Markov Lemma for Countable Alphabets

TL;DR

This paper introduces a version of the Markov lemma based on unified typicality that applies to both finite and countably infinite alphabets, enabling broader multiterminal source coding applications.

Contribution

It extends the Markov lemma to countable alphabets using unified typicality, overcoming previous limitations to finite alphabets.

Findings

Markov lemma extended to countable alphabets

Unified typicality retains key properties for infinite alphabets

Simplified verification of joint typicality sequences

Abstract

Strong typicality and the Markov lemma have been used in the proofs of several multiterminal source coding theorems. Since these two tools can be applied to finite alphabets only, the results proved by them are subject to the same limitation. Recently, a new notion of typicality, namely unified typicality, has been defined. It can be applied to both finite or countably infinite alphabets, and it retains the asymptotic equipartition property and the structural properties of strong typicality. In this paper, unified typicality is used to derive a version of the Markov lemma which works on both finite or countably infinite alphabets so that many results in multiterminal source coding can readily be extended. Furthermore, a simple way to verify whether some sequences are jointly typical is shown.