Open Access
2009 A survey of results for deletion channels and related synchronization channels
Michael Mitzenmacher
Probab. Surveys 6: 1-33 (2009). DOI: 10.1214/08-PS141


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 $p$.


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Michael Mitzenmacher. "A survey of results for deletion channels and related synchronization channels." Probab. Surveys 6 1 - 33, 2009.


Published: 2009
First available in Project Euclid: 9 July 2009

zbMATH: 1189.94058
MathSciNet: MR2525669
Digital Object Identifier: 10.1214/08-PS141

Primary: 94B50
Secondary: 68P30

Keywords: capacity bounds , Deletion channels , random subsequences , synchronization channels

Rights: Copyright © 2009 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.6 • 2009
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