mohatta2015.pdf

THE MATH 123
Figure 6.8
MLSD trellis diagram, three-path channel.
We can continue the process until the last received value for a block of data is
processed. At that point, we would use the best metric rule to determine the detected
symbol sequence. With this rule, we determine the best state by determining
the best path metric. The best state determines the detected values for the last
L — 1 symbols. Then, if we stored pointers to previous states, we would perform
a traceback from the best state, following the pointers to determine the rest of the
detected symbols. If we kept a path history, the path history for the best state
would determine the rest of the detected symbol values.
With the path memory approach, the path memory gets longer and longer as
more received values are processed. To keep memory down to reasonable length, a
decision depth can be used. After determining the path metrics for symbol k + D,
the best state is determined. In the path history for the best state, the detected
value for symbol k is taken as the final decision for symbol k. Thus, the path
memory can be shortened to storing only the past D — 1 symbols.