A new weighted (α,β)-norm information measure with application in coding theory

In the present communication, we introduce a quantity which is called weighted (α,β)-norm entropy and discuss its some major properties with Shannon and other entropies in the literature. Corresponding to the proposed entropy, a new weighted directed divergence measure has been introduced and its validity is established. Further, we give the application of (α,β)-norm entropy in coding theory and a coding theorem analogous to the ordinary coding theorem for a noiseless channel has been proved. The theorem states that the proposed entropy is the lower bound of mean code word length.