Deletion channel

A deletion channel is a communications channel model used in coding theory and information theory. In this model, a transmitter sends a bit (a zero or a one), and the receiver either receives the bit (with probability $p$ ) or does not receive anything without being notified that the bit was dropped (with probability $1-p$ ). Determining the capacity of the deletion channel is an open problem.^[1]^[2]

The deletion channel should not be confused with the binary erasure channel which is much simpler to analyze.

^ Mitzenmacher, Michael (2009), "A survey of results for deletion channels and related synchronization channels", Probability Surveys, 6: 1–33, doi:10.1214/08-PS141, MR 2525669.
^ Kanoria, Yashodhan; Montanari, Andrea (2013), "Optimal coding for the binary deletion channel with small deletion probability", IEEE Transactions on Information Theory, 59 (10): 6192–6219, doi:10.1109/TIT.2013.2262020, MR 3106824.

[1] Mitzenmacher, Michael (2009), "A survey of results for deletion channels and related synchronization channels", Probability Surveys, 6: 1–33, doi:10.1214/08-PS141, MR 2525669.

[2] Kanoria, Yashodhan; Montanari, Andrea (2013), "Optimal coding for the binary deletion channel with small deletion probability", IEEE Transactions on Information Theory, 59 (10): 6192–6219, doi:10.1109/TIT.2013.2262020, MR 3106824.

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