The purpose of this survey is to describe recent progress in the study of the binary deletion channel and related channels with synchronization errors, including a clear description of open problems in this area, with the hope of spurring further research. As an example, while the capacity of the binary symmetric error channel and the binary erasure channel have been known since Shannon, we still do not have a closed-form description of the capacity of the binary deletion channel. We highlight a recent result that shows that the capacity is at least $(1-p)/9$ when each bit is deleted independently with fixed probability $p$.
"A survey of results for deletion channels and related synchronization channels." Probab. Surveys 6 1 - 33, 2009. https://doi.org/10.1214/08-PS141