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We directly lower bound the information capacity for channels with i.i.d. deletions and duplications. Our approach differs from previous work in that we focus on the information capacity using ideas from renewal theory, rather than focusing on the transmission capacity by analyzing the error probability of some randomly generated code using a combinatorial argument. Of course, the transmission and information capacities are equal, but our change of perspective allows for a much simpler analysis that gives more general theoretical results. We then apply these results to the binary deletion channel to improve existing lower bounds on its capacity.