Journal of Mathematics Research
Some More Noiseless Coding Theorem on Generalized R-Norm Entropy
Abstract
A parametric mean length is defined as the quantity
$L_{R}^{\beta}=\frac{R}{R-1}\left[1-\frac{\sum_{i=1}^{N}p_{i}^{\beta}D^{-n_{i}\left(\frac{R-1}{R}\right)}}{\sum_{j=1}^{N}p_{j}^{\beta}}\right]$
\noindent where $R>0\left(\ne 1\right),\beta >0,\, p_{i} >0,\, \sum p_{i} =1,\, \, i=1,2,\dots,N.$ This being
the mean length of code words. Lower and upper bounds for $L_{R}^{\beta}$ are derived in terms of R-norm
information measure for the incomplete power distribution.
$L_{R}^{\beta}=\frac{R}{R-1}\left[1-\frac{\sum_{i=1}^{N}p_{i}^{\beta}D^{-n_{i}\left(\frac{R-1}{R}\right)}}{\sum_{j=1}^{N}p_{j}^{\beta}}\right]$
\noindent where $R>0\left(\ne 1\right),\beta >0,\, p_{i} >0,\, \sum p_{i} =1,\, \, i=1,2,\dots,N.$ This being
the mean length of code words. Lower and upper bounds for $L_{R}^{\beta}$ are derived in terms of R-norm
information measure for the incomplete power distribution.
This work is licensed under a Creative Commons Attribution 3.0 License.
Journal of Mathematics Research ISSN 1916-9795 (Print) ISSN 1916-9809 (Online)
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