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.