An algebraic approach to information theory

TL;DR

This paper introduces an algebraic framework for classical information theory, providing new computational tools and reinterpreting key theorems within an algebraic context.

Contribution

It presents a novel algebraic model for probability and information theory, offering fresh insights and methods for analysis.

Findings

Reformulation of probability and information theory theorems algebraically

Development of new computational and analytical tools

Enhanced understanding of classical information theory through algebraic structures

Abstract

This work proposes an algebraic model for classical information theory. We first give an algebraic model of probability theory. Information theoretic constructs are based on this model. In addition to theoretical insights provided by our model one obtains new computational and analytical tools. Several important theorems of classical probability and information theory are presented in the algebraic framework.