Variable length prefix (Δ, k)-codes

Abstract

A new perspective family of universal variable length prefix codes with a set of delimiters is introduced. The main seed of these codes is the binary representation of natural numbers in the two-base numeration system with the main radix 2 and the auxiliary radix 3. We construct extensions and generalizations of these (2,3)-codes, which we call (Δ, k)-codes. We prove that all (Δ, k)-codes are complete. Also for these codes we developed fast and efficient bit-wise and byte-wise encoding and decoding algorithms. Some representatives of (Δ, k)-codes family outperform the known closest to them Fibonacci codes either in text compression efficiency or in computational complexity.