On Estimation for a Binary-Symmetric Channel - Information Theory, IEEE Transactions on

We consider a binary-symmetric channel where the input, modeled as an infinite 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 finite. Here, we deal with two shortcomings: 1) 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) Simons’ estimator exhibits a serious negative bias when the distortion is great; our modification largely overcomes this deficiency while reducing the variance. Asymptotics for the proposed estimators are studied, and their properties are illustrated through numerical studies.