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Characterization of New Two Parametric Generalized Useful Information Measure  

Bhat, Ashiq Hussain (Post Graduate Department of Statistics University of Kashmir)
Baig, M. A. K. (Post Graduate Department of Statistics University of Kashmir)
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Journal of Information Science Theory and Practice / v.4, no.4, 2016 , pp. 64-74 More about this Journal
In this paper we define a two parametric new generalized useful average code-word length $L_{\alpha}^{\beta}$(P;U) and its relationship with two parametric new generalized useful information measure $H_{\alpha}^{\beta}$(P;U) has been discussed. The lower and upper bound of $L_{\alpha}^{\beta}$(P;U), in terms of $H_{\alpha}^{\beta}$(P;U) 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 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. Also we study the monotonic behavior of $H_{\alpha}^{\beta}$(P;U) with respect to parameters ${\alpha}$ and ${\beta}$. The important properties of $H_{{\alpha}}^{{\beta}}$(P;U) have also been studied.
Shannon's entropy; codeword length; useful information measure; Kraft inequality; Holder's inequality; Huffman codes; Shannon-Fano codes; Noiseless coding theorem;
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