mohatta2015.pdf

THE MATH 131
6.3.5.1 M-algorithm With the M-algorithm, path pruning is applied at each stage
of a tree search. Only M paths are kept. Steps shown in italics are only used in the
case of a finite decision depth. At each iteration, the following steps are performed.
1. Path Extension: Each path is extended, creating M M candidate paths (the
second M is the number of possible symbol values).
2. Detection of oldest symbol: The best candidate path is identified and the
oldest symbol in its path history becomes a detected symbol value.
3. Ambiguity check. Any candidate path whose oldest symbol value is not the
same as the detected symbol value is discarded (this step is sometimes omitted).
4. Path history truncation: The path histories are truncated to remove the oldest
symbol, now decided.
5. Viterbi pruning: Any paths that correspond to the same Viterbi state are
compared and the nonbest ones are discarded (this step is sometimes omitted).
6. Path selection: Of the remaining candidate paths, only the M best are kept.
Notice that the last step requires an additional sorting operation, which adds to
complexity.
The M-algorithm is considered a breadth-first approach, in that it prunes by
comparing paths of the same length.
6.3.5.2 T-algorithm The T-algorithm is similar to the M-algorithm, except that
the number of paths kept is not fixed, but determined by which path metrics pass
a threshold test.
6.3.5.3 Sequential decoding Sequential decoding is a depth-first approach. The
idea is to continue along a path in the tree as long as the metric growth is "reasonable"
in some sense. When this is not the case, a decision about which path to
"extend" next must be made. This involves comparing paths of unequal length.
6.3.6 Performance results
Like previous chapters, we consider a static, two-tap, symbol-spaced channel with
relative path strengths 0 and —1 dB and path angles 0 and 90 degrees. LE uses
a 31-tap, symbol-spaced filter centered on the first signal path and DFE uses a
16-tap, symbol-spaced filter whose first tap is aligned with the first signal path.
QPSK and root-Nyquist pulse shaping are assumed, so that MLSD has 4 states
and 16 branch metrics computed each iteration. Extra symbols are generated at
the beginning and end of each block to be equalized to avoid edge effects for LE and
DFE and to avoid having to implement metric and state-size transients for MLSD.
This creates performance issues at the edges, which are addressed by starting the
MLSD before the first symbol of interest and ending it after the final symbol of
interest.