# Finite-Length Bounds for Joint Source-Channel Coding with Markovian Source and Additive Channel Noise to Achieve Large and Moderate Deviation Bounds

## TL;DR

This paper establishes new finite-length bounds on error probabilities for joint source-channel coding with Markovian sources and channels, providing tight results in large and moderate deviation regimes.

## Contribution

It introduces novel upper and lower bounds for error probability in joint source-channel coding with Markovian processes, covering large and moderate deviation regimes.

## Key findings

- Bounds are tight in large deviation regimes
- Bounds are tight in moderate deviation regimes
- Applicable to ergodic Markov sources and channels

## Abstract

We derive novel upper and lower finite-length bounds of the error probability in joint source-channel coding when the source obeys an ergodic Markov process and the channel is a Markovian additive channel or a Markovian conditional additive channel. These bounds are tight in the large and moderate deviation regimes.