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We propose to use various trellis structures to characterize different types of insertion and deletion channels. We start with binary independent and identically distributed (i.i.d.) insertion or deletion channels, propose a trellis representation and develop a simulation based algorithm to estimate the corresponding information rates with independent and uniformly distributed inputs. This approach is then generalized to other cases, including channels with additive white Gaussian noise, channels with both insertions and deletions, and channels with intersymbol interference (ISI) where the latter model is motivated by the recent developments on bit-patterned media recording. We demonstrate that the proposed algorithm is an efficient and flexible technique to closely estimate the achievable information rates for channels with insertions and/or deletions with or without intersymbol interference when i.i.d. inputs are employed while we also provide some notes on the achievable information rates when Markov inputs are used. We emphasize that our method is useful for evaluating information rates for channels with insertion/deletions with additional impairments where there does not seem to be a hope of obtaining fully analytical results.