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In this work, we use various trellis structures to characterize insertion/deletion channels with intersymbol interference (ISI). We propose to use a two-element state vector to represent the channel memory and possible insertions/deletions, and develop a suitable trellis to describe the communication process. Using a simulation based approach, we compute the corresponding information rates. We show that, the proposed algorithm is an efficient and flexible technique to closely estimate the information rates for insertion/deletion channels with ISI.