Strong coordination of signals and actions over noisy channels with two-sided state information

TL;DR

This paper investigates how two nodes can coordinate signals over a noisy channel with two-sided state information, providing bounds and exact characterizations in special cases, and demonstrating the effectiveness of polar codes.

Contribution

It introduces a joint source-channel coding scheme for strong coordination over noisy channels with state information and characterizes the coordination region in key scenarios.

Findings

Complete characterization in perfect channel, lossless decoder, and independent source-channel cases.

Separation principle does not hold for joint source-channel strong coordination.

Polar codes achieve optimal inner bounds without random binning.

Abstract

We consider a network of two nodes separated by a noisy channel with two-sided state information, in which the input and output signals have to be coordinated with the source and its reconstruction. In the case of non-causal encoding and decoding, we propose a joint source-channel coding scheme and develop inner and outer bounds for the strong coordination region. While the inner and outer bounds do not match in general, we provide a complete characterization of the strong coordination region in three particular cases: i) when the channel is perfect; ii) when the decoder is lossless; and iii) when the random variables of the channel are independent from the random variables of the source. Through the study of these special cases, we prove that the separation principle does not hold for joint source-channel strong coordination. Finally, in the absence of state information, we show that polar codes achieve the best known inner bound for the strong coordination region, which therefore offers a constructive alternative to random binning and coding proofs.