On estimation for a binary-symmetric channel

We consider a binary-symmetric channel where the input, modeled as an infinite sequence of bits, is distorted by Bernoulli noise. In a paper by Simons (1991), a consistent estimator of the distortion, i.e., of the probability that a single bit is changed, is described under the basic assumption that the complexity of the input is finite. Here, we deal with two shortcomings. (1) The Simons´ estimator requires some information on the value of the complexity; we describe a modified approach through the generalized Bernoulli components in which determination of the complexity is not needed. (2) The Simons´ estimator exhibits a serious negative bias when the distortion is great; our modification largely overcomes this deficiency while reducing the variance. The asymptotics for the proposed estimators are studied, and their properties are illustrated through numerical studies