# Second Order Analysis for Joint Source-Channel Coding with Markovian Source

## TL;DR

This paper derives second order rates for joint source-channel coding with Markovian sources and compares it to separation schemes, introducing new distribution families to facilitate analysis.

## Contribution

It extends second order analysis to general Markov sources and channels, and introduces new distribution families for this purpose.

## Key findings

- Derived second order rates for Markov sources and DMC channels.
- Compared joint source-channel coding with separation scheme in second order regime.
- Introduced switched Gaussian convolution and *-product distributions.

## Abstract

We derive the second order rates of joint source-channel coding, whose source obeys an irreducible and ergodic Markov process when the channel is a discrete memoryless, while a previous study solved it only in a special case. We also compare the joint source-channel scheme with the separation scheme in the second order regime while a previous study made a notable comparison only with numerical calculation. To make these two notable progress, we introduce two kinds of new distribution families, switched Gaussian convolution distribution and *-product distribution, which are defined by modifying the Gaussian distribution.