Maximum likelihood binary shift-register synthesis from noisy observations

We consider the problem of estimating the feedback coefficients of a linear feedback shift register based on noisy observations. The problem of determining feedback coefficients in the absence of noise is now classical, Massey´s algorithm (1969). In the current approach to the problem of estimation with noisy observations, the coefficients are endowed with a probabilistic model and the problem. Gradient ascent updates to coefficient probabilities are computable using recursions developed by means of the EM algorithm. Reduced-complexity approximations are also developed by reducing the number of coefficients propagated at each stage. Applications of this method may include soft decision decoding and blind spread spectrum interception