- If DMS and the duo-binary channel is considered an information source
*Hidden Markov Process.*

- Its state diagram is

- Difference equation for the state probabilities can therefore be written as
- Alternatively

- Difference equation for the state probabilities can therefore be written as
- An alternative to the Markov process diagram is the Gallagher's diagram. The diagram represents the source and channel using state-dependent memoryless channel diagrams.

- In general, the entropy rate is given by

- The generation of same output sequence
*y̅*for two or more different sequences*x̅*is called catastrophic sequence system.

This means that if we knew a priori about the initial state*S*(*n*−1) (i.e, either*S*_{0}or*S*_{1}), we can decode*y̅*into sequence*x̅*. This is called state dependent decoding.- One way of measuring–how much of the information in
*y̅*is from*X*? is by computing the entropy rate*H'*(*Y*). And if*H'*(*Y*) ≡*H*(*X*), this means that*H'*(*Y*) is tracking . - Set–distinguishibility decoding may be implemented for initial state dependency.
- One way is to introduce a de–energized state
*S*_{2}. This is a unique state representing relaxedness of the channel also called start state.

- Another is by pre–coding. Non–Return–to–Zero–Inverted (NRZI) code is an example.

This results in*S*_{0}and*S*_{3}are said to form a closed irreducible recurrent non–null Markov chain also known as ergodic Markov chain.

- One way is to introduce a de–energized state

- One way of measuring–how much of the information in