- If DMS and the duo-binary channel is considered an information source
then the Markov process that exist within this information source is called Hidden Markov Process.
- Its state diagram is
- Difference equation for the state probabilities can therefore be written as
where
and
.
- Alternatively
where
and
.
- 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
where
![F = [column for S sub 0, column for S sub 1, ..., column for S sub i, ..., column for S sub k]](math/matrixFwithcolumniforSsubi.gif)
- 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 S0 or S1), 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
.
- 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 S2. 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 inStates S0 and S3 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 S2. This is a unique state representing relaxedness of the channel also called start state.
