Certain Coding Theorems Based on Generalized Inaccuracy Measure of Order $\alpha$ and Type $\beta$ and 1:1 Coding

Abstract

In this paper, A new mean codeword length $\L^t_{\beta}(U)$ is defined. We have established some noiseless coding theorems based on generalized inaccuracy measure of order $\alpha$ and type $\beta$. Further, we have defined mean codeword length $\L^t_{\beta, 1:1}(U)$ for the best one-to-one code. Also we have shown that the mean codeword lengths $\L^t_{\beta, 1:1}(U)$ for the best one-to-one code (not necessarily uniquely decodable) are shorter than the mean codeword length $\L^t_{\beta}(U)$. Moreover, we have studied tighter bounds of $\L^t_{\beta}(U)$. Keywords: Generalized inaccuracy measures; Codeword; mean codeword length; Kraft's inequality; Holder's inequality. 2010 Mathematics Subject Classification: 94A15, 94A17, 94A24, 26D15.