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A Binary Deletion Channel With a Fixed Number of Deletions



Suppose a binary string x = x1 . . . xn is being broadcast repeatedly over a faulty communication channel. Each time, the channel delivers a fixed number m of the digits (m < n) with the lost digits chosen uniformly at random and the order of the surviving digits preserved. How large does m have to be to reconstruct the message?



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[1]Drinea, E. and Mitzenmacher, M. (2007) Improved lower bounds for the capacity of i.i.d. deletion and duplication channels. IEEE Trans. Inform. Theory 53 26932714.
[2]Holenstein, T., Mitzenmacher, M., Panigrahy, R. and Wieder, U. (2008) Trace reconstruction with constant deletion probability and related results. In Proc. 19th Annual ACM–SIAM Symposium on Discrete Algorithms: SODA'08, pp. 389–398.
[3]Mitzenmacher, M. (2009) A survey of results for deletion channels and related synchronization channels. Probab. Surv. 6 133.



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