  Classical trellis-coded modulation (TCM) as introduced by Ungerboeck in
1976/1983 uses a signal constellation of twice the cardinality compared to an
uncoded transmission with one bit of redundancy per PAM symbol, i.e.,
application of codes with rates $\frac{n-1}{n}$ when $2^{n}$ denotes the
cardinality of the signal constellation. The original approach therefore only
comprises integer transmission rates, i.e., $R=\left\{ 2,\,3,\,4\,\ldots
\right\}$, additionally, when transmitting over an intersymbol interference
(ISI) channel an optimum decoding scheme would perform equalization and
decoding of the channel code jointly. In this paper, we allow rate adjustment
for TCM by means of puncturing the convolutional code (CC) on which a TCM
scheme is based on. In this case a nontrivial mapping of the output symbols of
the CC to signal points results in a time-variant trellis. We propose an
efficient technique to integrate an ISI-channel into this trellis and show that
the computational complexity can be significantly reduced by means of a reduced
state sequence estimation (RSSE) algorithm for time-variant trellises.
