Introduction to Set Shaping Theory

TL;DR

This paper introduces Set Shaping Theory, analyzing bijection functions that transform string sets into larger sets with a focus on minimizing information content for data compression.

Contribution

It defines a new theoretical framework for data transformation functions and identifies optimal functions for data compression applications.

Findings

Identified functions that minimize average information content

Demonstrated potential use in data compression

Provided mathematical analysis of set transformation functions

Abstract

In this article, we define the Set Shaping Theory whose goal is the study of the bijection functions that transform a set of strings into a set of equal size made up of strings of greater length. The functions that meet this condition are many but since the goal of this theory is the transmission of data, we have analyzed the function that minimizes the average information content. The results obtained show how this type of function can be useful in data compression.