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We consider a class of small-sample distribution estimators over noisychannels. Our estimators are designed for repetition channels, and rely onproperties of the runs of the observed sequences. These runs are modeled via aspecial type of Markov chains, termed alternating Markov chains. We show thatalternating chains have redundancy that scales sub-linearly with the lengths ofthe sequences, and describe how to use a distribution estimator for alternatingchains for the purpose of distribution estimation over repetition channels.

Alternating Markov Chains for Distribution Estimation in the Presence of Errors