On lower bounds for the capacity of deletion channels

We consider binary deletion channels, where bits are deleted independently with probability d. We extend the framework used to analyze the capacity of binary deletion channels established by Diggavi and Grossglauser [2001], improving on their lower bounds. In Diggavi and Grossglauser, the codewords are generated by a first order Markov chain. Our improvements arise from two considerations. First, Diggavi and Grossglauser consider typical outputs, where an output is typical if an N bit input produces an output of at least N(1-d)(1-ε) bits. We provide a stronger notion of a typical output that yields better bounds even for the cases studied in Diggavi and Grossglauser. Second, we consider codewords generated by more general processes than first order Markov chains.