Beyond Countable Alphabets: An Extension of the Information-Spectrum Approach

TL;DR

This paper extends the information-spectrum approach to general alphabets beyond countable sets, providing a unified method for deriving one-shot bounds in information theory using quantization and a new likelihood ratio concept.

Contribution

It introduces a novel extension of the information-spectrum method applicable to general alphabets, including new bounds for random number generation from correlated sources.

Findings

Derived one-shot bounds for random number generation on general alphabets.

Introduced a new likelihood ratio form for analysis.

Extended the applicability of the information-spectrum approach.

Abstract

A general approach is established for deriving one-shot performance bounds for information-theoretic problems on general alphabets beyond countable alphabets. It is mainly based on the quantization idea and a novel form of "likelihood ratio". As an example, one-shot lower and upper bounds for random number generation from correlated sources on general alphabets are derived.