On the Interactive Capacity of Finite-State Protocols

TL;DR

This paper investigates the maximum reliable simulation rate of finite-state protocols over noisy channels, showing that certain two-state and finite-state protocols can achieve the Shannon capacity, thus establishing their interactive capacity.

Contribution

It proves that all two-state protocols and many finite-state protocols can be simulated at Shannon capacity, providing the first exact interactive capacity results for these classes.

Findings

Two-state protocols can be simulated at Shannon capacity.

Rich families of finite-state protocols achieve Shannon capacity.

Establishes the interactive capacity for these protocols.

Abstract

The interactive capacity of a noisy channel is the highest possible rate at which arbitrary interactive protocols can be simulated reliably over the channel. Determining the interactive capacity is notoriously difficult, and the best known lower bounds are far below the associated Shannon capacity, which serves as a trivial (and also generally the best known) upper bound. This paper considers the more restricted setup of simulating finite-state protocols. It is shown that all two-state protocols, as well as rich families of arbitrary finite-state protocols, can be simulated at the Shannon capacity, establishing the interactive capacity for those families of protocols.