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message is sent through a channel where bits may beÌýdeleted or inserted without warning.Ìý How many independentÌýcopies of the altered message are required in order toÌýrecover the original message? This is harder than theÌýanalogous problem in which the bits are erased (but youÌýcan see they are gone) or altered (without warning) becauseÌýof the synchronization problem.Ìý We show that in the averageÌýcase, exp (c log^{1/3} n) transmissions are required forÌýreconstruction. Previously to this, a sub-polynomial boundÌýwas known, but only for small deletion rates and no insertion.ÌýThe best bound for deletion rates over 1/2 (even without insertion)Ìýwas superpolynomial: exp(c n^{1/3}) – no log in the exponent.

Joint work with Nina Holden and Yuval Peres.

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