On Estimation for a Binary-Symmetric Channel

We consider a binary symmetric channel where the input, modeled as an innnite sequence of bits, is distorted by a Bernoulli noise. In 8], 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 nite. Here, we deal with two shortcomings: 1. Simons' estimator requires some information on the value of the complexity; we describe a modiied approach through the generalized Bernoulli components in which determination of the complexity is not needed. 2. Simons' estimator exhibits a serious negative bias when the distortion is great; our modiication largely overcomes this deeciency while reducing the variance. Asymptotics for the proposed estimators are studied, and their properties are illustrated through numerical studies.