Empirical Coordination with Channel Feedback and Strictly Causal or Causal Encoding

TL;DR

This paper studies how feedback in a point-to-point communication setup enhances empirical coordination, showing it simplifies constraints and improves coordination with causal or strictly causal encoding.

Contribution

It characterizes the optimal information constraints for empirical coordination with feedback, revealing that feedback reduces complexity and enhances coordination possibilities.

Findings

Feedback improves coordination in both causal and strictly causal encoding.

Feedback reduces the number of auxiliary variables needed.

Feedback simplifies the information constraints for empirical coordination.

Abstract

In multi-terminal networks, feedback increases the capacity region and helps communication devices to coordinate. In this article, we deepen the relationship between coordination and feedback by considering a point-to-point scenario with an information source and a noisy channel. Empirical coordination is achievable if the encoder and the decoder can implement sequences of symbols that are jointly typical for a target probability distribution. We investigate the impact of feedback when the encoder has strictly causal or causal observation of the source symbols. For both cases, we characterize the optimal information constraints and we show that feedback improves coordination possibilities. Surprisingly, feedback also reduces the number of auxiliary random variables and simplifies the information constraints. For empirical coordination with strictly causal encoding and feedback, the information constraint does not involve auxiliary random variable anymore.