Multi-terminal Strong Coordination over Noisy Channels with Encoder Co-operation

TL;DR

This paper studies strong coordination over noisy multiple-access channels with encoder cooperation, deriving achievable regions and demonstrating that cribbing enhances coordination capabilities.

Contribution

It introduces a new achievable region for strong coordination with cribbing encoders and characterizes its tightness in deterministic MAC scenarios.

Findings

Cribbing improves the achievable coordination region.

Derived an achievable region based on joint source-channel coding.

Proved tightness of the inner bound for deterministic MACs without cribbing.

Abstract

We investigate the problem of strong coordination over a multiple-access channel (MAC) with cribbing encoders. In this configuration, two encoders observe independent and identically distributed (i.i.d.) samples of a source random variable each and encode the inputs to the MAC. The decoder which observes the output of the MAC together with side-information, must generate approximately i.i.d. samples of another random variable which is jointly distributed with the two sources and the side information. We also allow for possible encoder cooperation, where one of the encoders can non-causally crib from the other encoders input. Independent pairwise shared randomness is assumed between each encoder and the decoder at limited rates. Firstly, in the presence of cribbing, we derive an achievable region based on joint source-channel coding. We also prove that in the absence of cribbing, our inner bound is tight for the special case when the MAC is composed of deterministic links, and the sources are conditionally independent given the side information. We then explicitly compute the regions for an example both with and without cribbing between the encoders, and demonstrate that cribbing strictly improves upon the achievable region.