Empirical Coordination over Markov Channel with Independent Source

TL;DR

This paper investigates empirical coordination in joint source-channel coding over Markov channels, deriving bounds on achievable distributions using a novel typicality concept tailored for Markov structures.

Contribution

It introduces a new input-driven Markov typicality and provides single-letter inner and outer bounds for empirical coordination over Markov channels.

Findings

Established single-letter bounds for achievable joint distributions.

Developed a new typicality notion suited for Markov channel analysis.

Improved coordination analysis by exploiting Markov channel structure.

Abstract

We study joint source-channel coding over Markov channels through the empirical coordination framework. More specifically, we aim at determining the empirical distributions of source and channel symbols that can be induced by a coding scheme. We consider strictly causal encoders that generate channel inputs, without access to the past channel states, henceforth driving the Markov state evolution. Our main result is the single-letter inner and outer bounds of the set of achievable joint distributions, coordinating all the symbols in the network. To establish the inner bound, we introduce a new notion of typicality, the input-driven Markov typicality, and develop its fundamental properties. Contrary to the classical block-Markov coding schemes that rely on the blockwise independence for discrete memoryless channels, our analysis directly exploits the Markov channel structure and improves beyond the independence-based arguments.