*how to deal with initial state dependency and decoding?*

☛

This problem of initial state dependency with decoding can be tackled with **set–distinguishability** decoding. One way of achieving set–distinguishability is the introduction of a de–energized state . This is a unique state representing relaxedness of the channel. That is '*start state*'.

*x*

_{2}= 0 the entropy is same

*H*(

*X*) = 0.7219281.

❶

At time index *n*, if

*μ*

_{0}+

*μ*

_{1}+

*μ*

_{2}= 1, this means

☛

Another way of achieving set-distinguishability is to *initially* send either a pair of *x _{i}* = −1 or a pair of

*x*= +1. This

_{i}*ensures unambiguous identification*of either

*S*

_{0}or

*S*

_{1}due to

*y*= −2 and

*y*= +2 respectively. This initial sending signal is called '

*start signal*' and the symbol is called '

*start symbol*'.

There are number of ways of pre–coding the channel inputs. One common one is the **non–return–to–zero–inverted** (NRZI) code.

The NRZI pre–coded duo–binary channel becomes

If the states are defined as *S*^{(n)} = ⟨*β*^{(n−1)}, *α*^{(n−1)}⟩

*S*

_{1}and

*S*

_{2}cannot be entered. Hence they

*can*be initial states. States

*S*

_{0}and

*S*

_{3}are said to form a

*closed irreducible recurrent non–null*Markov chain. They are also known as

*ergodic*Markov chain. ❹

The trellis diagram for the NRZI pre–coded duo–binary channel is

*n*≥ 1

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Summary (p:6) ➽