New Families and New Members of Integer Sequence Based Coding Methods

Abstract

This paper presents Integer sequences that have the property of being additively and/or multiplicatively complete, Zekendorf, and unique Zekendorf. In addition, a generalized Elias coding scheme is developed. Features of Zekendorf sequence based and generalized Elias coding compression methods including compression rate, universality, asymptotic optimality, and coding complexity are analyzed.