Channel Capacity of Coding System on Tsallis Entropy and q-Statistics

TL;DR

This paper develops a theoretical framework for coding systems based on Tsallis entropy, deriving a generalized channel capacity formula that could impact data processing and related fields.

Contribution

It introduces a novel formulation of channel capacity using Tsallis entropy, extending traditional information theory to non-extensive entropy measures.

Findings

Derived a relation between code length and appearance probability.

Formulated a generalized channel capacity expression based on Tsallis entropy.

Potential applications in data processing and information theory.

Abstract

The field of information science has greatly developed, and applications in various fields have emerged. In this paper, we evaluated the coding system in the theory of Tsallis entropy for transmission of messages and aimed to formulate the channel capacity by maximization of the Tsallis entropy within a given condition of code length. As a result, we obtained a simple relational expression between code length and code appearance probability and, additionally, a generalized formula of the channel capacity on the basis of Tsallis entropy statistics. This theoretical framework may contribute to data processing techniques and other applications.