Maximum likelihood binary shift-register synthesis from noisyobservations

摘要

We consider the problem of estimating the feedback coefficients ofa linear feedback shift register based on noisy observations. Theproblem of determining feedback coefficients in the absence of noise isnow classical, Massey's algorithm (1969). In the current approach to theproblem of estimation with noisy observations, the coefficients areendowed with a probabilistic model and the problem. Gradient ascentupdates to coefficient probabilities are computable using recursionsdeveloped by means of the EM algorithm. Reduced-complexityapproximations are also developed by reducing the number of coefficientspropagated at each stage. Applications of this method may include softdecision decoding and blind spread spectrum interception