Improved Lower Bounds for the Capacity of i.i.d. Deletion and Duplication Channels

This paper considers the capacity of binary deletion channels, where bits are deleted independently with probability d. It improves significantly upon the best previous framework used to obtain provable lower bounds on this capacity by utilizing a stronger definition of a typical output from the channel. The new results give the best known provable bounds on the capacity for all values of d. Moreover, the techniques presented here extend to yield lower bounds for channels with certain types of random insertions, namely, duplications, or combinations of duplications and deletions. To demonstrate these techniques in this context, two binary channels are analyzed: a channel where each transmitted bit is copied with probability nu and a channel where each transmitted bit is copied a geometrically distributed number of times.