Second-Order Coding Rates for Channels with State

TL;DR

This paper investigates the fundamental limits of state-dependent channels with states known at both ends, providing capacity characterizations and second-order rates for various state processes.

Contribution

It offers new capacity results and second-order coding rate characterizations for channels with non-stationary, non-ergodic states, extending prior work.

Findings

Established epsilon-capacity for general state processes

Derived necessary and sufficient conditions for strong converse

Provided examples with i.i.d., Markov, and mixed states

Abstract

We study the performance limits of state-dependent discrete memoryless channels with a discrete state available at both the encoder and the decoder. We establish the epsilon-capacity as well as necessary and sufficient conditions for the strong converse property for such channels when the sequence of channel states is not necessarily stationary, memoryless or ergodic. We then seek a finer characterization of these capacities in terms of second-order coding rates. The general results are supplemented by several examples including i.i.d. and Markov states and mixed channels.