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We consider the problem of estimating unknown source distributions based on a small number of possibly erroneous observations. Errors are modeled as arising from sticky channels, which introduce repetitions of transmitted source symbols. Both the problems of estimating the distribution for known and unknown channel parameters are considered. We propose three heuristic algorithms and a method based on Expectation-Maximization for solving the problem. These algorithms represent a combination of iterative optimization techniques and Good-Turing estimators.