Finite-Length Analyses for Source and Channel Coding on Markov Chains

Joint Source { Channel Coding with Variable Length

Lectures on finite Markov chains

Variable Length Markov Chains

We study estimation in the class of stationary variable length Markov Ž . chains VLMC on a finite space. The processes in this class are still Markovian of high order, but with memory of variable length yielding a much bigger and structurally richer class of models than ordinary highorder Markov chains. From an algorithmic view, the VLMC model class has attracted interest in information theory ...

Expansion Coding for Channel and Source Coding

A general method of coding over expansion is proposed, which allows one to reduce the highly non-trivial problems of coding over analog channels and compressing analog sources to a set of much simpler subproblems, coding over discrete channels and compressing discrete sources. More specifically, the focus of this paper is on the additive exponential noise (AEN) channel, and lossy compression of...

Finite Markov Chains

This paper provides basic information and theorems about finite Markov chains. The inspiration for this paper came from Professor Laci Babai’s Discrete Mathematics lecture notes from the REU program of 2003. After reading through his chapter on Markov chains, I decided to proceed by answering as many exercises from the notes as possible. Below is what I have finished.