As stated above we wish to discard the least likely path and
select the most likely path, called the survivor path. At this point, the accumulated Hamming distance
for each candidate is calculated and the trellis path with the smallest Hamming distance entering that
state is selected, this is shown in Fig. 5.33. The trellis diagram presents the accumulated Hamming
distance at each state, this is shown as the boxed value.
So the accumulated Hamming distance for states a, b, c, and d are equal to 3, 3, 0, and 2, respectively.
Now each state has only a single state transition path entering it. The general procedure at this
time is to calculate a Hamming distance and update the accumulated Hamming value. Next compare
all state transitions and select the path with the smallest accumulated Hamming distance. This procedure
is simplified to perform the following operations: Add the metric, compare the state paths, and
select the survivor transition. In short, these functions are add, compare, and select (ACS). Hence it
is easy to see how the VA can be implemented using these repetitive operations [16].
Now we show the next group of received bits entering the Viterbi decoder and once again select
the surviving transition path for each state.
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