On the error exponent of variable-length block-coding schemes over finite-state Markov channels with feedback

TL;DR

This paper extends Burnashev's classic result to finite-state Markov channels with feedback, providing a single-letter characterization of the reliability function for variable-length coding when the channel state is causally observed at both ends.

Contribution

It introduces a novel single-letter characterization of the error exponent for finite-state Markov channels with feedback, utilizing stochastic control and convex analysis techniques.

Findings

Extended Burnashev's result to Markov channels with feedback

Derived a single-letter formula for the reliability function

Applied stochastic control and convex analysis methods

Abstract

The error exponent of Markov channels with feedback is studied in the variable-length block-coding setting. Burnashev's classic result is extended and a single letter characterization for the reliability function of finite-state Markov channels is presented, under the assumption that the channel state is causally observed both at the transmitter and at the receiver side. Tools from stochastic control theory are used in order to treat channels with intersymbol interference. In particular the convex analytical approach to Markov decision processes is adopted to handle problems with stopping time horizons arising from variable-length coding schemes.