C.E. A mathematical theory of communication. Bell System Technical Journal, 1948; 27:379-423,623-659
Sharma B.D, Man Mohan, Mitter J. On measure of â€˜usefulâ€™ information. Information and Control, 1978; 39:323-33.
Taneja H.C, Hooda D.S, Tuteja R.K. Coding theorems on a generalized â€˜usefulâ€™ information. Soochow Journal of Mathematics, 1985; 11:123-131
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