Introduction to Dynamic Unary Encoding

TL;DR

Dynamic unary encoding extends unary coding to all n-bit binary strings, creating a versatile method that partitions data into cycles, useful for encoding, transforms, and mathematical analysis.

Contribution

The paper introduces dynamic unary encoding, a novel method that encodes all n-bit strings and characterizes their cycle structures, expanding unary coding applications.

Findings

Partitions 2^n integers into n disjoint cycles

Provides encoding and decoding algorithms for dynamic unary

Demonstrates the cycle as a mathematical object

Abstract

Dynamic unary encoding takes unary encoding to the next level. Every n-bit binary string is an encoding of dynamic unary and every n-bit binary string is encodable by dynamic unary. By utilizing both forms of unary code and a single bit of parity information dynamic unary encoding partitions 2^n non-negative integers into n sets of disjoint cycles of n-bit elements. These cycles have been employed as virtual data sets, binary transforms and as a mathematical object. Characterization of both the cycles and of the cycle spectrum is given. Examples of encoding and decoding algorithms are given. Examples of other constructs utilizing the principles of dynamic unary encoding are presented. The cycle as a mathematical object is demonstrated.