Noiseless Coding Theorems on New Generalized Useful Information Measure of order α and β type


  • Ashiq Hussain Bhat
  • Mirza Abdul Khalique Baig University of Kashmir


Shannon’s entropy, codeword length, useful information measure, Kraft inequality, Holder’s inequality, Huffman codes, Shannon-Fano codes, Noiseless coding theorem


In this paper we define new generalized useful average code-word length  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  have also been studied.


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How to Cite

Bhat, A. H., & Baig, M. A. K. (2017). Noiseless Coding Theorems on New Generalized Useful Information Measure of order α and β type. Asian Journal of Fuzzy and Applied Mathematics, 4(6). Retrieved from