Efficient computation of trellis code generating functions

For trellis codes, generating function techniques provide the distance spectrum and a union bound on bit-error rate. The computation of the generating function of a trellis code may be separated into two stages. The first stage reduces the number of states as much as possible using low-complexity ap...

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Bibliographic Details
Published in:IEEE transactions on communications 2004-02, Vol.52 (2), p.219-227
Main Authors: Jun Shi, Wesel, R.D.
Format: Article
Language:English
Subjects:
Analytical models
Bit error rate
Codes
Communications Society
Convolutional codes
Error correction codes
Error probability
Modulation coding
Signal mapping
Studies
Sufficient conditions
Transfer functions
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Summary:For trellis codes, generating function techniques provide the distance spectrum and a union bound on bit-error rate. The computation of the generating function of a trellis code may be separated into two stages. The first stage reduces the number of states as much as possible using low-complexity approaches. The second stage produces the generating function from the reduced-state diagram through some form of matrix inversion, which has a relatively high complexity. In this paper, we improve on the amount of state reduction possible during the low-complexity first stage. We also show that for a trellis code that is a linear convolutional code followed by a signal mapper, the number of states may always be reduced from N/sup 2/ to ((N/sup 2/-N)/2)+1 using low-complexity techniques. Finally, we analytically compare the complexity of various matrix inversion techniques and verify through simulation that the two-stage approach we propose has the lowest complexity. In an example, the new technique produced the union bound in about half the time required by the best algorithm already in the literature.
ISSN:0090-6778
1558-0857
DOI:10.1109/TCOMM.2003.822702