Markov Capacity for Factor Codes with an Unambiguous Symbol

TL;DR

This paper investigates conditions under which certain factor codes with unambiguous symbols admit subshifts of finite type with specific properties, and explores their connection to Markov chain capacity in deterministic channels.

Contribution

It provides necessary and sufficient conditions for factor codes with unambiguous symbols to admit finite-type subshifts with specific properties and conjectures a link to Markov chain capacity.

Findings

Characterization of when factor codes admit finite-type subshifts with one-to-one and finite-to-one properties.

Conjecture relating finite-to-one property to the existence of capacity-achieving Markov chains.

Insight into the structure of factor codes on spoke graphs and their capacity implications.

Abstract

In this paper, we first give a necessary and sufficient condition for a factor code with an unambiguous symbol to admit a subshift of finite type restricted to which it is one-to-one and onto. We then give a necessary and sufficient condition for the standard factor code on a spoke graph to admit a subshift of finite type restricted to which it is finite-to-one and onto. We also conjecture that for such a code, this finite-to-one property is equivalent to the existence of a stationary Markov chain that achieves the capacity of the corresponding deterministic channel.