Empirical Coordination over Markov Channel with Independent Source
This work addresses coordination problems in communication networks with Markov channels, representing an incremental advance in information theory.
The paper tackles the problem of joint source-channel coding over Markov channels by determining which empirical distributions of source and channel symbols can be achieved through coding schemes with strictly causal encoders. The main result provides single-letter inner and outer bounds for achievable joint distributions, improving beyond classical independence-based arguments.
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.