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Maximum likelihood binary shift-register synthesis from noisy observations

We consider the problem of estimating the feedback coefficients of a linear feedback shift register (LFSR) based on noisy observations. In the current approach, the coefficients are endowed with a probabilistic model. 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.