An application of Markov chains in digital communication

Abstract

This contribution shows an application of Markov chains in digital
communication. A random sequence of symbols 0 and 1 is analyzed

by a state machine. The state machine switches to state "0" after detecting an unbroken sequence of $\omega$  zero symbols ($\omega$ being a fixed integer),

and to state "1" after detecting an unbroken sequence of $\omega$
ones. The task to nd the probabilities of each of these two states after
$n$ time steps leads to a Markov chain. We show the construction of the
transition matrix and determine the steady-state probabilities for the
time-homogeneous case.