Work

Kolmogorov Capacity with Overlap

Year: 2025

Type: article

Abstract: The notion of δ-mutual information between non-stochastic uncertain variables is introduced as a generalization of Nair's non-stochastic information functional. Several properties of this new quantity are illustrated and used in a communication setting to show that the largest δ-mutual information between received and transmitted codewords over ϵ-noise channels equals the (ϵ,δ)-capacity. This notion of capacity generalizes the Kolmogorov ϵ-capacity to packing sets of overlap at most δ and is a variation of a previous definition proposed by one of the authors. Results are then extended to more general noise models, including non-stochastic, memoryless, and stationary channels. The presented theory admits the possibility of decoding errors, as in classical information theory, while retaining the worst-case, non-stochastic character of Kolmogorov's approach.

Source: Entropy

DOI: 10.3390/e27050472

Authors: Anshuka Rangi, Massimo Franceschetti

Institution: University of California San Diego

Language: English

Topic: Error Correcting Code Techniques

Subfield: Computer Networks and Communications

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: National Science Foundation