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In this paper, we develop bounds on the achievable rate for deletion channels. Deletion channels occur when symbols are randomly dropped, and a subsequence of the transmitted symbols is received. Our initial motivation for studying these channels arose in the context of information transmission over finite-buffer queues in packet-switched networks, where the receiver does not have access to side-information on which packets were dropped. This also motivated our study on the effect of large alphabet sizes on the achievable rate.