Generalized information measure and some source coding theorems

Abstract

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.