## Probability Surveys

### A survey of results for deletion channels and related synchronization channels

Michael Mitzenmacher

#### Abstract

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 $p$.

#### Article information

Source
Probab. Surveys, Volume 6 (2009), 1-33.

Dates
First available in Project Euclid: 9 July 2009

https://projecteuclid.org/euclid.ps/1247144661

Digital Object Identifier
doi:10.1214/08-PS141

Mathematical Reviews number (MathSciNet)
MR2525669

Zentralblatt MATH identifier
1189.94058

#### Citation

Mitzenmacher, Michael. A survey of results for deletion channels and related synchronization channels. Probab. Surveys 6 (2009), 1--33. doi:10.1214/08-PS141. https://projecteuclid.org/euclid.ps/1247144661

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