This is accomplished by discarding the path with the
largest accumulated Hamming distance (see Fig. 5.34).
At this point we have compared four input groups of coded bits against all possible combinations
and accumulated the Hamming distances for each state. If we are forced to make a decision, at this
moment, on the transmitted bit stream we would choose the trellis path corresponding to the smallest
accumulated Hamming distance. For this example we chose the trellis path that terminates at the state
Hard Decision Decoding. In this section, we will make binary decisions on the bit sequence
entering the Viterbi algorithm, a block diagram showing these operations is provided (see Fig. 5.31).
Note that we have purposely excluded the de-interleaving operations in order to not clutter the block
diagram. Here binary decisions are made prior to performing the decoding operations, this type of
decoding is called hard decision decoding.
248 CHAPTER FIVE
a
b
c
d
2
0
a
b
c
d
2 1
0 1
2
0
a
b
c
d
2 1 1
0 1 1
1
2
0 0
2
2
0
1
(r = 11)
(r = 01)
(r = 01)
FIGURE 5.32 State transitions of the Viterbi decoding algorithm.
a
b
c
d
0
1
2
0
2
0
1
(r = 01) 3
3
0
2
FIGURE 5.33 Survivor state transitions of the Viterbi decoding algorithm for r 11 01 01 .
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