The first 2 received coded
bits are compared against all possibly transmitted bits and the Hamming distance is calculated for
each possibility. The next 2 received coded bits are also compared against all combinations as well.
The exhaustive comparison is shown in Fig. 5.32, where we have placed the Hamming distances next
to the state transitions.
The first trellis diagram compares ???11??? against the possible transmitted bits. The Hamming distance
between the locally generated bits and the bits that would have been transmitted, if a 0 was
encoded, is a 2. Similarly, the Hamming distance when comparing the received bits to those generated
if a 1 was encoded, is a 0. It is very premature to estimate the first encoded bit; however, you can see
that, so far, it has a value of 1.
The second trellis diagram compares ???01??? against the possible transmitted bits. Here four
Hamming distances are calculated for each state transition.
The third trellis diagram compares ???01??? against the possible transmitted bits, this time eight
Hamming distances are calculated for each state transition. At this point we need to make a decision
on what information to keep going forward in the decoding process.
As a result of comparing the third group of coded bits against all possible code words, each state
now has two trellis paths entering them.
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