The Zero-Error Feedback Capacity of State-Dependent Channels

TL;DR

This paper characterizes the zero-error feedback capacity of state-dependent channels, revealing scenarios where feedback enables positive capacity despite zero zero-error capacity without feedback, and discusses related constraints and state recovery.

Contribution

It establishes the zero-error feedback capacity for Gelfand-Pinsker channels and analyzes the effects of feedback, causality, and constraints on capacity and state recovery.

Findings

Feedback can enable positive zero-error capacity when it is zero without feedback.

Reveals that error-free transmission of a single bit may require multiple channel uses.

Discusses the impact of cost constraints and state recovery on capacity.

Abstract

The zero-error feedback capacity of the Gelfand-Pinsker channel is established. It can be positive even if the channel's zero-error capacity is zero in the absence of feedback. Moreover, the error-free transmission of a single bit may require more than one channel use. These phenomena do not occur when the state is revealed to the transmitter causally, a case that is solved here using Shannon strategies. Cost constraints on the channel inputs or channel states are also discussed, as is the scenario where---in addition to the message---also the state sequence must be recovered.