An application of generalized Tsalli’s-Havrda-Charvat entropy in coding theory through a generalization of Kraft inequality
Abstract
A parametric mean length is defined as the quantity , where α > 0 (≠ 1), β > 0, ui > 0, D > 1 is an integer, Σ pi = 1. This being the useful mean length of code words weighted by utilities, ui. Lower and Upper bounds form αβLu are derived in terms of ‘useful’ Tsalli’s-Havrda-Charvat information measure for power probability distribution Pβi.
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- Exponential Renyi’s entropy of ‘Type (a, ß)’ and new mean code-Word length
Dhanesh Garg · International Journal of Statistics and Applied Mathematics · 2017
In this paper, we introduce a quantity which is called exponential entropy of ‘type (a, s) ’ and discuss its some major properties corresponding to exponential entropy of concave function. Further, a new measure Las (A) called average codeword length of ‘type (a, s) ’ has been define and its relationship with a result of an exponential Reyni’s entropy of ‘type (a, s)’ has been discussed. Using Las (A) and Lsa (A) , coding theorem for discrete noiseless has been proved. At the end of the paper, we illustrate the veracity of the theorem by taking empirical data as given in the table 3.1 and 3.2.
- Generalized information measure and some source coding theorems
Dhanesh Garg · International Journal of Statistics and Applied Mathematics · 2017
A new measure called generalized information measure is defined and its relationship with a new mean codeword length is discussed. Consequently two noiseless coding theorems subject to Kraft’s inequality have been proved. Further, we have shown that the mean codeword length for the best one-to-one code (not necessarily uniquely decodable) are shorter than the mean codeword length for the best uniquely decodable code by no more than for D=2.
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