In the next two subsections we will present two versions of the VA, the first operating on hard decisions
and the second operating on soft bit values. In the latter version the actual decision on the transmitted
bits was made during the VA operations.
246 CHAPTER FIVE
a
b
c
d
00 00 00 00
11 11 11 11
11 11
10 10 10
01 01 01
10 10
01 01
00 00
FIGURE 5.29 Trellis diagram representation of the R 1/2 and K 3 convolutional code.
a
b
c
d
00 00 00 00
11 11 11 11
11 11
10 10 10
01 01 01
10 10
01 01
00 00
00
11
11
10
01
10
01
00
FIGURE 5.30 Trellis diagram path transitions for the 11011 input bit sequence.
PERFORMANCE IMPROVEMENT TECHNIQUES 247
Demodulator
Viterbi
Algorithm
Received
Symbols
Decoded Bit
Stream
Decision Device
{1, 0}
FIGURE 5.31 Hard decision decoding overview.
As discussed above, the VA calculates a measure of similarity between all the states at time equal
to tk and the received code word at time tk. When binary decisions have been made, the Hamming distance
can be used to measure the similarity.
Below we assume the received sequence is given as r 11 01 01 00 01 and we will build the trellis
diagram for each input-coded sequence that enters the Viterbi algorithm.
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